Free Printable MCQ Unit IV: System of Particles and Linear Momentum

1.

A ball of mass $m$ is dropped from rest from a height $h$ and collides elastically with the floor, rebounding to its original height. What is the magnitude of the average force applied by the floor on the ball during the time the ball is in contact with the floor?

a)

$zero$

b)

$mg$

c)

$2mg$

d)

$4mg$

e)

It cannot be determined without knowing the length of time that the ball is in contact with the floor.

2.

A block of mass $m$ is pulled by a rope along a horizontal surface with negligible friction. For time $t>0$ , the magnitude of the acceleration of the object as a function of time is given by the equation $a=Ae^{-kt}$ , where $A$ and $k$ are positive constants. Which of the following expressions determines the impulse exerted on the block by the rope during the time interval $0<t<t1$ ?

a)

$A\int_0^{t_1}e^{-kt}dt$

b)

$mA\ \frac{d}{dt}\left[e^{-kt}\right]_{t_1}$

c)

$A\ \frac{d}{dt}\left[e^{-kt}\right]_{t_1}$

d)

$mAt_1\left[e^{-kt}\right]$

e)

$mA\int_0^{t_1}e^{-kt}dt$

3.

Cart $A$ is traveling east when it collides with cart $B$ , which is traveling north. Cart $A$ has a mass of 3.05 kg, and cart $B$ has a mass of 2.10 kg. The two carts travel together as a single object on a horizontal surface at an angle $θ$ relative to due east, as shown above.

In one trial, the initial speed of cart A is 2.5 m/s and the initial speed of cart $B$ is 1.5 m/s. The angle $θ$ relative to east that the carts travel after the collision is most nearly

a)

$22^o$

b)

$36^o$

c)

$45^o$

d)

$54^o$

e)

$62^o$

4.

Three identical spheres are thrown from the same height above the ground. Sphere X is thrown vertically up, sphere Y is thrown horizontally, and sphere Z is thrown vertically down, as shown in figures 1, 2, and 3 above, respectively. All three spheres are thrown with the same speed. Air resistance is negligible.

Assume the spheres collide elastically with the ground. Which of the following ranks the spheres based on the rebound height after they collide with the ground?

a)

X>Y>Z

b)

Y > (X = Z)

c)

Z > Y > X

d)

( X = Z) > Y

e)

(X = Z) > Y

5.

Particle A and particle B, each of mass M, move along the x-axis exerting a force on each other. The potential energy of the system of two particles associated with the force is given by the equation $U=\frac{β}{r^2}$ , where r is the distance between the two particles and $β$ is a positive constant. At time t = 0, particle A is located at x = 2D with an initial speed of $v_o$ to the left, and particle B is at rest at the origin, as shown in the figure above.

At time $t=T_1$ , particle A is observed to be traveling with speed $\frac{2v_o}{3}$ to the left. The speed and direction of motion of particle B is

a)

$\frac{2v_o}{3}\ to\ the\ left$

b)

$\frac{v_o}{3}\ to\ the\ left$

c)

$\frac{v_o}{3}\ to\ the\ right$

d)

$\frac{2v_o}{3}\ to\ the\ right$

e)

$\frac{5v_o}{3}\ to\ the\ left$

6.

Particle A and particle B, each of mass M, move along the x-axis exerting a force on each other. The potential energy of the system of two particles associated with the force is given by the equation U = β / r ² , where r is the distance between the two particles and β is a positive constant. At time t = 0, particle A is located at x = 2D with an initial speed of v0 to the left, and particle B is at rest at the origin, as shown in the figure above.

Which of the following equations could be used to find r_MIN, the minimum distance between the masses as particle A approaches particle B?

a)

$\frac{\beta}{4D^2}\ +\ Mv_0^2\ =\ \frac{\beta}{r_{MIN}^2}\ +\ M\left(\frac{v_o}{2}\right)^2$

b)

$\frac{\beta}{4D^2}\ +\ \frac{1}{2}Mv_0^2\ =\ \frac{\beta}{r_{MIN}^2}\ +\ M\left(\frac{v_o}{2}\right)^2$

c)

$\frac{\beta}{4D^2}\ +\ \frac{1}{2}Mv_0^2\ =\ \frac{\beta}{r_{MIN}^2}\ +\ \frac{1}{2}Mv_o^2$

d)

$\frac{\beta}{4D^2}\ +\ \frac{1}{2}Mv_0^2\ =\ \frac{\beta}{r_{MIN}^2}\$

e)

$\frac{\beta}{4D^2}\ +\ Mv_0^2\ =\ \frac{\beta}{r_{MIN}^2}\$

7.

