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IB Physics SL - 2024 - Questionbank

Topic 2 All - Mechanics

All Questions for Topic 2 (Mechanics). Motion, Forces, Work, Energy, and Power, Momentum & Impulse

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Question 1

no calculator

easy

A car is travelling along a straight line for a total time of 100 ss. Throughout this time the driving force provided by the car is 1.2 kNkN and the total resistive force acting on the car is 500 NN.

Which row correctly shows the rate of change of momentum and the impulse of the car during the 100 ss.


Rate of change of momentumImpulse
\hspace{1.5em}A.\hspace{1.5em}7 ×102kgms2\times 10{^2}\,kg\,m\,s{^{-2}}\hspace{1.5em} 7 ×100kgms1\times 10{^0}\,kg\,m\,s{^{-1}} \hspace{1.5em}
\hspace{1.5em}B.\hspace{1.5em}7 ×102kgms2\times 10{^2}\,kg\,m\,s{^{-2}}7 ×104kgms1\times 10{^4}\,kg\,m\,s{^{-1}}
\hspace{1.5em}C.\hspace{1.5em}1.7 ×103kgms2\times 10{^3}\,kg\,m\,s{^{-2}}1.7 ×101kgms1\times 10{^1}\,kg\,m\,s{^{-1}}
\hspace{1.5em}D.\hspace{1.5em}1.7 ×103kgms2\times 10{^3}\,kg\,m\,s{^{-2}}1.7 ×105kgms1\times 10{^5}\,kg\,m\,s{^{-1}}

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Question 2

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easy

Which of the following units is not a unit of power?

  • A. \hspace{1em} W

  • B. \hspace{1em} J

  • C. \hspace{1em} N m s1^{-1}

  • D. \hspace{1em} J s1^{-1}

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Question 3

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easy

A builder uses a block and tackle pulley system to lift a bundle of materials of mass 15 kg to the top of a building of height 6 m in 9 s. What is the power delivered to the bundle? Assume g=10Nkg1g=10\,N\,kg^{-1}.

PH0125 [Image Source: Block-and-tackle-in-use.svg by Themightyquill licensed under CC BY-SA 4.0]\footnotesize{\textrm{[Image Source: Block-and-tackle-in-use.svg by Themightyquill licensed under CC BY-SA 4.0}]}

  • A. \hspace{1em} 10 W

  • B. \hspace{1em} 17 W

  • C. \hspace{1em} 100 W

  • D. \hspace{1em} 900 W

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Question 4

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easy

The diagram below shows a tennis ball of mass mm striking a wall with an initial velocity, uu, and rebounding with velocity vv. A second, softer ball of the same mass strikes the wall with the same speed but rebounds with a slower rebound speed.

PH0124

Which of the following statements is correct about the magnitudes of the impulse and change in momentum applied to the second ball compared to the first?


Impulse\hspace{1em}Change in momentum
\hspace{1.5em}A.\hspace{1.5em}GreaterSmaller
\hspace{1.5em}B.\hspace{1.5em}SmallerGreater
\hspace{1.5em}C.\hspace{1.5em}GreaterGreater
\hspace{1.5em}D.\hspace{1.5em}SmallerSmaller

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Question 5

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easy

The diagram below shows a car of mass m descending a slope. The car, initially at rest, covers a distance of 27m27\, m in 3.0s3.0\, s.

PH0123

The magnitude of the acceleration is given by

  • A. \hspace{1em} 3.0 ms2m\,s^{-2}

  • B. \hspace{1em} 6.0 ms2m\,s^{-2}

  • C. \hspace{1em} 9.0 ms2m\,s^{-2}

  • D. \hspace{1em} 81 ms2m\,s^{-2}

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Question 6

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easy

An object moves at constant velocity for a period of time, after which it undergoes uniform deceleration until it comes to rest. A velocity-time graph is plotted for this motion. On the graph, which of the following would represent the displacement of the object?

  • A. \hspace{1em} Gradient of the line connecting the initial and final velocities.

  • B. \hspace{1em} x-intercept

  • C. \hspace{1em} y-intercept

  • D. \hspace{1em} Area under the graph

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Question 7

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easy

A ball rolls horizontally off the edge of the top of a cliff. It hits the ground at a distance 2.0 mm from the base of the cliff with a vertical speed of 20 ms1m\,s^{-1}. What is the height of the cliff?

  • A. \hspace{1em} 20 m

  • B. \hspace{1em} 40 m

  • C. \hspace{1em} 60 m

  • D. \hspace{1em} 80 m

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Question 8

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easy

A basketball is launched at an angle and undergoes projectile motion. Air resistance is negligible. Which of the following is correct for the direction of its velocity vector and its acceleration vector at the highest point of its trajectory?


Direction of velocity vectorDirection of acceleration vector
\hspace{1.5em}A.\hspace{1.5em}horizontalno acceleration
\hspace{1.5em}B.\hspace{1.5em}no velocityno acceleration
\hspace{1.5em}C.\hspace{1.5em}no velocitydownward
\hspace{1.5em}D.\hspace{1.5em}horizontaldownward

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Question 9

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easy

A box is pulled by a child with a horizontal force of 5 NN. The box moves a horizontal distance of 4 mm in a time of 2 ss. The average power delivered by the child to the box is

  • A. \hspace{1em} 2.5 WW

  • B. \hspace{1em} 5.0 WW

  • C. \hspace{1em} 10 WW

  • D. \hspace{1em} 40 WW

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Question 10

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easy

Consider the weight, WW, of a skydiver falling through air with a drag force FdragF_{drag}

If the skydiver experiences terminal velocity, which of the following best represents the skydiver's motion by means of a free body diagram?


A.B.
PH0130A\hspace{1cm}PH0130B
\hspace{1cm}
C.D.
PH0130CPH0130D

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Question 11

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easy

A mass is attached to the mirror of a car by a string. As the car accelerates to the left, the string makes an angle with the vertical as shown in the diagram below.

PH0284Q

Which of the following shows the correct free-body diagram that represents the forces acting on this mass when it is accelerating?

A.B.
PH0284A\hspace{1cm}PH0284B
\hspace{1em}
C.D.
PH0284CPH0284D

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Question 12

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easy

Which of the following is not appropriate for measuring energy?

  • A. \hspace{1em} JJ

  • B. \hspace{1em} NmN\, m

  • C. \hspace{1em} kgms2kg\, m\, s^{-2}

  • D. \hspace{1em} kgm2s2kg \,m^{2} \,s^{-2}

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Question 13

no calculator

easy

The graph below shows the variation of the resultant force FF acting on a box with time tt.

PH0579q

The box starts to move from rest. Which of the following graphs shows the variation of the momentum pp of the box with time tt?

A.B.
PH0579a\hspace{1cm}PH0579b
\hspace{1em}
C.D.
PH0579cPH0579d

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Question 14

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easy

As a truck is brought to rest, the brakes apply a force of 5.1×103N5.1 \times 10^3\,N. Which answer best describes the magnitude of the change in momentum of the truck if the brakes are applied for 3.0 ss?

  • A. \hspace{1em} 15kNs15\,kN\,s

  • B. \hspace{1em} 15000Ns15000\,N\,s

  • C. \hspace{1em} 15.3kNs15.3\,kN\,s

  • D. \hspace{1em} 15300Ns15300\,N\,s

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Question 15

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easy

A football player bounced the ball off their head as shown while diving sideways

PH0146-1

Which of the following gives a Newton’s Third Law pair of forces that applies to this situation?


\hspace{6em} Force 1 \hspace{6em}\hspace{6em} Force 2 \hspace{6em}
\hspace{1.5em}A.\hspace{1.5em}Force of the ball on the playerForce of the ball on the earth
\hspace{1.5em}B.\hspace{1.5em}Force of the player on the earthForce of the ball on the player
\hspace{1.5em}C.\hspace{1.5em}Force of the earth on the ballForce of the ball on the earth
\hspace{1.5em}D.\hspace{1.5em}Force of the earth on the playerForce of the player on the ball

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Question 16

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easy

A coin is tossed vertically upwards from an original height of 1.5m1.5\, m above the ground. What is the maximum height reached above the ground if the coin was projected with an initial velocity of 3.0 ms1m\, s^{-1}? (Take g=10ms2g = 10\, m\, s^{-2})

  • A. 0.45m\hspace{1em} 0.45\, m

  • B. 1.50m\hspace{1em} 1.50\, m

  • C. 1.95m\hspace{1em} 1.95\, m

  • D. 6.00m\hspace{1em} 6.00\, m

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Question 17

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easy

[Maximum mark: 4]

  1. State the law of conservation of momentum. [2]

  2. A stationary body explodes into two pieces of mass as m1m_1 and m2m_2 in opposite directions.

    PH0463

    Just after the explosion, the ratio of the kinetic energy of m1m_1 to the kinetic energy of m2m_2 is found to be 9. Calculate the ratio of masses m1m2\dfrac{m_1}{m_2}. [2]

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Question 18

no calculator

easy

A ball of mass mm is falling vertically through the air. The drag force acting on the ball is given by kv2kv^2 where kk is constant and vv is the speed of the ball. What is the maximum speed reached by the ball?

  • A. kmg\hspace{1em} \dfrac{k}{mg}

  • B. mgk\hspace{1em} \dfrac{mg}{k}

  • C. kmg\hspace{1em} \sqrt{\dfrac{k}{mg}}

  • D. mgk\hspace{1em} \sqrt{\dfrac{mg}{k}}

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Question 19

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easy

The take off speed of a passenger aircraft is 75.0 ms1m\,s^{-1}. A plane starts from rest and accelerates at a steady rate of 1.25 ms2m\,s^{-2}. Which of the following correctly states the minimum duration of taxiing, and the minimum length of the runway needed for the take off?


Duration of TaxiingLength of the runway
\hspace{1.5em}A.\hspace{1.5em}75.0ms11.25ms2\dfrac{75.\,0m\,s^{-1}}{1.25\,m\,s^{-2}}(75.0ms1)2(2)(1.25ms2)\dfrac{(75.0\,m\,s^{-1})^2}{(2)(1.25\,m\,s^{-2})}
\hspace{1.5em}B.\hspace{1.5em}75.0ms11.25ms2\dfrac{75.0\,m\,s^{-1}}{1.25\,m\,s^{-2}}(75.0ms1)21.25ms2\dfrac{(75.0\,m\,s^{-1})^2}{1.25\,m\,s^{-2}}
\hspace{1.5em}C.\hspace{1.5em}(75.0ms1)2(2)(1.25ms2)\dfrac{(75.0\,m\,s^{-1})^2}{(2)(1.25\,m\,s^{-2})}75.0ms11.25ms2\dfrac{75.0\,m\,s^{-1}}{1.25\,m\,s^{-2}}
\hspace{1.5em}D.\hspace{1.5em}(75.0ms1)2(2)(1.25ms2)\dfrac{(75.0\,m\,s^{-1})^2}{(2)(1.25\,m\,s^{-2})}(75.0ms1)2(2)(1.25ms2)\dfrac{(75.0\,m\,s^{-1})^2}{(2)(1.25\,m\,s^{-2})}

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Question 20

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easy

A ball is projected in an environment where air resistance can be ignored.

