Momentum and Collisions Practice Test

1.

A 2-kg cart moves to the right at 3 m/s. What is its momentum?

a) 1.5 kg·m/s b) 3 kg·m/s c) 6 kg·m/s d) 9 kg·m/s

2.

The impulse experienced by an object is equal to:

a) the object's mass times its acceleration b) the object's weight times its displacement c) the change in the object's momentum d) the net force divided by time

3.

A 0.5-kg ball traveling at 10 m/s is stopped by a player in 0.2 seconds. What is the magnitude of the average force applied?

a) 5 N b) 10 N c) 25 N d) 50 N

4.

Which of the following statements is true about momentum?

a) Only objects with mass have momentum b) An object at rest can have momentum if it has mass c) Momentum is always conserved, regardless of external forces d) Momentum is a vector and depends on both mass and velocity

5.

A 3-kg object changes its velocity from 2 m/s to -4 m/s. What is the impulse delivered to it?

a) -18 kg·m/s b) 6 kg·m/s c) -6 kg·m/s d) -3 kg·m/s

6.

Two objects collide elastically in one dimension. Object A has mass 4 kg and velocity 3 m/s to the right, Object B has mass 6 kg and velocity −2 m/s (to the left). Using the relative velocity shortcut, what is the relative velocity after the collision?

a) 5 m/s b) -5 m/s c) 1 m/s d) -1 m/s

7.

An object of mass 1.5 kg moving at 5 m/s collides elastically with a stationary object of mass 0.5 kg. Find the final velocity of the moving object after the collision.

a) 3 m/s b) 1 m/s c) 4 m/s d) 0 m/s

8.

Explain why the relative velocity between two objects reverses direction after an elastic collision.

a) Because momentum is conserved b) Because kinetic energy is conserved c) Because of Newton's third law d) Because velocities exchange directions symmetrically

9.

A 3 kg cart moving at 10 m/s collides elastically with a 2 kg cart moving at 4 m/s in the opposite direction. Calculate the final velocity of the 3 kg cart.

a) -1.2 m/s b) 1.2 m/s c) 4.8 m/s d) -4.8 m/s

10.

In an elastic collision, why is it important to keep consistent sign conventions for velocity? What can go wrong if signs are mixed up?

a) The results can be physically incorrect b) The momentum conservation equation won't hold c) It may cause errors in relative velocity calculation d) All of the above

11.

Two carts with masses 5 kg and 3 kg move toward each other on a frictionless track. The 5 kg cart moves at 8 m/s, the 3 kg cart at 10 m/s in the opposite direction. They collide elastically. What is the velocity of the 3 kg cart after the collision?

a) 12.5 m/s b) 14 m/s c) -6 m/s d) -14 m/s

12.

A 2 kg ball moving at 6 m/s collides elastically with a 4 kg ball moving at 3 m/s in the same direction. What is the final velocity of the 2 kg ball?

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

13.

In a one-dimensional elastic collision, why does the relative velocity between two objects reverse its sign after the collision?

a) Because energy is transferred between objects b) Because momentum is conserved c) Because of Newton's third law acting on the collision forces d) Because both momentum and kinetic energy are conserved

14.

Two objects with masses 7 kg and 3 kg collide elastically. The 7 kg object moves at 4 m/s, and the 3 kg object moves at -6 m/s (opposite direction). What is the velocity of the 7 kg object after collision?

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

15.

A 1 kg ball moving at 5 m/s collides elastically with a 2 kg ball moving at 1 m/s in the same direction. Which object ends up moving faster after the collision?

a) 1 kg ball b) 2 kg ball c) Both move at the same speed d) Impossible to determine without more information

16.

A 4 kg cart moving at 3 m/s collides elastically with a 6 kg cart moving at -2 m/s. What is the final velocity of the 6 kg cart?

a) 1.2 m/s b) -3 m/s c) 4 m/s d) -1 m/s

17.

Explain why kinetic energy is conserved in elastic collisions but not in inelastic collisions.

a) Because elastic collisions do not deform objects b) Because no energy is converted to heat or sound in elastic collisions c) Because momentum is always conserved d) Both a and b

18.