A ball of mass m and velocity v contacts a hard surface at a 45° angle and bounces off the surface also at a 45° angle and at speed v, as shown in situation 1. Also shown is the force vector F representing the force exerted by the surface on the ball. Situation 2 shows the same ball moving with the same velocity and contacts a soft surface. The time of contact is greater with the soft surface than the hard surface. The ball bounces off the soft surface at an angle of 30° and with speed v₂<v. Which of the following vectors could represent the force exerted on the ball in situation 2.

a)

b)

c)

d)

e)

8.

Identical blocks 1 and 2 slide on a horizontal surface toward a stationary barrier. At time t = 0, block 1 collides with the barrier and slides backward. The blocks collide at time t = Δt. Assuming friction between the blocks and the horizontal surface to be negligible, which of the following statements is true about the two blocks?

a)

If the collision between block 1 and the wall is elastic, and the two blocks have an elastic collision, then the sum of the kinetic energy of blocks 1 and 2 before block 1 makes contact with the wall will be equal to the sum of the kinetic energy of blocks 1 and 2 after the collision between the blocks.

b)

If the collision between block 1 and the wall is elastic, and the two blocks have an inelastic collision, then the sum of the kinetic energy of blocks 1 and 2 before block 1 makes contact with the wall will be equal to the sum of the kinetic energy of blocks 1 and 2 after the collision between the blocks.

c)

If the collision between block 1 and the wall is not elastic, and the two blocks have an inelastic collision, then the sum of the kinetic energy of blocks 1 and 2 before block 1 makes contact with the wall will be less than the sum of the kinetic energy of blocks 1 and 2 after the collision between the block

d)

If the collision between block 1 and the wall is not elastic, and the two blocks have an inelastic collision, then the momentum of block 1 before it makes contact with the wall will be equal to the sum of the momenta of the two blocks after the collision between the blocks.

e)

If the collision between block 1 and the wall is not elastic, and the two blocks have an inelastic collision, then the momentum of block 1 before it makes contact with the wall will be equal to the sum of the momenta of the two blocks after the collision between the blocks.

9.

Three objects of mass m, 2m, and 3m are at positions (0,0), (2,3), and (4,0), respectively, as shown above. The center of mass is located at position

a)

(8/3,1)

b)

(1,8/3)

c)

(16,6)

d)

(8,2)

e)

(1,1/2)

10.

A person of mass 3M is standing on the left edge of a long, uniform board of mass M and length L that is floating in water, as shown in the figure above. The person walks slowly to the right edge of the board. The water exerts no drag forces on the board. The position of the center of mass of the board when the person is at the right edge of the board is

a)

5L/4

b)

3L/4

c)

L/4

d)

0

e)

−L/4

11.

Two small spheres are at rest on the x-axis of the coordinate system shown above. Sphere A of mass $m_1$ is located at position $x=d_1$ . Sphere B of mass $m_2$ , where $m_1≠m_2$ , is a distance $d_2$ to the right of sphere A. Which of the following is a correct expression for the location of the center of mass for the two-sphere system?

a)

$\frac{m_2d_2}{m_1+m_2}$

b)

$d_1\ +\ \frac{m_1d_2}{m_1+m_2}$

c)

$d_2\ +\ \frac{m_1d_1}{m_1+m_2}$

d)

$\frac{m_1d_1\ +\ m_2d_2}{m_1+m_2}$

e)

$d_1\ +\ \frac{m_2d_2}{m_1+m_2}$

12.

The net force F acting on an object that moves along a straight line is given as a function of time t by F(t)=κt²+ τ, where κ = 1 N/s² and τ = 1 N. What is the change in momentum of the object from t = 0 s to t = 3 s?

a)

6 kg⋅m/s

b)

10 kg⋅m/s

c)

12 kg⋅m/s

d)

30 kg⋅m/s

e)

It cannot be determined without knowing the initial momentum of the object.