PH0545

Which graph shows the variation of the resultant force RR acting on the ball with the height hh of the object?

A.B.
PH0545a\hspace{1cm}PH0545b
\hspace{1em}
C.D.
PH0545cPH0545d

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Question 21

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easy

Two eggs of equal mass fall from the same height onto a padded floor. One of them is broken while the other one bounces upwards intact. The time of collision is the same for both. Which of the following correctly describes the egg that exerts more force on the floor and the reason?


Egg exerting more forceReason
\hspace{1.5em}A.\hspace{1.5em}BrokenGreater change in momentum
\hspace{1.5em}B.\hspace{1.5em}BouncesLess change in momentum
\hspace{1.5em}C.\hspace{1.5em}BrokenLess change in momentum
\hspace{1.5em}D.\hspace{1.5em}BouncesGreater change in momentum

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Question 22

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easy

A block of wood is placed on a rough inclined surface. Which of the diagrams below correctly represents the forces acting on the block when it is at rest?


A.B.
PH0261A\hspace{1cm}PH0261B
\hspace{1cm}
\hspace{1cm}
C.D.
PH0261CPH0261D

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Question 23

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easy

The graph shows the variation with time tt of the velocity vv of a car traveling along a straight and level road.

PH0081

What time does it take for the car to travel a distance of 31.5m31.5\, m from tt = 0?

  • A.2s\hspace{1em} 2\, s

  • B.7s\hspace{1em} 7\, s

  • C.10s\hspace{1em} 10\, s

  • D.12s\hspace{1em} 12\, s

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Question 24

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easy

The graph shows the variation of velocity vv with time tt of a car.

PH0204

Which of the following can be deduced from the graph?

  • I.Displacement
    II.Acceleration
    III.Change in velocity


  • A. \hspace{1em} I only

  • B. \hspace{1em} II only

  • C. \hspace{1em} I and II only

  • D. \hspace{1em} I, II and III

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Question 25

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easy

A box of mass m is pulled across a horizontal surface with a force FF as shown in the diagram. The coefficient of dynamic friction between the box and the surface is µ. What is the energy transferred to thermal energy while a box is moved by a distance of dd?

PH0283-1

  • A. \hspace{1em} FdFd

  • B. \hspace{1em} (Fμmg)d(F-\mu mg)d

  • C. \hspace{1em} μmgd\mu mgd

  • D. \hspace{1em} mgdmgd

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Question 26

no calculator

easy

A car of mass mm and a truck of mass 3m3m travelling in opposite directions collide and stick together. The speeds of the car and the truck just before the crash are 2v2v and vv respectively. What is their speed after the collision?

  • A. 14v\hspace{1em} \dfrac{1}{4}v

  • B. 45v\hspace{1em} \dfrac{4}{5}v

  • C. 54v\hspace{1em} \dfrac{5}{4}v

  • D. 4v\hspace{1em} 4v

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Question 27

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easy

The engine of a racing car provides a forward thrust of 800N800\, N. The average of the total resistive forces acting on the car is 300N300\, N and the car covers a distance of 1.0km1.0\, km in 10s10\, s.

What is the average output power of the engine?

  • A. 5.0×103 W\hspace{1em} 5.0\times{10}^3\ W

  • B. 8.0×103 W\hspace{1em} 8.0\times{10}^3\ W

  • C. 5.0×104 W\hspace{1em} 5.0\times{10}^4\ W

  • D. 8.0×104 W\hspace{1em} 8.0\times{10}^4\ W

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Question 28

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easy

An electric motor is used to raise a block of mass 18.0 kg vertically to the top of a building at a constant speed of 1.5ms11.5\,m\,s^{-1}. If the power rating of the motor is 297 W, calculate the efficiency of the motor. Assume g=10Nkg1g=10\,N\,kg^{-1}

  • A. \hspace{1em} 9%

  • B. \hspace{1em} 75%

  • C. \hspace{1em} 61%

  • D. \hspace{1em} 91%

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Question 29

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easy

A box is pulled up a slope inclined at 30° to the horizontal by a force of FF. The angle between the direction of FF and the plane of the incline is also 30°.

PH0571

The box is pulled a distance of d up along the slope. What is the work done by F on the box?

  • A. Fdcos(30°)\hspace{1em} Fd\,cos(30°)

  • B. Fdcos(60°)\hspace{1em} Fd\,cos(60°)

  • C. Fdsin(30°)\hspace{1em} Fd\,sin(30°)

  • D. Fdcos2(30°)\hspace{1em} Fd\,cos^2(30°)

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Question 30

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easy

A block of mass 16 kg is pushed and released along a rough horizontal surface at an initial speed of 2ms12\,m\,s^{-1}.

PH0118

The block travels through a distance of 16 m and is brought to rest. What is the magnitude of the frictional force that brings the block to rest?

  • A. \hspace{1em} 2 N

  • B. \hspace{1em} 4 N

  • C. \hspace{1em} 8 N

  • D. \hspace{1em} 16 N

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Question 31

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easy

A box is sliding down an incline at a constant speed of 2ms12\, m\, s^{-1}. The angle of the incline is θ\theta.

PH0547

The magnitude of the total of the opposing forces is 16N16\, N. What is the force of gravity acting on the box?

  • A. 8sinθ\hspace{1em} \dfrac{8}{sin\theta}

  • B. 16sinθ\hspace{1em} \dfrac{16}{sin\theta}

  • C. 8cosθ\hspace{1em} \dfrac{8}{cos\theta}

  • D. 16cosθ\hspace{1em} \dfrac{16}{cos\theta}

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Question 32

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easy

A rocket ejects hot gas in space in a direction opposite to its travelling direction. What is correct for the magnitude of the momentum and the kinetic energy of the rocket?


\hspace{1em} Momentum \hspace{1em}\hspace{1em} Kinetic Energy\hspace{1em}
\hspace{1.5em}A.\hspace{1.5em}ConservedConserved
\hspace{1.5em}B.\hspace{1.5em}IncreasedConserved
\hspace{1.5em}C.\hspace{1.5em}ConservedIncreased
\hspace{1.5em}D.\hspace{1.5em}IncreasedIncreased

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Question 33

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easy

A table tennis ball of mass m is dropped on a level surface from a height HH. The ball rebounds to a height h<Hh < H after impact. Which of the following is correct about the nature of the collision and magnitude of the change in momentum (Δp\Delta p) of the ball as a result of this impact?


\hspace{1em} Nature of the collision \hspace{1em}\hspace{1em} Change in momentum Δp\Delta p \hspace{1em}
\hspace{1.5em}A.\hspace{1.5em}Elasticm(2gH2gh)m(\sqrt{2gH}-\sqrt{2gh})
\hspace{1.5em}B.\hspace{1.5em}Inelasticm(2gH2gh)m(\sqrt{2gH}-\sqrt{2gh})
\hspace{1.5em}C. \hspace{1.5em}Elasticm(2gH+2gh)m(\sqrt{2gH}+\sqrt{2gh})
\hspace{1.5em}D. \hspace{1.5em}Inelasticm(2gH+2gh)m(\sqrt{2gH}+\sqrt{2gh})

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Question 34

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easy

[Maximum mark: 8]

  1. Define distance. [1]

  2. An object moves in a straight line on a level road. The variation of the object's distance d with time t is shown on the graph below.

    PH0555-1

    1. Describe the motion of the object between t=0.5st=0.5\, s and t=1.0st=1.0\, s. [1]

    2. Calculate the instantaneous speed of the object at t=0.5st=0.5\, s. [2]

    3. On the axes below, sketch a possible graph of the variation of velocity v of the object with time t. There is no need to add values to the axes. [2]

      PH0555-B

    4. Determine the direction of the change in momentum of the object during the motion. [2]

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Question 35

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easy

A projectile is fired at an angle above the horizontal on the surface of Moon. Which of the following statements is correct about its motion:

  • A. \hspace{1em} The magnitude of the horizontal component of its velocity remains unchanged until it falls on the surface of the moon.

  • B. \hspace{1em} The magnitude of the vertical component of its velocity remains unchanged until it falls on the surface of the moon.

  • C. \hspace{1em} The magnitude of the horizontal component of its velocity decreases steadily until it falls on the surface of the moon.

  • D. \hspace{1em} The magnitude of the vertical component of its velocity decreases steadily until it falls on the surface of the moon.

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Question 36

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easy

A block of mass mm, initially at rest, is acted upon by two unequal forces F1F_1 and F2F_2 such that F1>F2F_1 > F_2 as shown in the diagram below. The forces act for a time tt.

PH0266

Which of the following correctly represents the magnitude of the final velocity of the block after time tt?

  • A. \hspace{1em} (F1+F2m)(t)(\dfrac{F_1+F_2}{m})(t)

  • B. \hspace{1em} (F1F2m)(t)(\dfrac{F_1-F_2}{m})(t)

  • C. \hspace{1em} (F2F1m)(t)(\dfrac{F_2-F_1}{m})(t)

  • D. \hspace{1em} (F1F2t)(m)(\dfrac{F_1-F_2}{t})(m)

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Question 37

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easy

A football player kicks a ball initially at rest. The ball reaches a speed of 36 kmh136\ km\,h^{-1} in a time of 0.5 s0.5\ s. Which of the following is the acceleration of the ball in terms of the gravitational acceleration, gg?

  • A. \hspace{1em} 0.2 gg

  • B. \hspace{1em} 0.5 gg

  • C. \hspace{1em} 2 gg

  • D. \hspace{1em} 7 gg

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Question 38

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A projectile is fired with a launch angle α\alpha above the horizontal and an initial velocity of 40 m s1^{-1} towards a cliff that rises 300 m above the plane of projection. The cliff is 120 m from the launch point.

PH0132

Assuming that air resistance has no effect on the motion, then the time of flight taken by the projectile to reach the cliff is given by

  • A. t=3\hspace{1em} t = 3 s

  • B. t=7.5\hspace{1em}t = 7.5 s

  • C. t=4cosα\hspace{1em}t = \dfrac{4}{cos\alpha}

  • D. t=3cosα\hspace{1em}t = \dfrac{3}{cos\alpha}

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Question 39

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A cargo container is released from an airplane. A parachute is opened remotely a few seconds later to land it safely. Which graph shows the variation of the vertical acceleration with time tt for the cargo container from when it leaves the plane until landing?


