Q: A 4,000 kg truck moves to the right at 10 m/s, while an 800 kg racecar moves to the left at 50 m/s. What is the total momentum of the system?

$$p_{\text{total}} = (4000 \times 10) + (800 \times -50) = 40000 - 40000 = 0\ \text{kg} \cdot \text{m/s}$$

Q: A 2-kg object moves with a velocity of 10 m/s at 37° above the horizontal. What is the horizontal component of its momentum?

$$p_x = 2 \times 10 \times \cos(37^\circ) = 2 \times 10 \times 0.8 = 16\ \text{kg} \cdot \text{m/s}$$

Q: A 150-g rock is thrown so that it has the same momentum as a 10-g bullet traveling at 900 m/s. What is the required speed of the rock?

$$v_{\text{rock}} = \frac{0.01 \times 900}{0.15} = 60\ \text{m/s}$$

Q: A 50 kg crate is at rest on a frictionless surface. You push it with a constant force of 100 N for 8 seconds. What is the impulse delivered to the crate?

$$J = F \Delta t = 100 \times 8 = 800\ \text{N} \cdot \text{s}$$

Q: A 100-g ball is thrown at 30 m/s and is in your hand for 0.2 s during the throw. What is the average force you exert on the ball?

$$F_{\text{avg}} = \frac{J}{\Delta t} = \frac{3}{0.2} = 15\ \text{N}$$

Q: A 150-g rubber ball moving at 40 m/s to the right hits a wall and bounces back at 45 m/s to the left. What is the impulse delivered to the ball?

$$J = m(v_f - v_0$) = 0.15 \times (-45 - 40) = 0.15 \times (-85) = -12.75\ \text{kg} \cdot \text{m/s}$$

Q: A 1200-kg car moving at 20 m/s crashes into a wall and comes to rest after compressing 1.0 m into the wall. Assuming constant acceleration, how long does the collision last?

$$t = \frac{2 \Delta x}{v_0$} = \frac{2 \times 1.0}{20} = 0.1\ \text{s}$$

Q: A 1-kg block moving at 20 m/s collides with a 9-kg block at rest. If the blocks stick together, what is their final speed?

$$v_f = \frac{1 \times 20 + 9 \times 0}{1 + 9} = \frac{20}{10} = 2\ \text{m/s}$$

Q: A 10.0-g bullet is fired into a 5-kg stationary block of wood and embeds itself. If the speed of the bullet-block system after the collision is 0.6 m/s, what was the original speed of the bullet?

$$v_{\text{bullet}} = \frac{(5 + 0.01) \times 0.6}{0.01} = \frac{3.006}{0.01} = 300.6\ \text{m/s}$$

Question 1

A 4,000 kg truck moves to the right at 10 m/s, while an 800 kg racecar moves to the left at 50 m/s. What is the total momentum of the system?

Accepted Answer

$$p_{	ext{total}} = (4000 	imes 10) + (800 	imes -50) = 40000 - 40000 = 0\ 	ext{kg} \cdot 	ext{m/s}$$

Question 2

A 2-kg object moves with a velocity of 10 m/s at 37° above the horizontal. What is the horizontal component of its momentum?

Accepted Answer

$$p_x = 2 	imes 10 	imes \cos(37^\circ) = 2 	imes 10 	imes 0.8 = 16\ 	ext{kg} \cdot 	ext{m/s}$$

Question 3

A 150-g rock is thrown so that it has the same momentum as a 10-g bullet traveling at 900 m/s. What is the required speed of the rock?

Accepted Answer

$$v_{	ext{rock}} = \frac{0.01 	imes 900}{0.15} = 60\ 	ext{m/s}$$

Question 4

A 50 kg crate is at rest on a frictionless surface. You push it with a constant force of 100 N for 8 seconds. What is the impulse delivered to the crate?

Accepted Answer

$$J = F \Delta t = 100 	imes 8 = 800\ 	ext{N} \cdot 	ext{s}$$

Question 5

A 100-g ball is thrown at 30 m/s and is in your hand for 0.2 s during the throw. What is the average force you exert on the ball?