13.

For an impulse-momentum experiment, students collect data on a collision between blocks A and B. A force probe attached to block A is used to measure the force exerted by block A on block B as a function of time during the collision. The data collected shows a positive force that is used to determine the impulse on block B. The force sensor is removed from block A and attached to block B, and the experiment is run again. Which of the following correctly describes how this affects the data and if the impulse on block B can still be determined?

a)

The data can only be used to determine the impulse on block A, not block B .

b)

The data can only be used to determine the impulse on block B, not block A.

c)

The data cannot be used to determine the impulse on block A or block B.

d)

The data can be used to determine the impulse on block B and block A.

e)

The data can be used to determine the force on block B.

14.

A large truck of mass 4M is traveling at a speed of V when it collides with a small car of mass M that is at rest. The truck and car stick together after the collision.

The speed of the center of mass of the truck-car system as the truck and car move off together is

a)

$\frac{1}{5}V$

b)

$\frac{4}{5}V$

c)

$V$

d)

$\frac{5}{4}V$

e)

$5V$

15.

A large truck of mass 4M is traveling at a speed of V when it collides with a small car of mass M that is at rest. The truck and car stick together after the collision.

During the collision, the car and truck exert forces on each other. Which of the following is a correct statement about these forces and gives evidence to support this statement?

a)

The forces the truck and car exert on each other must be external to the truck-car system because the momentum of the truck changes.

b)

The forces the truck and car exert on each other must be external to the truck-car system because the momentum of the car changes.

c)

The forces the truck and car exert on each other must be external to the truck-car system because the momentum of both the truck and car change.

d)

The forces the truck and car exert on each other must be internal to the truck-car system because the momentum of the center of mass of the truck-car system stays the same.

e)

The forces the truck and car exert on each other must be internal to the truck-car system because the momentum of the center of mass of the truck-car system changes.

16.

A large truck of mass 4M is traveling at a speed of V when it collides with a small car of mass M that is at rest. The truck and car stick together after the collision.

When the truck and car stuck together after the collision, the speed of the center of mass of the truck-car system is $V_f$ . If the truck and car have an elastic collision, the speed of the center of mass of the truck-car system is $V_{f2}$ . Which of the following expressions for $V_{f2}$ must be true?

a)

$v_{f2}>2v_f$

b)

$v_f<v_{f2}<2v_f$

c)

$v_{f2}=v_f$

d)

$\frac{1}{2}v_f<v_{f2}<v_f$

e)

$v_{f2}<\frac{1}{2}v_f$

17.

In an experiment, students use motion sensors to measure the speed of objects 1 and 2, of masses $m_1$ and $m_2$ , respectively, that collide head-on while moving along a smooth horizontal surface. Consider velocity to the right to be positive. All motion is along a straight line. The speeds of object 1 are $v_{1i}$ before the collision and $v_{1f}$ after the collision. The speeds of object 2 are $v_{2i}$ before the collision and $v_{2f}$ after the collision. Before the collisions, object 1 is moving to the right and and object 2 is moving to the left. Both objects reverse their direction of motion during the collision, as shown.

Which of the following expressions can be used to determine the magnitude of the impulse on object 1 ?

a)

$m_2(v_{2f}−v_{2i})$

b)

$m_1(v_{2f}−v_{2i})$

c)

$m_2(v_{1f}−v_{1i})$

d)

$\frac{2m_1v_{1i}}{\left(m_1+m_2\right)}$

e)

$\frac{\left(m_1-m_2\right)v_{1f}}{\left(m_1+m_2\right)}$

18.

In an experiment, students use motion sensors to measure the speed of objects 1 and 2, of masses m₁ and m₂, respectively, that collide head-on while moving along a smooth horizontal surface. Consider velocity to the right to be positive. All motion is along a straight line. The speeds of object 1 are v_1i before the collision and v_1f after the collision. The speeds of object 2 are v_2i before the collision and v_2f after the collision. Before the collisions, object 1 is moving to the right and and object 2 is moving to the left. Both objects reverse their direction of motion during the collision, as shown.

