Q: A child (30 kg) runs at 3 m/s and jumps onto a stationary 10 kg tire swing. If the swing hangs from a 2 m chain, how high does the child-swing system rise after the collision? (Assume no energy loss after grabbing the swing.)

$$h = \frac{v^2$}{2g} = \frac{(2.25)^2$}{2 \times 9.8} \approx 0.26 m$$

Q: A 2 kg cart moving at 3 m/s collides and sticks to a 1 kg cart at rest. What is their final velocity?

$$v' = \frac{m_1$ v_1$ + m_2$ v_2$}{m_1$ + m_2$} = \frac{2 \times 3 + 1 \times 0}{2 + 1} = 2 m/s$$

Question 1

Which of the following best describes a completely inelastic collision?

Accepted Answer

The objects stick together after the collision and move with a common velocity.

Question 2

A 2 kg ball moving at 5 m/s collides head-on with a stationary 3 kg ball in a perfectly elastic collision. What is the velocity of the 2 kg ball after the collision?

Accepted Answer

$$v_1$$' = \frac{2m_1 - $$m_2$$}{$$m_1$$ + $$m_2$$} $$v_1$$ = \frac{2 	imes 2 - 3}{2 + 3} 	imes 5 = \frac{1}{5} 	imes 5 = 1$$ m/s

Question 3

In a real-world car crash, two cars collide and stick together. Which type of collision is this, and what is true about the kinetic energy?

Accepted Answer

Completely inelastic; kinetic energy is not conserved.

Question 4

A 0.2 kg rubber ball is dropped from a height and bounces back to its original height. Which statement is true about the collision with the ground?

Accepted Answer

The collision is elastic and $$\Delta KE = 0.$$

Question 5

A 5.5 kg bowling ball moving at 9.0 m/s collides with a 0.825 kg pin at rest. After the collision, the pin moves at 15 m/s at 85° to the ball's original direction. What is the final velocity (magnitude) of the bowling ball?

Accepted Answer

About 3.4 m/s

Question 6

A child (30 kg) runs at 3 m/s and jumps onto a stationary 10 kg tire swing. If the swing hangs from a 2 m chain, how high does the child-swing system rise after the collision? (Assume no energy loss after grabbing the swing.)

Accepted Answer

$$h = \frac{v^2$}{2g} = \frac{(2.25)^2$}{2 	imes 9.8} \approx 0.26 m$$

Question 7

Which of the following is always conserved in any type of collision (elastic, inelastic, or completely inelastic) in the absence of external forces?

Accepted Answer

Momentum

Question 8

A 0.5 kg ball moving at 4 m/s collides elastically with a 1.5 kg ball at rest. What is the velocity of the 0.5 kg ball after the collision?

Accepted Answer

$$v_1$$' = \frac{$$m_1$$ - $$m_2$$}{$$m_1$$ + $$m_2$$} $$v_1$$ = \frac{0.5 - 1.5}{0.5 + 1.5} 	imes 4 = -2$$ m/s

Question 9

A ball of mass $$m_1$$ moving at $$v_1$$ collides elastically with a stationary ball of mass $$m_2. If$$ $$m_1$$ \gg $$m_2$$, what is the velocity of $$m_1$$ after the collision?

Accepted Answer

$$v_1$$' \approx $$v_1$$

Question 10

A 1 kg ball moving at 10 m/s collides inelastically with a 1 kg ball at rest. After the collision, the balls move separately. Which of the following is true?

Accepted Answer

Momentum is conserved, but some kinetic energy is lost.

Question 11

A 0.2 kg ball moving at 18 m/s collides elastically with a 1000 kg car moving at 14 m/s towards the ball. What is the speed of the ball after the collision?

Accepted Answer

About 46 m/s towards the car

Question 12

Which of the following best describes an elastic collision?

Accepted Answer

Objects bounce apart and kinetic energy is conserved.

Question 13

A 2 kg cart moving at 3 m/s collides and sticks to a 1 kg cart at rest. What is their final velocity?

Accepted Answer

$$v' = \frac{m_1$ v_1$ + m_2$ v_2$}{m_1$ + m_2$} = \frac{2 	imes 3 + 1 	imes 0}{2 + 1} = 2 m/s$$

Question 14

In a two-dimensional collision, which of the following must be conserved in both the x and y directions (assuming no external forces)?

Accepted Answer

Momentum

Question 15

A 1 kg ball moving at 2 m/s collides elastically with a 1 kg ball at rest. What are their velocities after the collision?

Accepted Answer

First ball stops, second ball moves at 2 m/s

Question 16

Which of the following is a necessary condition for momentum to be conserved in a system?

Accepted Answer

No external forces act on the system.

Question 17

A 3 kg object moving at 4 m/s collides and sticks to a 2 kg object moving at 1 m/s in the same direction. What is their final velocity?

Accepted Answer

$$v' = \frac{3 	imes 4 + 2 	imes 1}{3 + 2} = \frac{12 + 2}{5} = 2.8 m/s$$

Question 18

A ball collides with a wall and rebounds with the same speed it had before the collision. Which of the following is true?

Accepted Answer

The collision is elastic and kinetic energy is conserved.

Question 19

In a closed system, which of the following equations represents the conservation of momentum for a two-object collision?

Accepted Answer

$$m_1$$ $$v_1$$ + $$m_2$$ $$v_2$$ = $$m_1$$ $$v_1$$' + $$m_2$$ $$v_2$$'$$

Collisions & Momentum: Conservation Principles and Applications

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