A.B.
PH0033a1PH0033b1
C.D.
PH0033c1PH0033d1

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Question 40

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A student throws a ball with an initial velocity in the horizontal direction. Air resistance is negligible. At t=2.0st = 2.0\, s, the ball has travelled a distance xx in the horizontal direction and a distance yy in the vertical direction.

What are the horizontal and vertical distances covered at t=1.0st = 1.0\, s, in terms of xx and yy?


Horizontal distanceVertical distance
\hspace{1.5em}A.\hspace{1.5em}x2\dfrac{x}{2}y4\dfrac{y}{4}
\hspace{1.5em}B.\hspace{1.5em}x2\dfrac{x}{2}y2\dfrac{y}{2}
\hspace{1.5em}C.\hspace{1.5em}x4\dfrac{x}{4}y2\dfrac{y}{2}
\hspace{1.5em}D.\hspace{1.5em}x4\dfrac{x}{4}y4\dfrac{y}{4}

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Question 41

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[Maximum mark: 9]

  1. A ball of mass 0.20kg0.20\,kg moving on a frictionless horizontal plane collides elastically with a vertical wall.

    PH0643

    The variation of the force FF acting on the ball during the collision with time tt is shown on the graph below.

    PH0643_2

    The speed of the ball just before the impact is 5.0 ms15.0\ ms^{-1}. Calculate the maximum force exerted on the wall by the ball. [3]

  2. The wall is covered with a coating that causes an inelastic collision. The ball hits the wall with the same initial speed and bounces back with a speed of 3.0 ms13.0\ ms^{-1}.

    1. Explain, by considering the moments just before and after the collision, how the principle of conservation of energy applies to the collision. [2]

    2. Calculate the loss of the energy of the ball during the collision. [2]

    3. During this collision, the ball undergoes a change in momentum. Discuss whether the the law of conservation of momentum applies in this situation. [2]

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Question 42

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The graph below shows the variation of velocity vv of an object with time tt.

930ooo

Which of the following graphs shows how the displacement ss of the object, varies with tt?


A.\hspace{2cm}B.
930aaa930bbb
C.D.
930ccc930ddd

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Question 43

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A brick of weight 100N100\, N rests on a rough horizontal surface. A varying horizontal force is applied to the brick. The graph shows the variation of the magnitude of the frictional force with the magnitude of the applied force.

PH0542

What is the coefficient of the dynamic friction between the brick and the rough surface?

  • A. \hspace{1em} 0.2

  • B. \hspace{1em} 0.3

  • C. \hspace{1em} 0.4

  • D. \hspace{1em} 0.5

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Question 44

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A box of weight 400N400\, N is placed on a scale in an elevator. The scale reads 300N300\, N.

Which of the following is correct about the magnitude and direction of the acceleration of the elevator?


\hspace{1.5em} Magnitude \hspace{1.5em}\hspace{1.5em} Direction \hspace{1.5em}
\hspace{1.5em}A.\hspace{1.5em}0.25ms20.25\, m\,s^{-2}Upwards
\hspace{1.5em}B.\hspace{1.5em}0.25ms20.25\, m\,s^{-2}Downwards
\hspace{1.5em}C.\hspace{1.5em}2.5ms22.5\, m\,s^{-2}Upwards
\hspace{1.5em}D.\hspace{1.5em}2.5ms22.5\, m\,s^{-2}Downwards

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Question 45

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A ball of mass 0.5 kgkg strikes a vertical wall with a speed of 30ms130\,m\,s^{-1}. The magnitude of the change of the momentum of the ball is 22.5kgms122.5\,kg\,m\,s^{-1}. Calculate the speed of the ball just after it rebounds.

PH0247

  • A. \hspace{1em} 0ms10\,m\,s^{-1}

  • B. \hspace{1em} 5ms15\,m\,s^{-1}

  • C. \hspace{1em} 10ms110\,m\,s^{-1}

  • D. \hspace{1em} 15ms115\,m\,s^{-1}

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Question 46

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An object is moving at constant velocity. Which of the following could be the free-body diagram representing the forces acting on the object?

A.B.
PH0551A\hspace{1cm}PH0551B
\hspace{1em}
C.D.
PH0551CPH0551D

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Question 47

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A spring that obeys Hooke's Law is stretched a distance xx and stores energy EE.

What is the work done by the spring when it returns to the point where xx is reduced to half of its original value?


  • A. \hspace{1em} E4\dfrac{E}{4}

  • B. \hspace{1em} E2\dfrac{E}{2}

  • C. \hspace{1em} 3E4\dfrac{3E}{4}

  • D. \hspace{1em} 2E2E

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Question 48

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A car engine has an input power of Pin_{in} and efficiency of η\eta. Which of the following gives the wasted energy from the engine in time of tt?

  • A. \hspace{1em} Pin_{in} η\etat

  • B. \hspace{1em} Pin_{in} ηt\dfrac{\eta}{t}

  • C. \hspace{1em} Pin_{in}t - Pin_{in} η\etat

  • D. \hspace{1em} Pin_{in}t - ηt\dfrac{\eta}{t}

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Question 49

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An egg hits a wall covered with a soft material and sticks to it. The graph shows the variation of horizontal force FF acting on the egg with time tt during the collision.

PH0581q

The soft material on the wall is removed and an identical egg with the same initial speed collides with and sticks to the wall. Which graph shows the variation of horizontal force FF acting on the second egg with time tt during the collision? The graph for the first egg is shown as a dotted line.

A.B.
PH0581a\hspace{1cm}PH0581b
\hspace{1em}
C.D.
PH0581cPH0581d

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Question 50

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easy

The diagram below shows a person of mass 80 kgkg standing in an elevator of mass 800 kgkg. The elevator accelerates upwards at a rate of 1.2 ms1m\,s{^{-1}}.

PH0932

What is the normal contact force exerted on the person by the elevator?


  • A. \hspace{1em} 96 NN

  • B. \hspace{1em} 690 NN

  • C. \hspace{1em} 780 NN

  • D. \hspace{1em} 880 NN

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Question 51

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A boat is traveling along a straight line for a total time of one hour. The boat travels at a constant speed and covers a total distance of 2.4 kmkm. The thrust of the boat’s engine is 1.8 kNkN.

What is the energy exerted by the boat’s engine in one second?


  • A. \hspace{1em} 0.67 kJkJ

  • B. \hspace{1em} 1.2 kJkJ

  • C. \hspace{1em} 4.3 kJkJ

  • D. \hspace{1em} 78 kJkJ

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Question 52

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An object of mass mm rests on a rough surface. Another object of mass MM is connected to it with a rope.

PH0541-1

The image below shows the free-body diagram of horizontal forces on the object of mass mm.

PH0541-2

Which of the following correctly describes the Newton's 3rd Law force paired with F2F_2?

  • A. \hspace{1em} The pull of mass mm upwards on the earth.

  • B. \hspace{1em} The upward contact force on the mass mm.

  • C. \hspace{1em} The tension force to the right on the mass mm.

  • D. \hspace{1em} The friction force to the right on the surface.

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Question 53

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easy

A trolley is pushed in a level parking area of a market on a very rainy day. The rain fills the trolley at a rate of R kgs1R\ {kg\,s}^{-1}. Ignoring frictional forces, what is the force needed to move the trolley at a constant speed of vv?

  • A.  Rv\hspace{1em} \ R v

  • B. Rv\hspace{1em} \dfrac{R}{v}

  • C. vR\hspace{1em} \dfrac{v}{R}

  • D. R+v\hspace{1em} R+v

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Question 54

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A box of mass 2.0kg2.0\, kg starts to move on a level surface under the effect of a varying force FF. The variation of FF with the displacement ss of the object is shown in the graph below.

PH0566

What is the speed of the box at s=5ms=5\, m?

  • A. 5ms1\hspace{1em} 5\,m\,s^{-1}

  • B. 5ms1\hspace{1em} \sqrt{5}\,m\,s^{-1}

  • C. 15ms1\hspace{1em} 15\, m\,s^{-1}

  • D. 15ms1\hspace{1em} \sqrt{15}\, m\,s^{-1}

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Question 55

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A box with a mass of M rests on a balance in an elevator that is moving downwards. The elevator slows with an acceleration of g4\dfrac{g}{4}.

PH0543

Which of the following gives the reading of the balance?

  • A. 5Mg4\hspace{1em} \dfrac{5Mg}{4}

  • B. Mg\hspace{1em} Mg

  • C. 3Mg4\hspace{1em} \dfrac{3Mg}{4}

  • D. Mg2\hspace{1em} \dfrac{Mg}{2}

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Question 56

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easy

A varying force acts on a spring. The variation of the extension xx of the spring with force FF acting on it is shown in the graph below.

PH0564

The elastic potential energy stored in the spring is EE when the extension of the spring is ee. What is the work done by force on the spring to increase the extension from ee to 3e3e ?

  • A. 2E\hspace{1em} 2E

  • B. 4E\hspace{1em} 4E

  • C. 8E\hspace{1em} 8E

  • D. 9E\hspace{1em} 9E

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Question 57

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easy

Two blocks of masses mm and 2m2m approach each other and collide on a horizontal smooth surface. After the collision, they move together. The speeds of the blocks before the collision are 5v5v and 2v2v as shown.

PH0580

Which of the following correctly gives the speed of the blocks after the collision and the nature of the collision?


Speed after collisionNature of collision
\hspace{1.5em}A.\hspace{1.5em}3v3vElastic
\hspace{1.5em}B.\hspace{1.5em}v3\dfrac{v}{3}Elastic
\hspace{1.5em}C.\hspace{1.5em}3v3vInelastic
\hspace{1.5em}D.\hspace{1.5em}v3\dfrac{v}{3}Inelastic

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Question 58

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[Maximum mark: 12]

An elastic bungee cord of natural length 20m20\, m is being tested. A spherical object, originally at rest, is released from a platform. Air resistance and the mass of the cord are insignificant.

PH0644-000

  1. State the principle of conservation of energy. [2]

  2. Describe the energy changes that take place in the spherical object from the time it is released until it comes to rest for the first time. [2]

  3. Show that the speed of the object just before the cord starts to extend is approximately 20ms120\, m\, s^{-1}. [2]

  4. The magnitude of the average net\underline{\textrm{net}} force acting on the object by the cord between the point the cord starts to extend and the point where it reaches maximum extension is 360N360\, N. The time taken during the fall of the object between these points is 0.28s0.28\, s.