After analyzing the data, a student noticed that the motion sensor measuring the velocity of object 2 was not facing directly along the line of motion of object 2, but was angled slightly. How would this affect the data collected by the students?

a)

The actual speeds of object 2 are smaller in magnitude both before and after the collision.

b)

The actual speeds of object 2 are larger in magnitude both before and after the collision.

c)

There is no effect on the data

d)

The actual speeds of object 2 are smaller in magnitude before and larger in magnitude after the collision.

e)

The actual speeds of object 2 are larger in magnitude before and smaller in magnitude after the collision.

19.

Data were collected during an experiment that used two identical cars, car 1 and car 2, moving along a one-dimensional track. Car 1 moved toward and collided with stationary car 2, and data were collected. The data collected just before and just after the collision are shown below. (All velocities are represented in m/s .)

What conclusion can be made about the data taken in this experiment?

a)

Car 1 was more massive than car 2.

b)

Car 2 was more massive than car 1.

c)

The velocity measurements for car 1 were lower than the car’s actual speed.

d)

The velocity measurements for car 2 were higher than the car’s actual speed.

e)

The experiment was performed without error.

20.

A 0.5⁢ kg rubber ball initially moves with a speed of 10 m/s in the +x direction toward a stationary wall, as shown above. The ball bounces back off of the wall with a speed of 5 m/s in the −x direction. Which of the following best represents the rate of change of the ball’s momentum dp/dt as a function of time?

a)

b)

c)

d)

e)

21.

Cart A of mass 2 m is moving with velocity v to the right on a horizontal frictionless track, as shown above, when it collides with cart B of mass m. Cart B is initially at rest, and the collision is perfectly elastic. Which of the following best describes the motion of the carts immediately after the collision?

a)

Cart A is moving to the left, and cart B is moving to the right

b)

Cart A is moving to the left, and cart B remains stationary

c)

Cart A is stationary, and cart B is moving to the right.

d)

Both carts move to the right, and they are stuck together.

e)

Both carts move to the right, but they are not stuck together.

22.

Two carts of equal mass are on a horizontal surface with negligible friction. Cart A is approaching cart B, which is at rest, as shown in Figure 1 above. Attached to cart B is a spring that is initially compressed. At the moment cart A collides with cart B, the spring is released and pushes on cart A, as shown in Figure 2 above. Which of the following correctly states what happens to the kinetic energy and the momentum of the two-cart system as a result of the collision compared to those quantities before the collision?

a)

Kinetic energy: Increases; Magnitude of Momentum: Decreases

b)

Kinetic energy: Increases; Magnitude of Momentum: Stays the same

c)

Kinetic energy: Increases; Magnitude of Momentum: Increases

d)

Kinetic energy: Stays the same; Magnitude of Momentum: Decreases

e)

Kinetic energy: Stays the same; Magnitude of Momentum: Stays the same

23.

A firecracker of mass 2m is moving at a speed v in the positive x-direction. It explodes and breaks up into two identical fragments, each of mass m. After the explosion, one fragment moves at the same speed v but in the negative x-direction. The speed of the second fragment must be

a)

v

b)

2v

c)

3v

d)

4v

e)

5v

24.

A space shuttle has a mass of 90,000⁢ kg. In order to stay in a circular orbit, it must have a velocity of 8000m/s. The pilot discovers that the shuttle has slowed down to 7900m/s and the shuttle’s speed needs to increase. If the thrusters exert a constant force of 50,000N, how long do the thrusters have to exert this force in order to return the shuttle to orbital velocity?

a)

30 s

b)

60 s

c)

120 s

d)

180 s

e)

240 s

25.

In an experiment, students use a force sensor to apply a force of magnitude F to an object of mass m

m that is initially at rest. The force is exerted in the +x-direction for a time t = T. The impulse exerted on the device is J. Which of following procedure changes would result in an impulse 2 J being exerted on an object?

a)

Exert a force of magnitude F/2 on an object of mass m for a time t = T.

b)

Exert a force of magnitude F/2 on an object of mass 2m for a time t = 2T.

c)

Exert a force of magnitude F on an object of mass 2m for a time t = 2T.

d)

Exert a force of magnitude 2F on an object of mass m for a time t = 2T.

e)

Exert a force of magnitude 2F on an object of mass m for a time t = T/2.

26.