In a perfectly inelastic collision, two objects stick together after colliding. What happens to the total kinetic energy of the system?

a) It remains the same b) It increases c) It decreases d) It becomes zero

19.

A 5 kg object moving at 7 m/s collides elastically with a 3 kg object moving at 2 m/s in the same direction. Find the final velocity of the 5 kg object.

a) 5 m/s b) 8 m/s c) 3 m/s d) 7 m/s

20.

Why is the relative velocity shortcut only valid for elastic collisions?

a) Because only elastic collisions conserve kinetic energy b) Because momentum conservation does not apply in other collisions c) Because it assumes objects stick together d) Because it only works when objects have equal masses

21.

Derive the formula for the final velocity of two objects after a perfectly inelastic collision.

a) By equating initial and final kinetic energies b) By applying conservation of momentum and using the fact that the objects stick together c) By applying Newton's second law to the collision d) By assuming equal masses and solving for velocity

22.

Using the relative velocity shortcut for elastic collisions, explain why \(v_{1i} - v_{2i} = -(v_{1f} - v_{2f})\) holds true.

a) It is a result of kinetic energy conservation and Newton's third law b) It comes from momentum not being conserved c) It assumes that the masses are equal d) It is only true for inelastic collisions

23.

A 3 kg object moving at 6 m/s collides perfectly inelastically with a 2 kg object moving at 4 m/s. What is their final velocity?

a) 5.2 m/s b) 4.8 m/s c) 5.0 m/s d) 4.6 m/s

24.

Two carts, 4 kg and 6 kg, collide elastically. The 4 kg cart moves at 3 m/s toward the 6 kg cart at rest. Find the velocity of the 4 kg cart after the collision.

a) 1.2 m/s b) -1.8 m/s c) 3 m/s d) 0 m/s

25.

A 2 kg ball moving at 5 m/s collides elastically with a 3 kg ball moving at -2 m/s. What is the velocity of the 3 kg ball after collision?

a) 6 m/s b) -1 m/s c) 2 m/s d) 0 m/s

26.

Which formula correctly represents the conservation of momentum in a two-object collision?

a) \( m_1v_{1,i} + m_2v_{2,i} = m_1v_{1,f} + m_2v_{2,f} \) b) \( \frac{1}{2}m_1v_{1,i}^2 + \frac{1}{2}m_2v_{2,i}^2 = \frac{1}{2}m_1v_{1,f}^2 + \frac{1}{2}m_2v_{2,f}^2 \) c) \( v_f = \frac{m_1v_{1,i} + m_2v_{2,i}}{m_1 + m_2} \) d) \( \vec{F} = m\vec{a} \)

27.

Which formula correctly gives the final velocity of object 1 after an elastic collision in one dimension?

a) \( v_{1,f} = \frac{(m_1 - m_2)v_{1,i} + 2m_2v_{2,i}}{m_1 + m_2} \) b) \( v_{1,f} = \frac{m_1v_{1,i} + m_2v_{2,i}}{m_1 + m_2} \) c) \( v_{1,f} = v_{1,i} \) d) \( v_{1,f} = \frac{m_1v_{1,i} - m_2v_{2,i}}{m_1 - m_2} \)

28.

During a collision, if the total kinetic energy before collision is 100 J and after is 80 J, what is the percentage loss of kinetic energy?

a) 20% b) 25% c) 80% d) 100%

29.

A 0.5 kg bullet traveling at 400 m/s embeds itself in a 2 kg block at rest. What is the velocity of the block plus bullet immediately after impact?

a) 80 m/s b) 100 m/s c) 50 m/s d) 0 m/s

30.

A 0.2 kg bullet traveling at 500 m/s embeds itself in a 1.3 kg block initially at rest on a frictionless surface. After the collision, the combined block rises vertically by 0.20 m. How much kinetic energy was lost during the collision?

a) 21,672 J b) 21,667 J c) 21,680 J d) 21,600 J

Momentum and Collisions Practice Test

30 Questions – Mixed Conceptual & Calculations