    1. Show that the mass of the object is approximately 5.0kg5.0\, kg. [2]

    2. On the graph below, sketch how the the elastic potential energy EEE_{E} of the spring changes with the vertical displacement ss as the cord stretches. There is no need to add values to the axes. [2]

    PH0644-111

    1. The extension of the cord at the point in time when the object has zero acceleration is 11m11\, m. Determine the spring constant of the cord. [2]

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Question 59

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A robot is used to move boxes in a factory. A box is pulled up a slope inclined at 30°\degree to the horizontal by a rope connected to the robot. The tension TT in the rope is 45N45 \,N. Friction acts between the box and the ramp.

PH0618

  1. Define work done by a force. [2]


  1. The box is moving at a constant speed. It covers 1.2m1.2\,m in 3.0s3.0\,s.

    1. Show that the output power of robot 18W18\,W. [2]

    2. During the pull, the robot has a potential difference of 24V24\,V across the terminals of its battery and a current of 3.0A3.0\,A derived from the battery. Determine the efficiency of the robot in this situation. [2]

    3. The emf of the battery is 32 VV. Calculate the internal resistance of the battery. [2]


  1. The rope connecting the robot and the box breaks at a height of 1.5m1.5\,m from the ground level.

    1. The maximum height above the ground level reached by the box is 1.505m1.505\,m. Show that the work done by friction on the box after the break up to reach the maximum height is 0.15J0.15\,J. [2]

    2. Determine the coefficient of dynamic friction between the box and the incline. [3]

    3. The box experiences friction both on the way up the slope and also as it slides back down the slope. On the graph below, sketch the variation of the speed vv of the box with the time tt passed from when the rope breaks until the box reaches the ground level. [2]

      PH0618iii

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Question 60

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[Maximum mark: 13]

    1. Define acceleration. [1]

    2. A car is moving on a straight road. The variation of the car's velocity vv with time tt is seen in the graph below.

      PH0425

      Describe, in terms of acceleration, the motion of the car. [2]

  1. A truck with a speed of 20 ms1m\,s^{-1} passes by a stationary car. The car starts to move with an acceleration of 4 ms2m\,s^{-2} just as the truck goes past. Both of the vehicles move in the same direction.

    PH0425-1

    1. Show that the time needed for the car to overtake the truck is 10 ss. [3]

    2. On the graph below, draw the variation in speed of both vehicles with time during the first 10 seconds of the motion and comment about the areas under the graphs without calculation. [4]

    PH0425-2

  2. In an accident scene, skid marks of a car stretching 100 m are found. According to the manufacturer of the car’s tires, the deceleration that the car experiences with skidding tires is 5 ms2m\,s^{-2}.

    PH0425-3

    Determine whether the car exceeded the speed limit of 72 kmh1km\,h^{-1}. [4]

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Question 61

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medium

A small object is fired horizontally at a speed of 300 m s1^{-1} from the top of a building. Air resistance is negligible. The object lands 900 m from the base of the building. What is the height of the building?

  • A. \hspace{1em} 15 m

  • B. \hspace{1em} 34 m

  • C. \hspace{1em} 44 m

  • D. \hspace{1em} 88 m

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Question 62

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medium

An airplane of weight WW is flying horizontally with constant velocity. The total forward thrust of the engines is 3W3\,W. Which of the following gives the magnitude of the force of the air on the plane?

  • A. 4W\hspace{1em} 4\,W

  • B. 3W\hspace{1em} 3\,W

  • C. \hspace{1em} 10W\sqrt{10} \,W

  • D. \hspace{1em} 8W\sqrt{8} \,W

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Question 63

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[Maximum mark: 9]

The graph shows how the speed v of a car varies with time t.

PH0553

  1. State the difference between average and instantaneous accelerations. [2]

  2. Calculate the instantaneous acceleration of the car at t=1.0st=1.0\, s. [2]

  3. Determine, with explanation, whether the car covers more distance before or after the car reaches a constant speed. [5]

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Question 64

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[Maximum mark: 7]

While practising, a table tennis player hits a ball of mass 2.8 gg that collides with the floor and then bounces back from the wall. The speed of the ball just before reaching the floor is 8.0 ms1m \, s^{-1}. The ball leaves the floor with an angle of 65°\degree to the floor as shown.

PH1004

  1. Due to the collision with the floor, the ball losses 30%\% of its initial kinetic energy. Show that the leaving speed of the ball from the floor is around 7 ms1m \, s^{-1}. [2]

  2. The ball strikes the wall just as it reaches the highest point of its motion. Determine the horizontal distance between the bounce point and the wall. [3]

  3. The ball collides elastically with the wall, with the time of contact during the collision is 0.040s 0.040\, s. Calculate the average horizontal force exerted by the wall on the ball during the collision. [2]

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Question 65

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[Maximum mark: 12]

    1. A spacecraft is moving in a zero gravity zone in space with constant speed. Its pilot decided to accelerate by burning fuel. The burned fuel is ejected backwards from the rocket with a constant speed of 2.5×102ms12.5\times{10}^2\, m\, s^{-1} relative to the rocket at a constant rate of 2.0×102kgs12.0\times{10}^2\, kg\, s^{-1}.

      Show that the net force on the rocket due to the ejection of burnt fuel is 5×104N5 \times 10^4 \,N. [1]

    2. The spacecraft has a mass of 4.2×103kg4.2\times{10}^3\, kg at the instant that it starts to burn the fuel. Calculate the acceleration of the spacecraft after 1.0s1.0\, s has passed. [2]

  1. The spacecraft enters the atmosphere of Mars and slows down due to friction. To decelerate its speed more to reach a safe landing speed, the operator runs the propeller that pushes against the gas in the atmosphere.

    1. By referring to Newton's Third Law, outline why there is a force acting on the spacecraft due to the propeller. [2]

    2. The average density of the Mars atmosphere is 0.020kgm30.020\, kg\,m^{-3}. The radius of the propeller blades is 1.2m1.2\, m. At a given instant, the average force slowing force from the propeller to is 1.4kN1.4\, kN.

      Assuming that the propellor causes all gas that it passes through to come to rest relative to the falling spaceship, estimate the speed of the spaceship at this instant. [4]

    3. The landing legs of the spacecraft have springs that can compress as the spacecraft makes contact with the ground. Explain how this decreases the average force acting on the spacecraft as it lands. [3]

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Question 66

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[Maximum mark: 13]

  1. Define momentum. [1]

  2. A golf ball of mass 45g45\,g moving with a constant velocity of 2.0ms12.0\,m\,s^{-1} undergoes a head-on collision with a stationary ball of mass 2.0kg2.0\,kg. The line that joins the centres of the balls is along the direction of the velocity of the golf ball.

    PH0462

    1. Use Newton's Third Law and Second Law to deduce why the change in momentum of the golf ball is equal and opposite to the change in momentum of the stationary ball during the collision. [3]

    2. The variation of force acting on the golf ball FgF_g with the time tt during the collision is shown in the graph.

      PH0462-1 Created with Geogebra (https://www.geogebra.org/)\footnotesize{\textrm{Created with Geogebra (https://www.geogebra.org/)}}

      Show that the magnitude of the change in momentum of the golf ball is approximately 0.09kgms10.09\,kg\,m\,s^{-1}. [2]

    3. Calculate the speed of the golf ball just after the collision. [3]

    4. Discuss whether the collision is elastic or inelastic. [4]

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Question 67

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medium

An object is moving in a straight line. The graph shows the variation of the velocity vv of the object with time tt.

PH0539

Which of the following is correct according to the graph?

  • I.At point A, the object changes its direction.
    II.At point C the object is at rest.
    III.The magnitude of the acceleration at point D is greater than at point B.


  • A. I only

  • B. II only

  • C. I and II only

  • D. II and III only

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Question 68

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[Maximum mark: 9]

The motion of an object released from a high place in a vacuum is observed. The variation of its velocity with time is recorded and the following graph is obtained.

PH0557-A

  1. Discuss the role that observations play in the development of scientific understanding. [1]

  2. Other than velocity and time, list two quantities that can be obtained from the graph. [2]

    1. The height of the release point is 70 m70\ m. Show that the speed v1v_1 of the object just before the contact with the ground is 37ms137\, m\,s^{-1}. [2]

    2. The object rebounds from the ground with a speed v2v_2 of 17ms117\,m\,s^{-1}. The mass of the object is 8.0kg8.0\, kg and the contact time during the rebound is 0.50s0.50\, s.

      Calculate the average force acting on the object from the ground. [4]

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Question 69

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A car is moving with a kinetic energy of 105J{10}^5\,J.

Estimate the order of magnitude of its momemtum.

  • A. 103kgms1\hspace{1em} {10}^3\,kg\,m\,s^{-1}

  • B. 104kgms1\hspace{1em} {10}^4\,kg\,m\,s^{-1}

  • C. 105kgms1\hspace{1em} {10}^5\,kg\,m\,s^{-1}

  • D. 106kgms1\hspace{1em} {10}^6\,kg\,m\,s^{-1}

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Question 70

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A spring of spring constant 200Nm1200\, N\, m^{-1} is compressed by 6.0cm6.0 \,cm. A box is placed against the spring.

PH0563 [Source: Created with chemix - https://chemix.org/]\footnotesize{\textrm{[Source: Created with chemix - https://chemix.org/]}}

At the point where the box has moved 4.0cm4.0\, cm, how much work has been done by the spring on the box?

  • A. 0.16J\hspace{1em} 0.16\, J

  • B. 0.20J \hspace{1em} 0.20\, J\

  • C. 0.32J\hspace{1em} 0.32\, J

  • D. 0.36J \hspace{1em} 0.36\, J\

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Question 71

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The position of a body is located with a motion detector at constant time intervals.

PH0535

The distance between two successive positions of the body is given in terms of a constant dd. Which of the following graphs could be the variation of velocity vv of the body with time t?

A.B.
PH0535a\hspace{1cm}PH0535b
\hspace{1em}
C.D.
PH0535cPH0535d

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Question 72

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An object is thrown vertically upwards on the surface of the moon. The maximum height that the object can reach is h. When the object reaches the height of h3\dfrac{h}{3} above the surface, what is the ratio


Kinetic energy of the object at h3 Gravitational potential energy of the object at h3 \hspace{3cm} \dfrac{Kinetic\ energy\ of\ the\ object\ at\ \frac{h}{3}\ }{Gravitational\ potential\ energy\ of\ the\ object\ at\ \frac{h}{3}\ }


  • A. 1\hspace{1em} 1

  • B. 23\hspace{1em} \dfrac{2}{3}

  • C. 32\hspace{1em} \dfrac{3}{2}

  • D. 2\hspace{1em} 2

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Question 73

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A motorised toy car starts from rest, with the motor delivering increasing power to the car over time as shown in the graph below.

PH0131

Assuming no energy losses, which of the following gives the kinetic energy of the car after 8.0 seconds?