In an experiment to study collisions, block A with of mass m₁ is moving speed v₀ when it collides with block B of mass m₂ which is initially at rest. After the collision, the blocks stick together and move off with speed v_f. For a series of collisions, block A is given different initial velocities. The graph of v_f as a function of v₀ is shown. How would doubling mass m₁ change the graph?

Link for the graph is: https://assets.learnosity.com/organisations/537/VH911053.g02.png

a)

The slope of the graph line would be less.

b)

The slope of the graph line would be greater.

c)

The graph line would no longer be linear.

d)

There would be no effect on the graph.

e)

The change cannot be determined without knowing the ratio of m₁/m₂

27.

The magnitude of a force as a function of time can be represented by $F(t)=Rt^2−St+Z$ .

The direction of the force does not change. If the force is exerted on an object of mass M, the change in velocity of the object between t = 0 and t = T seconds is

a)

$2RT-S$

b)

$\frac{2RT}{M}-\ \frac{S}{M}$

c)

$\frac{1}{3}RT^3-\frac{1}{2}\ ST^2\ +\ ZT$

d)

$\frac{1}{3}\ \frac{RT^3}{M}-\frac{1}{2}\ \frac{ST^2}{M}\ +\ \frac{ZT}{M}$

e)

$\frac{RT^2}{M}-\frac{ST^{ }}{M}\ +\ \frac{Z}{M}$

28.

Object A has a mass of M and is moving in the +x direction. It collides with object B , which has a mass of 2M and is initially at rest. After the collision, object B has a final velocity of v in the +x direction. Which of the following best describes the impulse object B exerts on object A during the collision

a)

-2Mv

b)

-Mv

c)

0

d)

+Mv

e)

+2Mv

29.

A ball of mass m is dropped from rest at a height h and collides elastically with the floor, rebounding to its original height. What is the magnitude of the net impulse on the ball during the collision with the floor?

a)

$zero$

b)

$m\sqrt{gh}$

c)

$m\sqrt{2gh}$

d)

$m\sqrt{4gh}$

e)

$m\sqrt{8gh}$

30.

Suppose you wish to qualitatively test the validity of the impulse-momentum theorem by rolling various balls along a table toward a wood block. When each ball reaches the block, it pushes the wood block forward, and the ball bounces backward, away from the block. Which of the following describes the best procedure for the experiment and a correct interpretation of possible results?

a)

Use balls of the same mass and with the same initial speed but with different amounts of elasticity and repeat this procedure for each ball. If balls that rebound with less speed cause greater movement of the block, this is consistent with the prediction of the theorem.

b)

Use balls of different masses but with the same amount of elasticity and the same initial speed and repeat this procedure for each ball. If smaller-mass balls cause more movement of the block, this is consistent with the prediction of the theorem.

c)

Use identical balls with the same initial speed but blocks of different masses and repeat this procedure for each block. If the ball rebounds with more speed when it pushes a large block than when it pushes a smaller block, this is consistent with the prediction of the theorem.

d)

Use balls with different masses but with the same amount of elasticity and same initial speed and repeat this procedure for each ball. If the balls that rebound with more speed cause less movement of the block, this is consistent with the prediction of the theorem.

e)

Use balls of the same mass and with the same amount of elasticity but roll them toward the block at different speeds and repeat this procedure for each speed. If the balls traveling at higher speed cause less movement of the block, this is consistent with the prediction of the theorem.

31.

In an experiment, block 1 is given an initial speed v₀ toward block 2, which is initially at rest. The blocks are on a track that has a motion detector set up, as shown above. When the two blocks collide, there is a completely inelastic collision and the blocks move together with speed v_f. The blocks were both placed on a balance, and it is determined that they have the same mass.

The experiment is repeated for four different initial speeds, and the data are shown in the chart below. It appears that the resulting data are not accurate. Which measurement most likely produced errors in the data seen in the chart below?

V₀ (m/s) 1 2 3 4

v_f (m/s) 0.42 0.85 1.33 1.70

a)

The mass of block 1 is accurate, but the mass of block 2 is actually less massive than recorded.

b)

Both mass values are accurate, but v₀ is actually larger than recorded.

c)

The motion sensor was positioned too close to block 1

d)

The final velocity recorded was taken too long after the collision.

e)

The data recorded is accurate within acceptable experimental error.

32.