Accepted Answer

$$F_{	ext{avg}} = \frac{J}{\Delta t} = \frac{3}{0.2} = 15\ 	ext{N}$$

Question 6

A 150-g rubber ball moving at 40 m/s to the right hits a wall and bounces back at 45 m/s to the left. What is the impulse delivered to the ball?

Accepted Answer

$$J = m(v_f - v_0$) = 0.15 	imes (-45 - 40) = 0.15 	imes (-85) = -12.75\ 	ext{kg} \cdot 	ext{m/s}$$

Question 7

A 1200-kg car moving at 20 m/s crashes into a wall and comes to rest after compressing 1.0 m into the wall. Assuming constant acceleration, how long does the collision last?

Accepted Answer

$$t = \frac{2 \Delta x}{v_0$} = \frac{2 	imes 1.0}{20} = 0.1\ 	ext{s}$$

Question 8

Which of the following is true for a perfectly inelastic collision?

Accepted Answer

Momentum is conserved, mechanical energy is not conserved, and the objects stick together after the collision.

Question 9

A 1-kg block moving at 20 m/s collides with a 9-kg block at rest. If the blocks stick together, what is their final speed?

Accepted Answer

$$v_f = \frac{1 	imes 20 + 9 	imes 0}{1 + 9} = \frac{20}{10} = 2\ 	ext{m/s}$$

Question 10

A 10.0-g bullet is fired into a 5-kg stationary block of wood and embeds itself. If the speed of the bullet-block system after the collision is 0.6 m/s, what was the original speed of the bullet?

Accepted Answer

$$v_{	ext{bullet}} = \frac{(5 + 0.01) 	imes 0.6}{0.01} = \frac{3.006}{0.01} = 300.6\ 	ext{m/s}$$

Question 11

Two blocks of equal mass undergo a head-on elastic collision. Object A moves to the right at 5 m/s, while Object B moves to the left at 3 m/s. What are their final velocities?

Accepted Answer

Object A: $$-3 m/s$$, Object B: $$5 m/s$$

Question 12

A 40-kg skater runs parallel to a 3-kg skateboard. Both are moving to the right at 10 m/s. The skater jumps on the board. What is the final speed of the system?

Accepted Answer

$$v_f = \frac{40 	imes 10 + 3 	imes 10}{40 + 3} = \frac{430}{43} = 10\ 	ext{m/s}$$

Question 13

A 6-g bullet is fired upwards at 800 m/s into a 1.2-kg wooden block at rest. The bullet emerges at 150 m/s. What is the maximum height the block reaches after the collision?

Accepted Answer

$$v_{	ext{block}} = \frac{0.006 	imes (800 - 150)}{1.2} = 3.25\ 	ext{m/s}$$;\ h = \frac{$$v^2$$}{2g} = \frac{$$(3.25)^2$$}{2 	imes 9.8} \approx 0.54\ 	ext{m}$

Question 14

Which of the following statements about the center of mass (C.O.M) is correct?

Accepted Answer

The center of mass is closer to the more massive objects in the system.

Question 15

Three weights are placed along the y-axis: a 1.0-kg at +2.00 m, a 1.50-kg at the origin, and a 7.5-kg at –1.5 m. Where is the center of mass?

Accepted Answer

$$y_{	ext{com}} = \frac{1.0 	imes 2.00 + 1.5 	imes 0 + 7.5 	imes (-1.5)}{1.0 + 1.5 + 7.5} = \frac{2.00 - 11.25}{10.0} = -0.925\ 	ext{m}$$

Question 16

A 10-kg crate moving at 20 m/s collides and sticks to a 30-kg crate at rest. After the collision, the crates compress a spring with $$k = 500\ 	ext{N/m}. $$What is the maximum compression of the spring?

Accepted Answer

$$v_f = \frac{10 	imes 20}{40} = 5\ 	ext{m/s}$$;\ \frac{1}{2} (40) $$(5^2$$) = \frac{1}{2} (500) $$x^2$$ \Rightarrow x = 2\ 	ext{m}$

Question 17

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

Accepted Answer

The system must be isolated, with only internal forces acting.

Momentum, Impulse, and Collisions – Study Notes

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