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

$$\text{Total momentum} = 4,000 \times 10 + 800 \times (-50) = 40,000 - 40,000 = 0\ \text{kg}\cdot\text{m/s}$$

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

$$p_y = 2 \times 10 \times \sin(37^\circ) = 2 \times 10 \times 0.601 = 12.02\ \text{kg}\cdot\text{m/s}$$

Q: You throw a 150-g rock to have the same momentum as a 10-g bullet traveling at 900 m/s. How fast must you throw the rock?

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

Q: A 50 kg crate is pushed with a constant 100 N force for 8 seconds. What is the impulse delivered to the crate?

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

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

$$F_{\text{avg}} = \frac{J}{\Delta t} = \frac{0.1 \times 30}{0.2} = \frac{3}{0.2} = 15\ \text{N}$$

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 slams into a wall and comes to a stop after compressing 1.0 m into the wall. What is the average force exerted by the wall?

$$F_{\text{avg}} = \frac{\Delta p}{\Delta t} = \frac{1200 \times (-20)}{\Delta t}$$, where $$\Delta t = \frac{2 \Delta x}{v_0$} = \frac{2 \times 1}{20} = 0.1\ \text{s}$$, so $$F_{\text{avg}} = \frac{-24,000}{0.1} = -240,000\ \text{N}$$

Q: A 0.6 kg ball is caught while moving at 10 m/s. What is the impulse delivered to the ball during the catch?

$$J = m(v_f - v_0$) = 0.6 \times (0 - 10) = -6\ \text{kg}\cdot\text{m/s}$$

Q: Two objects, A (4 kg) moving right at 12 m/s and B (5 kg) moving left at 9 m/s, collide. What is the total momentum of the system before the collision?

$$p_{\text{sys}} = 4 \times 12 + 5 \times (-9) = 48 - 45 = 3\ \text{kg}\cdot\text{m/s}$$

Q: On a frictionless air hockey table, puck A (0.250 kg) moves right and collides with puck B (0.38 kg) at rest. After the collision, A moves left at 0.12 m/s and B moves right at 0.65 m/s. What was the initial velocity of puck A?

$$v_{A,i} = \frac{0.250 \times 0.12 + 0.38 \times 0.65}{0.250} = \frac{0.03 + 0.247}{0.250} = 1.108\ \text{m/s}$$

Question 1

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

Accepted Answer

$$	ext{Total momentum} = 4,000 	imes 10 + 800 	imes (-50) = 40,000 - 40,000 = 0\ 	ext{kg}\cdot	ext{m/s}$$

Question 2

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

Accepted Answer

$$p_y = 2 	imes 10 	imes \sin(37^\circ) = 2 	imes 10 	imes 0.601 = 12.02\ 	ext{kg}\cdot	ext{m/s}$$

Question 3

You throw a 150-g rock to have the same momentum as a 10-g bullet traveling at 900 m/s. How fast must you throw the rock?

Accepted Answer

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

Question 4

A 50 kg crate is pushed with a constant 100 N force for 8 seconds. What is the impulse delivered to the crate?

Accepted Answer

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

Question 5

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

Accepted Answer

$$F_{	ext{avg}} = \frac{J}{\Delta t} = \frac{0.1 	imes 30}{0.2} = \frac{3}{0.2} = 15\ 	ext{N}$$

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 slams into a wall and comes to a stop after compressing 1.0 m into the wall. What is the average force exerted by the wall?

Accepted Answer

$$F_{	ext{avg}} = \frac{\Delta p}{\Delta t} = \frac{1200 	imes (-20)}{\Delta t}$$, where $$\Delta t = \frac{2 \Delta x}{v_0$} = \frac{2 	imes 1}{20} = 0.1\ 	ext{s}$$, so $$F_{	ext{avg}} = \frac{-24,000}{0.1} = -240,000\ 	ext{N}$$

Question 8

A 0.6 kg ball is caught while moving at 10 m/s. What is the impulse delivered to the ball during the catch?

Accepted Answer

$$J = m(v_f - v_0$) = 0.6 	imes (0 - 10) = -6\ 	ext{kg}\cdot	ext{m/s}$$

Question 9

Two objects, A (4 kg) moving right at 12 m/s and B (5 kg) moving left at 9 m/s, collide. What is the total momentum of the system before the collision?

Accepted Answer

$$p_{	ext{sys}} = 4 	imes 12 + 5 	imes (-9) = 48 - 45 = 3\ 	ext{kg}\cdot	ext{m/s}$$

Question 10

On a frictionless air hockey table, puck A (0.250 kg) moves right and collides with puck B (0.38 kg) at rest. After the collision, A moves left at 0.12 m/s and B moves right at 0.65 m/s. What was the initial velocity of puck A?

Accepted Answer

$$v_{A,i} = \frac{0.250 	imes 0.12 + 0.38 	imes 0.65}{0.250} = \frac{0.03 + 0.247}{0.250} = 1.108\ 	ext{m/s}$$

Question 11

A 4-kg sniper rifle shoots a 5-g bullet at 600 m/s. What is the recoil speed of the rifle?

Accepted Answer

$$v_{	ext{rifle}} = -\frac{m_{	ext{bullet}} v_{	ext{bullet}}}{m_{	ext{rifle}}} = -\frac{0.005 	imes 600}{4} = -0.75\ 	ext{m/s}$$

Question 12

A 70-kg sled moves at 10 m/s to the right when a 30-kg box is dropped vertically onto it. What is the final speed of the system?

Accepted Answer

$$v_f = \frac{70 	imes 10}{70 + 30} = \frac{700}{100} = 7\ 	ext{m/s}$$

Question 13

Two toy carts collide head-on on a frictionless surface. Cart A (0.50 kg, 2 m/s) and Cart B (0.30 kg, -2 m/s) have final velocities of -1 m/s and 3 m/s, respectively. What type of collision is this?

Accepted Answer

Elastic

Question 14

A 1 kg block moving at 20 m/s collides with a 9 kg block at rest and sticks to it. What is the final speed of the system?

Accepted Answer

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

Question 15

A 1000 kg car traveling east at 20 m/s collides with a 3000 kg truck heading north at 10 m/s. The vehicles lock together. What is the magnitude of their final velocity?

Accepted Answer

$$v_f = \sqrt{\left(\frac{1000 	imes 20}{4000}\$$right)^2$$ + \left(\frac{3000 	imes 10}{4000}\$$right)^2$$} = \sqrt{(5)^2$ + (7.5)^2$} = \sqrt{25 + 56.25} = \sqrt{81.25} = 9.02\ 	ext{m/s}$$

Question 16

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

Accepted Answer

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

Question 17

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

Accepted Answer

$$y_{	ext{com}} = \frac{1.0 	imes 2.00 + 1.50 	imes 0 + 7.5 	imes (-1.5)}{1.0 + 1.5 + 7.5} = \frac{2.00 + 0 - 11.25}{10} = \frac{-9.25}{10} = -0.925\ 	ext{m}$$

Linear Momentum: Concepts, Problems, and Applications

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