Momentum and Collisions Practice Test

1.

What is the correct definition of momentum?

a) The force applied to an object multiplied by the time b) The product of an object’s mass and its velocity c) The energy an object has due to its motion d) The acceleration of an object times its mass

2.

If a 3 kg object is moving at 4 m/s, what is its momentum?

a) 12 N b) 7 m/s c) 1.33 m/s d) 12 kg·m/s

3.

What does the impulse-momentum theorem state?

a) Momentum is conserved in all types of collisions b) The net impulse on an object is equal to its change in momentum c) Impulse is the rate of change of acceleration d) An object in motion remains in motion unless acted upon by an impulse

4.

A force of 10 N is applied to a 2 kg object for 3 seconds. What is the impulse delivered to the object?

a) 30 kg·m/s b) 6.67 m/s c) 5 N d) 60 kg·m/s

5.

Which principle allows momentum to be conserved in an isolated system?

a) Newton’s third law b) The work-energy theorem c) The law of universal gravitation d) The conservation of momentum

6.

When a gun fires a bullet, the gun recoils backward. What principle explains this recoil?

a) Energy conservation b) Impulse-momentum theorem c) Conservation of momentum d) Conservation of energy

7.

In an explosion, the total momentum of the system immediately after the explosion is:

a) Greater than before b) Zero c) Equal to the initial momentum d) Less than before

8.

Which best describes the motion of the center of mass of a system with no external forces?

a) It moves randomly b) It accelerates continuously c) It moves at constant velocity d) It oscillates about the origin

9.

What distinguishes a perfectly inelastic collision from other types of collisions?

a) The total kinetic energy increases b) Objects rebound with equal speeds c) The objects stick together after collision d) Both momentum and kinetic energy are conserved

10.

Which equation represents the relative velocity condition for elastic collisions?

a) \( v_{1f} + v_{2f} = v_{1i} + v_{2i} \) b) \( v_{1f} - v_{2f} = v_{1i} - v_{2i} \) c) \( v_{1i} - v_{2i} = -(v_{1f} - v_{2f}) \) d) \( m_1v_{1f} + m_2v_{2f} = m_1v_{1i} + m_2v_{2i} \)

11.

A force acts on a 2 kg object such that its velocity changes from 4 m/s to -2 m/s over 0.5 seconds. What is the average force exerted on the object?

a) -12 N b) -24 N c) 12 N d) 24 N

12.

A varying force is applied to a 1.5 kg object given by \( F(t) = 6t \). What is the impulse delivered from \( t = 0 \) to \( t = 3 \) s?

a) 18 N·s b) 27 N·s c) 9 N·s d) 36 N·s

13.

Two blocks, 2 kg and 3 kg, are moving toward each other on a frictionless track at 5 m/s and 2 m/s respectively. What is the velocity of the center of mass?

a) 1 m/s b) -1 m/s c) 0.2 m/s d) -0.2 m/s

14.

An object of mass \( m \) is subject to a net force \( F(t) = A \cos(\omega t) \). What is the expression for the change in momentum from \( t = 0 \) to \( t = T \)?

a) \( A \sin(\omega T) \) b) \( \frac{A}{\omega} \sin(\omega T) \) c) \( A \omega T \) d) \( \frac{A}{\omega} (1 - \cos(\omega T)) \)

15.

A 4 kg object traveling at 6 m/s collides elastically with a 2 kg object at rest. What is the final velocity of the 4 kg object?

a) 2 m/s b) 4 m/s c) -2 m/s d) 1 m/s

16.

Two identical carts undergo an elastic collision on a frictionless track. Cart A is moving at 2 m/s and Cart B is at rest. What are their velocities after the collision?

a) A: 2 m/s, B: 0 m/s b) A: 0 m/s, B: 2 m/s c) A: 1 m/s, B: 1 m/s d) A: -1 m/s, B: 1 m/s

17.

A 0.2 kg ball bounces off a wall elastically, changing velocity from +10 m/s to -10 m/s in 0.01 s. What is the average force during the collision?

a) 200 N b) 400 N c) -400 N d) -200 N

18.

Two objects collide in 1D. Object A has mass \( m \) and initial velocity \( v \), and object B is at rest with mass \( 2m \). After an elastic collision, what is A's final velocity?

a) \( -v \) b) \( 0 \) c) \( \frac{v}{3} \) d) \( -\frac{v}{3} \)

19.

In a two-object system with no external forces, the center of mass is initially at rest. After an explosion, one object moves at 4 m/s to the right. If the masses are 2 kg and 1 kg, what is the velocity of the second object?

a) 4 m/s to the left b) 2 m/s to the left c) 8 m/s to the left d) 0 m/s

20.

Which condition must be true for relative velocity reversal \( v_{1i} - v_{2i} = -(v_{1f} - v_{2f}) \) to apply in a collision?

a) Only momentum is conserved b) Only energy is conserved c) Both momentum and kinetic energy are conserved d) The collision must be perfectly inelastic

21.

A 1.5 kg cart traveling at 3 m/s collides inelastically with a 2.5 kg cart at rest. What is the final velocity of the combined mass?

a) 1.2 m/s b) 1.8 m/s c) 3.0 m/s d) 0.9 m/s

22.

An object experiences a force \(\ F(t) = 4t^2 \) for \( 0 \le t \le 2 \). What is the impulse delivered over this interval?

a) 4 N·s b) 8 N·s c) \( \frac{32}{3} \) N·s d) 16 N·s

23.

In a head-on elastic collision, a 1 kg ball moving at 6 m/s strikes a stationary 3 kg block. What is the final velocity of the 1 kg ball?

a) -3 m/s b) 3 m/s c) 0 m/s d) -4.5 m/s

24.

A 2 kg object moving east at 3 m/s explodes into two pieces, 1.2 kg and 0.8 kg. If the 1.2 kg piece moves east at 4 m/s, what is the velocity of the 0.8 kg piece?

a) -3 m/s (west) b) 0 m/s c) -1.5 m/s (west) d) 1.5 m/s (east)

25.

Two blocks stick together after a collision and move with a final speed of 2 m/s. If one block is 1 kg moving at 5 m/s and the other is initially at rest, what is the mass of the second block?

a) 1 kg b) 1.5 kg c) 2.5 kg d) 1.25 kg

26.

Which of the following best describes the motion of the center of mass during an internal explosion in space?

a) It accelerates opposite to the largest fragment b) It moves in the direction of the most massive fragment c) It remains at constant velocity d) It moves toward the lower mass object

27.

An object of mass \(\ m \) is subject to a time-dependent force \(\ F(t) = kt \). What is the change in velocity from \(\ t = 0 \) to \(\ t = T \)?

a) \( \frac{kT^2}{m} \) b) \( \frac{kT}{m} \) c) \( \frac{kT^2}{2m} \) d) \( \frac{k}{m} \)

28.

In an elastic collision in 1D, two objects of unequal mass collide. Which condition is always true?

a) Their relative velocity is zero afterward b) Their final velocities are equal c) Their kinetic energies are equal afterward d) Their relative velocity reverses

29.

A projectile of mass 0.1 kg moving at 600 m/s embeds itself in a 0.9 kg block. What is the final velocity of the combined object?

a) 60 m/s b) 66.7 m/s c) 54.5 m/s d) 100 m/s

30.

In a system of particles with no external forces, which of the following quantities must remain constant?

a) Total mass b) Total kinetic energy c) Total momentum d) Both a and c

Momentum and Collisions Practice Test

30 Questions – Mixed Conceptual & Calculations