  • A. \hspace{1em} 0.20 J

  • B. \hspace{1em} 5.0 J

  • C. \hspace{1em} 160 J

  • D. \hspace{1em} 320 J

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Question 74

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A motor uses a cable to pull a trolley up an inclined plane at a constant velocity.

PH0035

Which of the following statements about the energy changes of the trolley during its motion are correct?

  • I.The work done by the engine has greater magnitude than the work done by friction.
    II.The total of kinetic and potential energy of the trolley increases.
    III.The gain in gravitational potential energy of the trolley has the same magnitude as the work done by the engine.


  • A. \hspace{1em} I and II only

  • B. \hspace{1em} I and III only

  • C. \hspace{1em} II and III only

  • D. \hspace{1em} I, II and III

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Question 75

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A ball with mass mm is released from a height of hh and undergoes free fall. The ball hits the ground and rebounds vertically. On rebound, the ball reaches a maximum height of hh'. The time taken for the collision is TT. What are the magnitude of the average net force on the ball and change in kinetic energy of the ball?


\hspace{1em} Change in kinetic energy \hspace{1em}\hspace{1em} Average force \hspace{1em}
\hspace{1.5em}A.\hspace{1.5em}mg(hh)mg(h-h')m(2gh+2gh)T\dfrac{m(\sqrt{2gh} + \sqrt{2gh'})}{T}
\hspace{1.5em}B.\hspace{1.5em}mg(hh)mg(h'-h)m(2gh2gh)T\dfrac{m(\sqrt{2gh} - \sqrt{2gh'})}{T}
\hspace{1.5em}C.\hspace{1.5em}mg(hh)mg(h'-h)m(2gh+2gh)T\dfrac{m(\sqrt{2gh} + \sqrt{2gh'})}{T}
\hspace{1.5em}D.\hspace{1.5em}mg(hh)mg(h-h')m(2gh2gh)T\dfrac{m(\sqrt{2gh} - \sqrt{2gh'})}{T}

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Question 76

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A stationary nucleus of uranium-238 undergoes alpha decay to form thorium-234. The initial speed of the alpha particle is vv. What is correct about the magnitude of the thorium-234 velocity and its direction?


MagnitudeDirection
\hspace{1.5em}A.\hspace{1.5em}4234v\dfrac{4}{234}v\hspace{1.5em}Same as the alpha particle\hspace{1.5em}
\hspace{1.5em}B.\hspace{1.5em}234238v\dfrac{234}{238}vOpposite to the alpha particle
\hspace{1.5em}C.\hspace{1.5em}234238v\dfrac{234}{238}vSame as the alpha particle
\hspace{1.5em}D.\hspace{1.5em}4234v\dfrac{4}{234}vOpposite to the alpha particle

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Question 77

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A ball of mass 0.1kg0.1\,kg moves horizontally with a speed 5.0ms15.0\,m\,s^{-1}, hits a vertical wall and rebounds with speed of 3.0ms13.0\,m\,s^{-1}. The graph records the variation of force with time tt.

PH0344

What is FmaxF_{max}?

  • A. \hspace{1em} 4 NN

  • B. \hspace{1em} 8 NN

  • C. \hspace{1em} 40 NN

  • D. \hspace{1em} 80 NN

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Question 78

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An inclined plane makes an angle θ\theta with the horizontal. An object with mass mm is just about to slide on the inclined plane.

PH0853aaaa

Which of the following is correct about the coefficient of static friction μs\mu_s and the free body diagram of the mass?


\hspace{1.5em} μs\mu_s \hspace{1.5em}\hspace{1.5em}Free body diagram \hspace{1.5em}
\hspace{1.5em}A.\hspace{1.5em}sinθsin \thetaPH0853a
\hspace{1.5em}B.\hspace{1.5em}sinθsin \thetaPH0853b
\hspace{1.5em}C.\hspace{1.5em}tanθtan \thetaPH0853c
\hspace{1.5em}D.\hspace{1.5em}tanθtan \thetaPH0853d

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Question 79

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The variation of displacement of a trolley with time tt is shown on the graph below.

PH0538-1a

The magnitudes of the instantaneous velocities of the trolley at times t1t_1 and t2t_2 are v1v_1 and v2v_2 respectively. Which of the following correctly compares the instantaneous velocities with the magnitude of the average velocity of the trolley for the whole of the motion shown?


v1v_1v2v_2
A.Greater than the average velocityGreater than the average velocity
B.Greater than the average velocityLess than the average velocity
C.Less than the average velocityGreater than the average velocity
D.Less than the average velocityLess than the average velocity

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Question 80

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A ball is released from rest at a height h above the ground. At each bounce At each bounce 75% of its kinetic energy is lost. Which graph represents the variation of the ball's velocity v with time t from the beginning of motion until the moment just before the third bounce? Assume the acceleration of the ball is in in the negative direction and that air resistance is negligible.


A.B.
PH0331A\hspace{1cm}PH0331B
\hspace{1cm}
C.D.
PH0331CPH0331D

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Question 81

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A block of mass 4.0 kg rests on an inclined plane.

PH0330

The coefficient of static friction between the block and the plane μs\mu _s is 0.4.

Which of the following gives the angle of inclination at which the block will start to slide?

  • A. \hspace{1em} sin1(0.4)sin^{-1}(0.4)

  • B. \hspace{1em} tan1(0.4)tan^{-1}(0.4)

  • C. \hspace{1em} cos1(0.4)cos^{-1}(0.4)

  • D. \hspace{1em} tan1(0.6)tan^{-1}(0.6)

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Question 82

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Two objects of mass MM and mm are connected via a frictionless pulley. The rope attached to the object of mass MM makes an angle θ\theta with the horizontal. The objects are at rest.

PH0034

For the large mass, which expressions are correct for the force of friction Ff_f and the normal force N


\hspace{3em} Ff_f \hspace{3em}\hspace{4em} N\hspace{4em}
\hspace{1.5em}A.\hspace{1.5em}mgmg cosθ\thetaMgmgMg - mg sinθ\theta
\hspace{1.5em}B.\hspace{1.5em}mgmg sinθ\thetaMgmgMg - mg sinθ\theta
\hspace{1.5em}C.\hspace{1.5em}mgmg sinθ\thetaMgmgMg - mg cosθ\theta
\hspace{1.5em}D.\hspace{1.5em}mgmg cosθ\thetaMgmgMg - mg cosθ\theta

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Question 83

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A ball is released from rest and falls vertically for 3 seconds on Earth. Air resistance is negligible. What is the average speed of the ball during the motion?

  • A. \hspace{1em} 3 ms1m\,s^{-1}

  • B. \hspace{1em} 10 ms1m\,s^{-1}

  • C. \hspace{1em} 15 ms1m\,s^{-1}

  • D. \hspace{1em} 30 ms1m\,s^{-1}

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Question 84

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[Maximum mark: 11]

  1. State the difference between distance and displacement. [2]

  2. A dart player throws a dart horizontally with the speed of 15ms115 \,m\, s^{-1} to hit a dartboard. The vertical displacement of the dart is 0.35m0.35\,m. Air resistance is negligible.

    PH0424

    1. Show that the time taken for the dart to reach the centre of the dartboard is approximately 0.3 s. [2]

    2. Calculate the angle to the horizontal, in degrees, of the velocity of the dart as it hits the dartboard. [3]

    3. Determine the displacement of the dart. [2]

    4. On the axes below, sketch how the square of the velocity v2v^2 of the dart varies with the square of time t2t^2. [2]

      (no need to add values on the axes)

      PH0424-1

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Question 85

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A point PP is subjected to three simultaneous forces of magnitudes FA>FB>FCF_A > F_B > F_C. Point PP is in equilibrium. Which of the following statements is not always true about the magnitudes of the forces?

  • I.FA=FB+FCF_A = F_B + F_C
    II.FAFB+FCF_A \leq F_B + F_C
    III.FA>FBFCF_A > F_B - F_C


  • A. \hspace{1em} I only

  • B. \hspace{1em} I and II only

  • C. \hspace{1em} I and III only

  • D. \hspace{1em} II and III only

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Question 86

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A box of mass 2kg2 \,kg is pushed with an initial speed of 10ms110\,m\,s^{-1} on a rough horizontal floor. A uniform frictional force of 10N10\, N acts on the box. What is the distance travelled by the box at the instant when the kinetic energy of the box is halved?

  • A. \hspace{1em} 10 m

  • B. \hspace{1em} 5 m

  • C. \hspace{1em} 2 m

  • D. \hspace{1em} 1 m

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Question 87

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[Maximum mark: 11]

  1. Define power. [2]

  2. A mass of 2.0 kgkg is pulled by a variable horizontal force FF on a smooth surface. A thread attached to the mass passes over an ideal pulley and supports another mass of 3.0 kgkg.

    PH0460 [Created with Chemix (https://chemix.org)]\small{\textrm{[Created with Chemix (https://chemix.org)]}}

    The variation of FF with the distance dd moved by the mass of 2.0 kgkg is shown in the graph.

    PH0460-1a [Source: Created with GeoGebra by Tom Walsh- https://www.geogebra.org/m/jrWMapS7]\footnotesize{\textrm{[Source: Created with GeoGebra by Tom Walsh- https://www.geogebra.org/m/jrWMapS7]}}

    1. Calculate work done, in JJ, on the 2.0 kgkg mass by the force FF when the mass travelled 0.90 mm. [2]

    2. Calculate the final speed of the 2.0 kgkg mass. [3]

  3. On another occasion, the horizontal force is no longer applied and the 2.0 kgkg mass is replaced with a motor which pulls the 3.0 kgkg mass with a constant speed of 0.50 ms1m\,s^{-1}.

    PH0460-2 [Created with Chemix (https://chemix.org)]\small{\textrm{[Created with Chemix (https://chemix.org)]}}

    1. On the graph, show the variation of the change in gravitational potential energy ΔEp\Delta E_p of the mass with time tt. [2]

      (no need to add values to the axes)

      PH0460b [Source: Created with GeoGebra by Tom Walsh- https://www.geogebra.org/m/jrWMapS7]\footnotesize{\textrm{[Source: Created with GeoGebra by Tom Walsh- https://www.geogebra.org/m/jrWMapS7]}}

    2. The power supplied to the motor is 20 WW. Calculate the efficiency of the motor. [2]

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Question 88

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[Maximum mark: 11]

  1. The diagram below shows a water slide. As a test, an object is released from point AA, 6.0 mm above the ground level. Point BB at the end of the slide is 2.0 mm above the ground level. Location CC is the point of contact of the slide with the ground. The slide approximates a circular shape at this point.

    PH0617

    Air resistance and friction on the object are negligible.

