Subjects

IB Physics SL - 2024 - Questionbank

2.4 - Momentum & Impulse

Momentum, Impulse, Force-Time Graphs, Conservation of Momentum, Elastic and Inelastic Collisions

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Question 1

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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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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 3

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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 4

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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 5

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[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 6

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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 7

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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 8

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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 9

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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 10

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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 11

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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 12

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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 13

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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 14

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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 15

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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 16

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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 17

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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 18

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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 19

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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 20

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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 21

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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 22

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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 23

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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 24

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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 25

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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 26

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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 27

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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 28

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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 29

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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 30

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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 31

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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 32

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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 33

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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 34

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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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