Object A of mass M is moving east at speed v. It collides with object B of mass 2M that was initially at rest. The motion of the objects before and after the collision is along the same line. After the collision, object A is moving west at a speed of v/3. What is the speed of object B immediately after the collision?

a)

v/3

b)

v/2

c)

2v/3

d)

v

e)

2v

33.

A student drops a bag of mass m onto a cart of mass M that is sliding with speed v₀ along a horizontal track with negligible friction. Immediately after the bag lands in the cart, the cart-bag system moves with speed v_f. Which of the following statements correctly relates the two speeds and gives a correct reason for this relationship?

a)

v_f<v₀, because some of the cart-bag system’s mechanical energy is dissipated.

b)

v_f<v₀, because the kinetic energy of the bag decreases.

c)

v_f>v₀, because the kinetic energy of the bag decreases.

d)

v_f>v₀, because the linear momentum of the bag is added to the linear momentum of the cart.

e)

v_f=v₀, because the bag is moving perpendicular to the cart.

34.

In the diagram above, a block of mass M is initially at rest on a horizontal surface at the base of an inclined plane. The surface and plane have negligible friction. The block is struck by a projectile of mass m traveling with a horizontal velocity v_i. The projectile becomes embedded in the block, and they move together to the right with speed v_f.

Which of the following is a correct expression for v_f ?

a)

$\sqrt{gh}$

b)

$\sqrt{v_i^2\ +\ 2gh}$

c)

$\frac{m}{\left(m+M\right)}v_i$

d)

$\frac{m}{M}v_i$

e)

$\frac{M}{m}v_i$

35.

An arrow of mass m and speed v₀ strikes and sticks to one end of a meterstick of mass M as shown in the diagram above. The meterstick is initially at rest on a horizontal surface and free to move without friction. The speed of the center of mass of the stick-arrow system after the arrow strikes is given by which of the following expressions?

a)

$\frac{1}{2}\left(M+m\right)v_0^2$

b)

$\frac{mv_0}{M}$

c)

$\frac{mv_0}{M+m}$

d)

$\frac{v_0}{2}$

e)

$0$

36.

Two blocks of masses M and 2M are on a frictionless horizontal surface, as shown above, and are held in place with a compressed spring of negligible mass between them. If the blocks are then released and the block of mass 2M leaves the spring with a velocity v, the velocity of the center of mass of the blocks is

a)

$zero$

b)

$-\frac{v}{2}$

c)

$-\frac{2v}{3}$

d)

$-\frac{3v}{2}$

e)

$-2v$

37.

The graph above shows a variable force F that acts on an object as it moves along a straight line as a function of time t. What is the change in momentum of the object from t = 2 s to t = 4 s ?

a)

1 kg•m/s

b)

2 kg•m/s

c)

4 kg•m/s

d)

6 kg•m/s

e)

8 kg•m/s

38.

A 300 g cart with a force sensor attached starts at rest on a track. The force sensor exerts a force on the cart to speed it up. The graph above shows the force F exerted by the sensor on the cart as a function of time t. The change in the cart’s momentum during the time interval shown is most nearly

a)

4.0 N • s

b)

8.5 N • s

c)

13 N • s

d)

25 N • s

e)

30 N • s

39.

The uniform rod of length L shown above is supported by holding end X so that the rod makes an angle 60° with the horizontal floor. There is no friction acting between the rod and the floor. When the support at X is removed, the rod falls under the influence of gravity. Which of the following best describes the movement of end Y as the rod falls?

a)

It moves $\frac{1}{2}L$ to the left.

b)

It remains at rest.

c)

It moves $\frac{1}{4}L$ to the right.

d)

It moves $\frac{1}{2}L$ to the right.

e)

It moves $\frac{3}{4}L$ to the right.

40.

Blocks A, B, and C are aligned along a straight line on a horizontal frictionless surface. The masses of the blocks are M, 2M, and 3M, respectively. Block A is initially moving to the right along the same line at a speed v, as shown in the figure above. Blocks B and C are initially at rest. Block A collides with and sticks to block B. The two blocks then collide with and stick to block C. What is the speed of block C after the collisions?

a)

0

b)

v/6

c)

v/3

d)

v/2

e)

6v

41.