    1. Draw the free-body diagram of the forces acting on the object as it passes point DD. [2]

      PH0617aa

    2. At the instant the object passes point CC, explain why there is acceleration and yet no work is done. [2]

  2. The object slides from point AA to point BB and is launched from point BB with an angle.

    1. Show that the speed of the object at point BB is approximately 8.9 m s18.9\ m\ s^{-1} [2]

    2. At point BB, the object is launched into the air and lands in a pool of water that is 2.2 mm below point BB.

      PH0617cc

      After 1.1 ss, it reaches the surface of the water. Show that the angle θ\theta of the launch above the horizontal is approximately 22°\degree. [3]

    3. Calculate the horizontal distance travelled by the object between losing contact with the slide and reaching the water. [2]

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Question 89

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[Maximum mark: 8]

  1. Define displacement. [1]

  2. A table tennis ball is thrown horizontally from the top of a building. The variation of the ball's horizontal displacement ss with time tt is shown on the graph below.

    PH0554-1

    1. State which quantity is given by the gradient of the tangent to the graph at any time during the motion. [1]

    2. On the graph below, sketch the expected variation of horizontal displacement with time when air resistance is ignored. The original curve is given as a dashed line. [2]

      PH0554-2

  3. A stone is then launched with a horizontal speed of 20ms120\, m\,s^{-1} from a height of 12m12\, m above the ground.

    PH0554-3-1

    Determine the magnitude of the displacement of the stone when it hits the ground if air resistance is considered to be negligible. [4]

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Question 90

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[Maximum mark: 13]

  1. In a game, players try to hit a moving cart by projecting a ball at an angle from a spring-loaded launcher.

    PH0845aaaa

    When the spring is fully uncompressed, it extends to the open end of the barrel. The frictional forces acting on the ball are negligible.

    1. State the main energy changes taking place when the ball is moving inside the barrel. [2]

    2. The following data is available:

      Mass of the ball: 0.065kg0.065\, kg
      The compression of the spring before release: 0.22m0.22\, m
      The spring constant: 10Nm110\, Nm^{-1}

      Show that the launch speed of the ball at the end of the barrel is approximately 2.3ms12.3\, m\,s^{-1}. [3]

  2. When launching the ball, the spring applies a force for 0.022s0.022\, s. Determine the average net force acting on the ball during this time interval [2]

  3. One competitor aligned the launcher at 30°30\degree above the horizontal. At the instant the ball left the launcher, it was 1.25m1.25\, m directly above the front of a moving cart which was moving at a steady speed of 2.1ms12.1\, m\,s^{-1} directly away from the launcher.

    PH0845aaa1

    1. Show that the time taken for the ball to displace 1.25m1.25\, m vertically downward after leaving the barrel is around 0.64s0.64\, s. [3]

    2. The length of the cart is 35cm35\, cm

      Deduce whether or not the ball will hit the top of the cart. [3]

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Question 91

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A projectile is launched horizontally on Earth with initial speed of 3.0ms13.0\, m\,s^{-1} from a height of 5.0 m5.0\ m above the ground.

PH0851aaaa

What is the magnitude of the displacement of the stone when it reaches the ground?


  • A. \hspace{1em} 5.0 m5.0\ m

  • B. \hspace{1em} 8.0 m8.0\ m

  • C. \hspace{1em} 34 m\sqrt{34}\ m

  • D. \hspace{1em} 51 m\sqrt{51}\ m

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Question 92

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[Maximum mark: 12]

In an experiment, the free-fall of a ball bearing is used to measure the acceleration due to gravity. The ball bearing is suspended with an electromagnet. Then it is released from a height of hh above a table.

PH0511_A [Source: Created with chemix - https:// chemix.org/]\footnotesize{\textrm{[Source: Created with chemix - https:// chemix.org/]}}

The time t needed for the ball bearing to reach the ground after release is measured. The experiment is repeated for different values of hh. The theoretically predicted relationship between time t and h is

t2=2hgt^2=\dfrac{2h}{g}

  1. State why there is a need to collect data for a range of values of hh to verify this relationship. [1]

  2. The experimental data for t2t^2 and h are plotted on the graph below.

    PH0511q

    1. Draw the line of best fit for the plotted data on the graph. [1]

    2. Suggest whether the data is consistent with the theoretical prediction. [2]

    3. By using the line of best fit, determine a value for g and state the units. [4]

  3. The theoretical relationship is for an object falling in a vacuum.

    1. Compare the experimental result to the accepted value of g and suggest a reason for the discrepancy. [2]

    2. State and explain whether the source of error in (c)(i) is a systematic or random error. [2]

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Question 93

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[Maximum mark: 5]

A box half filled with sand is pulled by a motor at a constant speed of 2.0ms12.0\,m\,s^{-1} on a frictionless surface. During the motion, sand is added to the box from above at a constant rate of σkgs1\sigma\,kg\,s^{-1}.

PH0464

  1. State the condition related to the mass of an object in order for the equation Fnet=maF_{net}=ma to be equivalent to the equation Fnet=ΔptF_{net}=\dfrac{\Delta p}{t} . [1]

  2. The force applied by the motor on the box is 0.11N0.11\,N. Determine σ\sigma. [2]

  3. The motor has an efficiency of 75%. Calculate the total power provided to the motor. [2]

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Question 94

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Two bodies of masses 2 kg and 3 kg are connected by a thread and pulled in the upward direction with an acceleration of g due to an upward force F.

PH0245

The thread between the masses is cut. Which of the following is correct for the bodies just after the cut?


Acceleration of 3 kg massAcceleration of 2kg mass
\hspace{1.5em}A.\hspace{1.5em}gg
\hspace{1.5em}B.\hspace{1.5em}4gg
\hspace{1.5em}C.\hspace{1.5em}4g4g
\hspace{1.5em}D.\hspace{1.5em}g4g

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Question 95

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A stationary object explodes and splits into two parts of masses mm and 2m2m. Mass mm moves north with a velocity of 2v2v and mass 2m2m moves south with a velocity of vv. Calculate the total change in linear momentum of the system as a result of the explosion.

PH0248

  • A. \hspace{1em} Zero

  • B. \hspace{1em} 1.5mv1.5mv

  • C. \hspace{1em} 4mv4mv

  • D. \hspace{1em} 6mv6mv

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Question 96

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An object of mass mm rests on a rough surface. Another object of mass MM is connected to it via a frictionless pulley. The coefficient of dynamic friction between the surface and the object of mass mm is μ\mu.

PH0205

When the object of mass MM is released, the objects accelerate. What is the acceleration of the system?

  • A. \hspace{1em} gMM+m\dfrac{gM}{M+m}

  • B. \hspace{1em} gmM+m\dfrac{gm}{M+m}

  • C. \hspace{1em} g(Mμm)M+m\dfrac{g(M-\mu m)}{M+m}

  • D. \hspace{1em} g(μmM)M+m\dfrac{g(\mu m-M)}{M+m}

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Question 97

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[Maximum mark: 9]

A cannonball is fired horizontally from a cannon positioned at the edge of a cliff.

PH0562

  1. In the context of Newton's Laws, explain why the cannon recoils to the left when the cannonball is fired. [2]

  2. The initial recoil speed of the cannon is 1.0ms11.0\, m{\,s}^{-1} and its mass is 1200 kg.

    1. After the ball is fired, the cannon rolls to the left and experiences a resistive force of 8.0 kN8.0\ kN as it rolls. Determine the distance covered by the cannon. [2]

    2. The mass of the cannonball is 9.0 kg9.0\ kg. Show that the magnitude of the velocity of the ball after being fired is approximately 133ms1133\, {m\, s}^{-1}. [2]

    3. Calculate the magnitude of the displacement of the cannonball after 5.0s5.0\, s. Air resistance can be ignored. [3]

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Question 98

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The graph shows the variation of velocity vv of a ball with time tt.

PH0532

The initial speed of the ball is very high. Which of the following statements could be true for the ball?

  • A. It is thrown vertically upward in the presence of air resistance.

  • B. It is thrown vertically upward in the absence of air resistance.

  • C. It is thrown vertically downward in the presence of air resistance.

  • D. It is thrown vertically downward in the absence of air resistance.

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Question 99

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A system that consists of two light identical springs connected in series stores a total elastic potential energy EpE_p when a load is added to the springs. One of the springs is then removed and the same load is added to the remaining spring.

PH0084

In terms of EpE_p, what is the total elastic potential energy stored in the single spring situation?

  • A. \hspace{1em} 2 EpE_p

  • B. \hspace{1em} EpE_p

  • C. \hspace{1em} 0.5 EpE_p

  • D. \hspace{1em} 0.25 EpE_p

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Question 100

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[Maximum mark: 9]

Two blocks of masses 3.0 kgkg and 4.0 kgkg are held stationary with a thread connecting the blocks. The mass of 3.0 kgkg is on a rough incline that makes an angle of 30° with the ground and it starts to slip up when the other mass is slightly more than 4.0 kgkg.

PH0559MS

  1. State two differences between static friction and dynamic friction [2]

  2. Calculate the coefficient of static friction between the mass of 3.0 kg and the rough surface. [3]

  3. The thread connecting masses breaks and the mass of 3.0 kgkg slides down. Show that the acceleration of the mass of 3.0 kgkg is around 1.5 ms2m\,s^{-2}. The coefficient of dynamic friction between 3.0 kgkg mass and the rough surface is 0.40. [2]

  4. Determine the speed of the mass of 3.0 kgkg after it has moved through a vertical height of 1.0 mm. [2]

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Question 101

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The diagram shows the forces acting on a block as it slides down an inclined plane with constant acceleration. WW is the weight of the block, FF is the friction force, μd\mu_d is the coefficient of dynamic friction and gg is the gravitational field strength. The plane is inclined at an angle θ\theta to the horizontal.

PH0083

Which expression gives the acceleration of the block?

  • A. \hspace{1em} gsinθgμdcosθgsin\theta - g\mu_dcos\theta

  • B. \hspace{1em} gcosθgμdsinθgcos\theta - g\mu_dsin\theta

  • C. \hspace{1em} WsinθWμdcosθWsin\theta - W\mu_dcos\theta

  • D. \hspace{1em} WcosθWμdsinθWcos\theta - W\mu_dsin\theta

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Question 102

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[Maximum mark: 7]

Three identical cylinders sit inside a cup. Their radius of each is 5 cm and their centres of mass are marked in the diagram. The lines connecting the centres of the masses pass through the contact points between the cylinders.

PH0560-AA

  1. Draw and label the free-body diagram for the cylinder M3M_3 [2]

    PH0560-A

    1. For analysis purposes, the three cylinders can at times be considered as a single object consisting of the mass of the all cylinders. Explain why this simplification may be useful. [1]

    2. The reaction force of the ground on M3M_3 is 30N30 \,N. Show that the mass of each cylinder is around 1.0 kg. [2]

  2. Determine the force that mass M3M_3 exerts on M1M_1 [2]

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Question 103

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The graph shows the variation of length of a spring of original length l0l_0 as it is stretched to length ll by a variable force

PH0264

The work done against the spring is represented by which of the following?

