Question 1

In a two-dimensional elastic collision between two spheres, one of which is initially at rest, which of the following quantities is always conserved?

Accepted Answer

Both the total kinetic energy and the total linear momentum (in all directions)

Question 2

Given two particles, A and B, with masses $$m_A$$ and $$m_B$$, and initial velocities $$\vec{v}_{A1}$$ and $$\vec{v}_{B1}$$, what is the formula for the velocity of the center of mass before the collision?

Accepted Answer

$$\vec{V}_{CM} = \frac{m_A \vec{v}_{A1} + m_B \vec{v}_{B1}}{m_A + m_B}$$

Question 3

A 0.5 kg ball (A) moving at 4.0 m/s collides elastically with a 0.3 kg ball (B) at rest. After the collision, ball A moves at 2.0 m/s at an angle $$\alpha$$ from the original direction. What is the speed of ball B after the collision?

Accepted Answer

$$v_{B2} = 2.67\ \mathrm{m/s}$$

Question 4

Which of the following statements about the collision and scattering planes in a 3D collision is correct?

Accepted Answer

The collision plane is defined by the initial velocities, while the scattering plane is defined by the final velocities.

Question 5

In a completely inelastic collision, which of the following is true?

Accepted Answer

Momentum is conserved, but kinetic energy is not.

Question 6

For a two-dimensional collision, how many independent equations are available from conservation laws?

Accepted Answer

Two from momentum and one from energy, for a total of three.

Question 7

What is the reduced mass $$\mu$$ for two colliding particles with masses $$m_A$$ and $$m_B$$?

Accepted Answer

$$\mu = \frac{m_A m_B}{m_A + m_B}$$

Question 8

A 1D elastic collision occurs between two objects. If the initial velocity of object A is $$v_{A1}$$ and object B is at rest, what is the final velocity of object B ($$v_{B2}) $$after the collision?

Accepted Answer

$$v_{B2} = \frac{2 m_A}{m_A + m_B} v_{A1}$$

Question 9

In a 3D collision, how many dynamic parameters must be specified to completely determine the outcome?

Accepted Answer

Three

Question 10

Which of the following best describes the center of mass reference frame in a collision problem?

Accepted Answer

A frame in which the total momentum is zero.

Question 11

A particle of mass $$m_A$$ moving with velocity $$v_{A1}$$ collides with a stationary particle of mass $$m_B. If $$the collision is perfectly inelastic, what is the final velocity $$v_f of $$the combined mass?

Accepted Answer

$$v_f = \frac{m_A v_{A1}}{m_A + m_B}$$

Question 12

Which of the following is a correct statement about the energy in an inelastic collision?

Accepted Answer

Some kinetic energy is converted into internal energy or other forms.

Question 13

In a laboratory reference frame, which of the following is true for a two-body elastic collision where one body is initially at rest?

Accepted Answer

The total momentum and total kinetic energy are both conserved.

Question 14

If the internal energy change $$Q_{int} in a $$collision is zero, what type of collision is it?

Accepted Answer

Elastic

Question 15

A 0.5 kg ball moving at 4.0 m/s collides elastically with a 0.3 kg ball at rest. After the collision, the 0.5 kg ball moves at 2.0 m/s at an angle of $$60^\circ$$ from its original direction. What is the angle $$\beta at $$which the 0.3 kg ball moves after the collision?

Accepted Answer

$$\beta = 36.9^\circ$$

Question 16

Which of the following is NOT a valid step in solving a general collision problem using the center of mass reference frame?

Accepted Answer

Ignore the masses of the colliding objects.

Question 17

In a two-dimensional collision, if you are given the final velocity of one particle and the scattering angle, what is the minimum number of additional parameters you need to fully solve the collision?

Accepted Answer

One

Question 18

Which of the following best describes the maximal dissipated energy in a collision compatible with a given scattering angle?

Accepted Answer

It is the maximum amount of kinetic energy that can be converted to internal energy while still satisfying conservation of momentum and the given scattering angle.

Momentum, Impulse, and Collisions: Multi-Dimensional Analysis and Examples

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