The force F exerted on a ball during a collision with a wall is given as a function of time t by the equation , w $F(t)=αt-βt^2$ here $α=400\ \frac{N}{s}$ and $β=4000\ \frac{N}{s^2}$ . The ball first contacts the wall at t = 0, and the collision lasts for 0.10 s. What is the magnitude of the change in momentum of the ball?

a)

0

b)

0.67 kg•m/s

c)

3.33 kg•m/s

d)

3.60 kg•m/s

e)

The change in momentum of the ball cannot be determined without knowing the mass of the ball.

42.

Two balls, A and B, have the same mass and diameter but are made from different types of rubber. The balls are dropped from the same height above the floor. After colliding with the floor, ball A bounces higher than ball B bounces. Which of the following quantities must necessarily be larger for ball A than for ball B?

a)

The average force exerted by the floor

b)

The amount of time in contact with the floor

c)

The impulse exerted by the floor

d)

The momentum just before colliding with the floor

e)

The kinetic energy just before colliding with the floor

43.

Object X of mass m is moving to the right with a speed of 3 m/s when it collides with object Y of mass m that is moving to the right with a speed of 2 m/s, as shown above. After the collision, X is moving to the right with a speed of 2 m/s and Y is moving to the right with a speed of 3 m/s. Which of the following is true of the collision?

a)

It is elastic because momentum is conserved.

b)

It is elastic because kinetic energy is conserved.

c)

It is inelastic because momentum is not conserved.

d)

It is inelastic because kinetic energy is not conserved.

e)

More information is needed to determine whether the collision is elastic or inelastic.

44.

Two spheres of uniform density are located a distance L apart, as shown in the figure below. The left sphere has a mass $M_1$ , and the right sphere has a mass $M_2$ . The center of mass of the two spheres is labeled point P. Which of the following is a correct expression for the distance from point P to the center of the left sphere?

a)

$\frac{M_1}{M_2}L$

b)

$\frac{\left(M_1+M_2\right)}{M_1}L$

c)

$\frac{\left(M_1+M_2\right)}{M_2}L$

d)

$\frac{M_2}{\left(M_1+M_2\right)}L$

e)

$\frac{M_1}{\left(M_1+M_2\right)}L$

45.

The graph of velocity as a function of time shown above is for a 10 kg box moving along the x-axis. Based on the graph, which of the following is a true statement?

a)

The linear momentum of the box is constant over the entire time frame.

b)

The linear momentum of the box is only constant between 2 and 5 seconds.

c)

The linear momentum of the box is constant between 0

and 2 seconds.

d)

The maximum linear momentum of the box is 7 kg⋅m/s

e)

The minimum linear momentum of the box is 40 kg⋅m/s

46.

A 0.060 kg tennis ball moving at 15 m/s strikes a tennis racket and rebounds at 10 m/s in the opposite direction, as shown above. The ball is in contact with the racket for 0.030 s.

What is the magnitude of the average force exerted by the racket on the ball?

a)

5 N

b)

10 N

c)

20 N

d)

25 N

e)

50 N

47.

A block on a level horizontal surface of negligible friction is initially traveling at 20 m/s to the left. A horizontal force F is exerted to the right on the block for the time interval 0 < t < 0.10 s. The magnitude of the force is given as a function of time t by the equation F = αt , where α = 240 N/s and t is in seconds.

What is the magnitude of the change in momentum of the block due to the horizontal force?

a)

1.2 kg • m/s

b)

12 kg • m/s

c)

24 kg • m/s

d)

240 kg • m/s

e)

The change in momentum of the block cannot be determined without knowing the block’s mass.

48.

In order to model the motion of an extinct ape, scientists measure its hand and arm bones. From shoulder to wrist, the arm bones are 0.60 m long and their mass is 4.0 kg. From wrist to the tip of the fingers, the hand bones are 0.10 m long and their mass is 1.0 kg. In the model above, each bone is assumed to have a uniform density.

When the arm and hand hang straight down, the distance from the shoulder to the center of mass of the arm-hand system is most nearly

a)

0.25 m

b)

0.35 m

c)

0.37 m

d)

0.50 m

e)

0.93 m

MCQ Unit IV: System of Particles and Linear Momentum

Total questions: 48

Worksheet time: 2hrs 36mins

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