  • A. \hspace{1em} The area marked X.

  • B. \hspace{1em} The area marked Y.

  • C. \hspace{1em} The area marked Z.

  • D. \hspace{1em} The sum of the areas marked Y and Z

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Question 104

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Block AA of mass mA=3.0kgm_A=3.0\,kg rests above the flat horizontal surface of block BB of mass mB=6.0kgm_B=6.0\,kg, which in turn rests on a smooth horizontal surface as shown.

PH0153

The coefficients of static and kinetic friction between AA and BB are μs=0.2\mu_s=0.2 and μk=0.1\mu_k=0.1 respectively. A horizontal force of F=7.0NF=7.0\,N is applied towards the right on block AA. Assuming acceleration due to gravity g10ms2g \approx 10\,m\,s^{-2}, the direction and magnitude of acceleration aBa_B of block BB are:


\hspace{1em} Direction of aBa_B \hspace{1em}\hspace{1em} Magnitude of aBa_B \hspace{1em}
\hspace{1.5em}A.\hspace{1.5em}To the left1.0ms21.0\,m\,s^{-2}
\hspace{1.5em}B.\hspace{1.5em}To the left0.5ms20.5\,m\,s^{-2}
\hspace{1.5em}C.\hspace{1.5em}To the right1.0ms21.0\,m\,s^{-2}
\hspace{1.5em}D.\hspace{1.5em}To the right0.5ms20.5\,m\,s^{-2}

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Question 105

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A tennis ball with mass 60g60\, g travels horizontally with constant speed uu. The ball hits a stationary racket and rebounds in the opposite direction with a horizontal speed vv. The time for the collision is 5.0ms5.0\, ms.

What is the magnitude of the force on the ball?


  • A. \hspace{1em} 0.06(uv)0.06(u-v)

  • B. \hspace{1em} 0.06(u+v)0.06(u+v)

  • C. \hspace{1em} 12(uv)12(u-v)

  • D. \hspace{1em} 12(u+v)12(u+v)

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Question 106

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A ball of mass mm strikes a vertical wall with a speed of vv. It bounces back with the same speed. The angle between the wall and the trajectory of the incoming ball is θ1\theta_1. The angle between the wall and the trajectory of the ball after the bounce is θ2\theta_2. During the collision, the only force that acts on the ball is normal to the wall.

PH0587

What is the magnitude of the change in momentum of the ball?

  • A. 2mv(cosθ1)\hspace{1em} 2mv(cos\,\theta_1)

  • B. 2mv(sinθ1)\hspace{1em} 2mv(sin\,\theta_1)

  • C. 2mv(sin(θ1+θ2))\hspace{1em} 2mv(sin(\theta_1+\theta_2))

  • D. 2mv(cos(θ1+θ2))\hspace{1em} 2mv(cos(\theta_1+\theta_2))

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Question 107

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A firecracker is at rest just before exploding. Upon exploding, the firecracker splits into two unequal parts which are projected in exactly opposite directions. Which of the following must be true?

  • A. \hspace{1em} The total kinetic energy of the firecracker remains unchanged before and after the explosion.

  • B. \hspace{1em} The kinetic energy of the two parts after the explosion is identical.

  • C. \hspace{1em} The total momentum of the firecracker is unchanged after the explosion.

  • D. \hspace{1em} The velocities of the two parts are exactly equal in magnitude but opposite in direction.

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Question 108

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[Maximum mark: 9]

A ball of mass 1.6kg1.6\, kg is dropped from a very high building. The only forces acting on the ball are the force of gravity and air resistance. The graph shows the variation of the vertical velocity vv of the ball with time tt.

PH0552-1

    1. Define terminal speed. [1]

    2. State the terminal speed of the ball. [1]

  1. Estimate the vertical displacement of the ball during the 10.0s10.0\,s of motion. [2]

    1. Calculate the instantaneous acceleration of the ball at t=2.0s.t=2.0\, s. [2]

    2. Determine the magnitude of the vertical component of the force of air resistance at t=2.0st=2.0\, s [3]

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Question 109

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An object is thrown vertically upwards at the edge of a cliff at height hh above the ground. When the object passes the edge of the cliff while falling downwards, a second, identical object is released from rest. Air resistance is negligible. What increases for the second object as the two objects fall?

  • A. \hspace{1em} Acceleration

  • B. \hspace{1em} Distance from the ground

  • C. \hspace{1em} Velocity relative to the object released earlier

  • D. \hspace{1em} Distance from the object released earlier

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Question 110

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A car decelerates with a constant rate until it stops.

Which graph shows the variation of speed of the car with the distance travelled?

A.\hspace{2cm}B.
PH0850aaPH0850bb
C.D.
PH0850ccPH0850dd

[Source: Image created using https://ophysics.com/t4.html]\footnotesize{\textrm{[Source: Image created using https://ophysics.com/t4.html]}}

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Question 111

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A mass moving with a constant speed uu encounters a rough surface and comes to a stop. The mass takes a time tt to stop after encountering the rough surface.

PH0544

The coefficient of dynamic friction between the rough surface and the mass is 0.40. Which of the following expressions gives the initial speed uu?

  • A. 0.2gt\hspace{1em} 0.2gt

  • B. 0.4gt\hspace{1em} 0.4gt

  • C. gt\hspace{1em} gt

  • D. 2.5gt\hspace{1em} 2.5gt

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Question 112

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A race car starts to race on a straight horizontal race track from rest. The car's engine has a constant power output and the car experiences a resistive force that increases proportionally with its speed.

Which graph represents the variation with distance ss of the power PP required by the engine to overcome the resistive force?

A.B.
PH0038-A\hspace{1cm}PH0038-B
\hspace{1em}
C.D.
PH0038-CPH0038-D

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Question 113

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A body is moving in a straight line with a constant acceleration of aa. Its speed increases from uu to vv in a time of tt. Consider the folloing expressions:

  • I.ut+(vu)t2ut+\dfrac{(v-u)t}{2}
    \hspace{1em}
    II.vt12at2vt-\dfrac{1}{2} at^2
    \hspace{1em}
    III.(vu)t2\dfrac{(v-u)t}{2}

Which expression(s) can be used to determine the displacement of the body during the time interval tt?

  • A. I only

  • B. II only

  • C. I and II only

  • D. II, and III only

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Question 114

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Three identical masses are connected as shown with a string that passes over an ideal pulley. The tension in the string connecting m1m_1 and m2m_2 is T1T_1. The tension of the string attached to m3m_3 is T2T_2.

PH0546

The acceleration of the m3m_3 is g4\dfrac{g}{4}.

Which of the following is correct for T2T_2 and the acceleration of m1m_1?


T2\hspace{1.5em} \bf{T_2} \hspace{1.5em}Acceleration of m1\bf{m_1}
\hspace{1.5em}A.\hspace{1.5em}5T13\dfrac{5T_1}{3}g4-\dfrac{g}{4}
\hspace{1.5em}B.\hspace{1.5em}3T15\dfrac{3T_1}{5}g4\dfrac{g}{4}
\hspace{1.5em}C.\hspace{1.5em}5T13\dfrac{5T_1}{3}g4\dfrac{g}{4}
\hspace{1.5em}D.\hspace{1.5em}3T15\dfrac{3T_1}{5}g4-\dfrac{g}{4}

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Question 115

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An object of mass mm with a speed of 3.0ms13.0\, m\,s^{-1} collides horizontally with a stationary box of mass 2m2m. After the collision, the object and the box move together.

PH0588

The friction acting on the box and the object is 6.0N6.0\, N.

Which expression gives total distance travelled by the combined objects before coming to rest after the collision?

  • A. m16\hspace{1em} \dfrac{m}{16}

  • B. m12\hspace{1em} \dfrac{m}{12}

  • C. m8\hspace{1em} \dfrac{m}{8}

  • D. m4\hspace{1em} \dfrac{m}{4}

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Question 116

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A trapeze artist is swinging from position A to position C as shown in the diagram.

PH0634a [Source: Image created using Images by OpenClipart-Vectors from Pixabay - https ://pixabay.com]\footnotesize{\textrm{[Source: Image created using Images by OpenClipart-Vectors from Pixabay - https ://pixabay.com]}}


The combined mass of the artist and the swing is 70 kgkg, the length of the rope of the swing is LL and the tension in the rope at position B is TT.

Which expression gives the kinetic energy at position B?


  • A.  L(T700)2\hspace{1em} \ \dfrac{L\left(T-700\right)}{2}

  • B.  LT2\hspace{1em} \ \dfrac{LT}{2}

  • C.  LT\hspace{1em} \ LT

  • D.  L(T+700)2\hspace{1em} \ \dfrac{L\left(T+700\right)}{2}

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Question 117

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A car is moving on a horizontal road. The variation of velocity vv of a car with time tt can be seen in the graph below.

PH0537qqq

Which of the following graphs shows the variation of displacement ss of the car with time tt?

A.B.
PH0537aaa\hspace{1cm}PH0537bbb
\hspace{1em}
C.D.
PH0537cccPHN0537ddd

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Question 118

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A roller coaster goes around the inside of a loop of radius RR, shown in the diagram. The combined mass of a car and the passengers is MM.

PH0639a


When the car is at its highest point, the normal reaction force of the track on the car is equal to half of the weight of the car and passengers.

Which expression gives the kinetic energy at the top of the loop?

  • A. \hspace{1em} 0

  • B. \hspace{1em} RMg4\dfrac{RMg}{4}

  • C. \hspace{1em} 3RMg4\dfrac{3RMg}{4}

  • D. \hspace{1em} RMgRMg

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Question 119

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An object is released from rest from a very high building. Air resistance is not negligible. Which of the following graphs shows the variation of the gravitational potential energy of the object with time?


A.B.
PH0244A\hspace{1cm}PH0244B
\hspace{1cm}
C.D.
PH0244CPH0244D

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Question 120

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An object starts to move in a straight line under the effect of two opposite forces of 12N12\, N and 16N16\, N.

PH0548

After 5s5\,s, the displacement of the object is 25m25 \,m. What is the mass of the object?

  • A. 1kg\hspace{1em} 1\,kg

  • B. 2kg\hspace{1em} 2\,kg

  • C. 3kg\hspace{1em} 3\,kg

  • D. 4kg\hspace{1em} 4\,kg

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Question 121

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hard

Two masses of 2kg2\, kg and 4kg4\, kg are connected with a string that passes over a pulley. They are released from rest. Energy is lost in the pulley due to friction.

