2.2 - Forces

Consider the weight, $W$, of a skydiver falling through air with a drag force $F_{drag}$

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.
		$\hspace{1cm}$
$\hspace{1cm}$
C.			D.

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.

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

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

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

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

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

A ball of mass $m$ is falling vertically through the air. The drag force acting on the ball is given by $kv^2$ where $k$ is constant and $v$ is the speed of the ball. What is the maximum speed reached by the ball?

• A. $\hspace{1em} \dfrac{k}{mg}$

• B. $\hspace{1em} \dfrac{mg}{k}$

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

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

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

Which graph shows the variation of the resultant force $R$ acting on the ball with the height $h$ of the object?

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

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

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

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

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

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

A brick of weight $100\, N$ 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.

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

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

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

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

The diagram below shows a person of mass 80 $kg$ standing in an elevator of mass 800 $kg$. The elevator accelerates upwards at a rate of 1.2 $m\,s{^{-2}}$.

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

• A. $\hspace{1em}$ 96 $N$

• B. $\hspace{1em}$ 690 $N$

• C. $\hspace{1em}$ 780 $N$

• D. $\hspace{1em}$ 880 $N$

An object of mass $m$ rests on a rough surface. Another object of mass $M$ is connected to it with a rope.

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

Which of the following correctly describes the Newton's 3rd Law force paired with $F_2$?

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

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

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

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

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 $\dfrac{g}{4}$.

Which of the following gives the reading of the balance?

• A. $\hspace{1em} \dfrac{5Mg}{4}$

• B. $\hspace{1em} Mg$

• C. $\hspace{1em} \dfrac{3Mg}{4}$

• D. $\hspace{1em} \dfrac{Mg}{2}$

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

• A. $\hspace{1em} 4\,W$

• B. $\hspace{1em} 3\,W$

• C. $\hspace{1em}$ $\sqrt{10} \,W$

• D. $\hspace{1em}$ $\sqrt{8} \,W$

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

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

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

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

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

• A. $\hspace{1em}$ $sin^{-1}(0.4)$

• B. $\hspace{1em}$ $tan^{-1}(0.4)$

• C. $\hspace{1em}$ $cos^{-1}(0.4)$

• D. $\hspace{1em}$ $tan^{-1}(0.6)$

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

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

A point $P$ is subjected to three simultaneous forces of magnitudes $F_A > F_B > F_C$. Point $P$ is in equilibrium. Which of the following statements is not always true about the magnitudes of the forces?

• I.	$F_A = F_B + F_C$
  II.	$F_A \leq F_B + F_C$
  III.	$F_A > F_B - F_C$

• 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

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.

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

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

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

• A. $\hspace{1em}$ $\dfrac{gM}{M+m}$

• B. $\hspace{1em}$ $\dfrac{gm}{M+m}$

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

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

[Maximum mark: 9]

Two blocks of masses 3.0 $kg$ and 4.0 $kg$ are held stationary with a thread connecting the blocks. The mass of 3.0 $kg$ 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 $kg$.

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 $kg$ slides down. Show that the acceleration of the mass of 3.0 $kg$ is around 1.5 $m\,s^{-2}$. The coefficient of dynamic friction between 3.0 $kg$ mass and the rough surface is 0.40. [2]
   

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

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

Which expression gives the acceleration of the block?

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

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

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

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

[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.

1. Draw and label the free-body diagram for the cylinder $M_3$ [2]
   

   

2. 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 $M_3$ is $30 \,N$. Show that the mass of each cylinder is around 1.0 kg. [2]
      

3. Determine the force that mass $M_3$ exerts on $M_1$ [2]
   

Block $A$ of mass $m_A=3.0\,kg$ rests above the flat horizontal surface of block $B$ of mass $m_B=6.0\,kg$, which in turn rests on a smooth horizontal surface as shown.

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

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

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

• A. $\hspace{1em} 0.2gt$

• B. $\hspace{1em} 0.4gt$

• C. $\hspace{1em} gt$

• D. $\hspace{1em} 2.5gt$

Three identical masses are connected as shown with a string that passes over an ideal pulley. The tension in the string connecting $m_1$ and $m_2$ is $T_1$. The tension of the string attached to $m_3$ is $T_2$.

The acceleration of the $m_3$ is $\dfrac{g}{4}$.

Which of the following is correct for $T_2$ and the acceleration of $m_1$?

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

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

• A. $\hspace{1em} 1\,kg$

• B. $\hspace{1em} 2\,kg$

• C. $\hspace{1em} 3\,kg$

• D. $\hspace{1em} 4\,kg$

[Maximum mark: 12]

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

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

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

   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]
      

      

   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]
      

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

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

• A. $\hspace{1em} 0.1g\,$

• B. $\hspace{1em} 0.5g\,$

• C. $\hspace{1em} g\,$

• D. $\hspace{1em} 5g\,$

[Maximum mark: 11]

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

2. A block of mass 2.0 $kg$ is placed on another block of mass 5.0 $kg$. 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 $F$.

   

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

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

      (no need to add values on the axis)

      

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

   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 $12\,N$ acting on the block at the top. The drag force $D$ on the blocks is given by $D=2.5 \times 10^{-2}\,v^2$ where $v$ is the speed of the blocks. Calculate the top speed of the blocks for this force. [2]
   

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

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

• A. $\hspace{1em}$ $m < \frac{W}{g}$

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

• C. $\hspace{1em}$ $m > \frac{W}{g}$

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