PH0568

When the 2kg2\, kg mass has gained a gravitational potential energy of EE, the 4kg4\, kg mass has a kinetic energy of 12E\dfrac{1}{2}E. How much energy has been lost to friction up to that point in time?

  • A. E4\hspace{1em} \dfrac{E}{4}

  • B. E2\hspace{1em} \dfrac{E}{2}

  • C. E\hspace{1em} E

  • D. 2E\hspace{1em} 2E

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Question 122

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[Maximum mark: 12]

  1. Define Newton's First Law. [2]

  2. A block of mass 2.0 kgkg slides at the constant speed of vv on a rough inclined plane. A string attached to the hanging mass of 0.50 kgkg passes over a pulley and supports the block. The slope of the incline is 25°.

    PH0440 [Source: Created with Chemix - https://chemix.org/]\small{\textrm{[Source: Created with Chemix - https://chemix.org/]}}

    1. Show that the direction of the motion of the box is down the slope. [3]

    2. Draw and label a free-body diagram for the forces acting on the block. [2]

      PH0440-2

    3. Determine the coefficient of dynamic friction between the block and the inclined plane. [3]

    4. In reality, air resistance will also have an effect on the motion of the block and the calculated coefficient of friction. If air resistance were taken into account for this constant speed scenario, discuss how the calculated value would be affected. [2]

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Question 123

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hard

A metal ball of mass mm is released from a height of hh above a massless platform attached to a vertical spring.

PH0565 [Source: Created with chemix - https://chemix.org/]\footnotesize{\textrm{[Source: Created with chemix - https://chemix.org/]}}

The spring constant of the spring is given by mgh\dfrac{mg}{h}. The ball hits the spring and compresses it. When the spring is compressed by a distance hh, what is the speed of the ball?

(Energy transfer only happens between spring and ball and the kinetic energy of the spring can be ignored)

  • A. 2h\hspace{1em} \sqrt{2h}

  • B. 2gh\hspace{1em} \sqrt{2gh}

  • C. 3h\hspace{1em} \sqrt{3h}

  • D. 3gh\hspace{1em} \sqrt{3gh}

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Question 124

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A rocket is moving in the absence of a gravitational field with constant speed. It starts to accelerate by burning fuel. At the start, the fuel contributes to most of the mass of the rocket. The burned fuel is ejected backwards from the rocket with a constant speed of vv relative to the rocket and a constant rate of σ kgs1\sigma\ {kg\,s}^{-1}. Which graph shows the variation of acceleration aa of the rocket with time tt as most of the fuel is used?

A.B.
PH0583a\hspace{1cm}PH0583b
\hspace{1em}
C.D.
PH0583cPH0583d

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Question 125

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[Maximum mark: 11]

  1. Define potential energy. [1]

  2. A body of mass 2.0 kgkg is pushed with an initial speed of 1.2 ms1m\,s^{-1} down the slope of a frictionless 30o^o incline from a height of hh. As soon as it reaches the bottom of the incline, it begins to move on a rough horizontal table where it comes to rest momentarily after colliding with a spring of spring constant 32 Nm1N\,m^{-1}. (Air friction is ignored)

    PH0459 [Created with Chemix (https://chemix.org)]\small{\textrm{[Created with Chemix (https://chemix.org)]}}

    1. The speed of the body is 3.06 ms1m\,s^{-1} when it reaches the bottom of the incline. Calculate hh. [2]

    2. The distance between the bottom of the slope and the body's position is xx. On the graph, sketch the variation of the square of the speed v2v^2 of the body with distance xx

      (no need to add values to the axes)

      PH0459-1

    3. At the instant that the body stops momentarily, the spring is compressed as 0.43 mm. The coefficient of friction between the body and the rough surface is 0.40. Determine the distance that the body covered on the horizontal rough surface between the point of leaving the ramp and stopping momentarily. [4]

  3. The incline is replaced with one of a steeper gradient. The body is pushed at the same speed from the same height. Explain the effect of the increase in gradient on the maximum compression of the spring in comparison to the maximum compression in the original situation. [2]

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Question 126

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A jet of water with a cross sectional area of AA strikes perpendicular to a wall at a speed of vv. After the collision, the water loses all of its horizontal speed and falls to the ground. The magnitude of the force created on the wall due to the water is FF.

Which expression give the density of the water?


  • A. FAv2\hspace{1em} \dfrac{F}{Av^2}

  • B. FAv\hspace{1em} \dfrac{F}{Av}

  • C. FAv\hspace{1em} FAv

  • D. FAv2\hspace{1em} FAv^2

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Question 127

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An apple falls 5 m in height from a tree. It rebounds from the ground with a quarter of its striking speed. The apple is in contact with the ground for approximately 0.1 ss. What is an estimate of the magnitude of the average net force on the apple when it strikes the ground?

  • A. \hspace{1em} 100^0 N

  • B. \hspace{1em} 101^1 N

  • C. \hspace{1em} 102^2 N

  • D. \hspace{1em} 103^3 N

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Question 128

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A stone is thrown vertically upward in the presence of air resistance. Which of the following graphs best shows the variation of velocity vv of the stone with time tt until it reaches the maximum height above the ground?

A.B.
PH0533aaPH0533bb
\hspace{1em}
C.D.
PH0533ccPH0533dd

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Question 129

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A box of mass 3kg3\, kg is placed on a box of mass 7kg7\, kg. The coefficient of static friction between the surfaces of the boxes is 0.5. A horizontal force FF is applied to the 7kg7\, kg box which sits on a frictionless surface.

PH0549

What is the maximum value of FF that can move the boxes without the 3kg3\,kg box slipping?

  • A. 0.1g\hspace{1em} 0.1g\,

  • B. 0.5g\hspace{1em} 0.5g\,

  • C. g\hspace{1em} g\,

  • D. 5g\hspace{1em} 5g\,

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Question 130

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An object is launched horizontally from a height in a vacuum. Which of the following graphs correctly shows how the square of the velocity v2v^2 of the object varies with the square of time t2t^2?

A.B.
PH0534A\hspace{1cm}PH0534B
\hspace{1em}
C.D.
PH0534CPH0534D

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Question 131

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[Maximum mark: 11]

  1. Define Newton's Third Law. [2]

  2. A block of mass 2.0 kgkg is placed on another block of mass 5.0 kgkg. The blocks sit on a frictionless surface, but the coefficient of static friction between the blocks is 0.50. The block at the top is pulled with a varying horizontal force FF.

    PH0441-1

    1. Calculate the magnitude of the maximum force FmaxF_{max} which results in both of the blocks moving together without slipping. [3]

    2. On the graph, sketch how the force of static friction FfF_f acting on the bottom block varies with the force FF. [2]

      (no need to add values on the axis)

      PH0441

      FmaxF_{max} is your answer to (b)(i) and draw your graph up to FmaxF_{max}

    3. According to Newton's Third Law, there must be another force paired with the weight of the top block. Describe this force. [2]

  3. On another occasion, the blocks are moved with the help of a force of 12N12\,N acting on the block at the top. The drag force DD on the blocks is given by D=2.5×102v2D=2.5 \times 10^{-2}\,v^2 where vv is the speed of the blocks. Calculate the top speed of the blocks for this force. [2]

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Question 132

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A 74 kg boy starts to ride a 6.0 kg bicycle from rest. The graph shows how the acceleration aa of the bicycle varies with the distance travelled xx.

PH0039

What is the total work done by the boy?

  • A. \hspace{1em} 0.3 kJ

  • B. \hspace{1em} 3.7 kJ

  • C. \hspace{1em} 4.0 kJ

  • D. \hspace{1em} 6.0 kJ

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Question 133

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An object of mass 1.0kg1.0 \, kg rests on a rough surface. Another object of mass 2.0kg2.0\, kg is connected to it with a string.

PH0572a

When the objects are released, the masses accelerate at g2\dfrac{g}{2}. The work done by the tension of the string on the 1.0kg1.0\, kg mass is 40J40\,J. Which of the following is correct for the 1.0kg1.0 \,kg mass during this period?


Magnitude of the force of friction /NDistance travelled
\hspace{1.5em}A.\hspace{1.5em}104.0m4.0\, m
\hspace{1.5em}B.\hspace{1.5em}54.0m4.0\, m
\hspace{1.5em}C.\hspace{1.5em}102.0m2.0\, m
\hspace{1.5em}D.\hspace{1.5em}52.0m2.0\, m

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Question 134

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A train, initially at rest, accelerates steadily at 1.0 ms21.0\ m\, s^{-2}. The distance travelled during each successive second, for the first five seconds of its motion, was recorded in meters. Which of the following correctly represents the distance covered in each successive second?

(Diagram is not to scale)


\hspace{1.5em}A.\hspace{3.5em}PH0265A
\hspace{1.5em}B.\hspace{3.5em}PH0265B
\hspace{1.5em}C.\hspace{3.5em}PH0265C
\hspace{1.5em}D.\hspace{3.5em}PH0265D

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Question 135

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A piece of metal of weight WW is suspended by two identical strings. Each string passes through a pulley and is attached to a block of mass mm. The system is in equilibrium

PH0329Q [Created with Chemix (https://chemix.org)]\footnotesize{\textrm{[Created with Chemix (https://chemix.org)]}}

What must be true for mm such that the two strings attached to the piece of metal are almost horizontal?

  • A. \hspace{1em} m<Wgm < \frac{W}{g}

  • B. \hspace{1em} W2g<m<Wg\frac{W}{2g} < m < \frac{W}{g}

  • C. \hspace{1em} m>Wgm > \frac{W}{g}

  • D. \hspace{1em} m<W2gm < \frac{W}{2g}

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Question 136

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A mass of mm kgkg is hung on the end of the spring. When the system is in equilibrium, the elastic potential energy stored in the spring is EE.

A downward force is then applied to the system causing the total elastic potential energy stored to double. This is shown in the diagram below.

933o [© Revision Village 2022. Created with https://chemix.org/]

The downward force is then removed, and the system oscillates about the equilibrium position.

What is the magnitude of the downward force and the kinetic energy of the mass as it passes the equilibrium position?

You may assume friction and air resistance are negligible.


Magnitude of downward forceKinetic energy of mass as it passes equilibrium
\hspace{1.5em}A.\hspace{1.5em}(2\sqrt {2} - 1)mgmgEE
\hspace{1.5em}B.\hspace{1.5em}(2\sqrt {2} - 1)mgmg(3 - 2 2)E\sqrt {2}) E
\hspace{1.5em}C.\hspace{1.5em}2mg\sqrt {2}\,mgEE
\hspace{1.5em}D.\hspace{1.5em}2mg\sqrt {2}\,mg(3 - 2 2)E\sqrt {2}) E

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