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 momentum of the racecar?

$$\text{p} = 800 \times 50 = 40,000\ \text{kg} \cdot \text{m/s}$$\text{ to the left}$

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

$$\text{p}_y = 2 \times 10 \times \sin(37^\circ) = 12.04\ \text{kg} \cdot \text{m/s}$$

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

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

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?

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

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?

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

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

$$v_f = \frac{70 \times 10}{70 + 30} = 7\ \text{m/s}$$

Q: A 1 kg block moving at 20 m/s collides with a 9 kg block initially at rest. If the 1 kg block sticks to the 9 kg block, what is the final speed of the system?

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

Q: A 1000 kg car traveling east at 20 m/s slams into a 3000 kg truck heading north at 10 m/s. The vehicles become locked together. What is the magnitude of their final velocity?

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

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 momentum of the racecar?

Accepted Answer

$$	ext{p} = 800 	imes 50 = 40,000\ 	ext{kg} \cdot 	ext{m/s}$$	ext{ to the left}$

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

$$	ext{p}_y = 2 	imes 10 	imes \sin(37^\circ) = 12.04\ 	ext{kg} \cdot 	ext{m/s}$$

Question 3

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

Accepted Answer

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

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

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

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

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

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

Accepted Answer

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

Question 9

Two toy carts collide head-on on a frictionless surface. Cart A has a mass of 0.50 kg and an initial velocity of 2 m/s. Cart B has a mass of 0.30 kg and initial velocity –2 m/s. After the collision, the final velocities of A and B are –1 m/s and 3 m/s, respectively. What type of collision was this?

Accepted Answer

Elastic

Question 10

A 1 kg block moving at 20 m/s collides with a 9 kg block initially at rest. If the 1 kg block sticks to the 9 kg block, what is the final speed of the system?

Accepted Answer

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

Question 11

A 1000 kg car traveling east at 20 m/s slams into a 3000 kg truck heading north at 10 m/s. The vehicles become locked 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$$} = \sqrt{(5)^2$ + (7.5)^2$} = \sqrt{25 + 56.25} = \sqrt{81.25} \approx 9.02\ 	ext{m/s}$$

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, and they continue moving right. What is the final speed of the system?

Accepted Answer

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

Question 13

A 70-kg hockey player skates at 5 m/s and collides head-on with a 110-kg player at 4 m/s. They become entangled after the collision. What is their final velocity?

Accepted Answer

$$v_f = \frac{70 	imes 5 + 110 	imes (-4)}{70 + 110} = \frac{350 - 440}{180} = \frac{-90}{180} = -0.5\ 	ext{m/s}$$

Question 14

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

Accepted Answer

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

Question 15

A solid cylinder of mass 5 kg and radius 2 m rotates about its center with 120 RPM. What is its angular momentum?

Accepted Answer

$$L = I \omega = \frac{1}{2} 	imes 5 	imes 2^2$ 	imes \left(\frac{2\pi 	imes 120}{60}ight) = 10 	imes 4\pi = 40\pi \approx 125.66\ 	ext{kg} \cdot 	ext{m}^2 / 	ext{s}$$

Question 16

An ice skater spins at 120 RPM with arms wide open (moment of inertia 6 kg $$m^2). $$When she closes her arms (moment of inertia 4 kg $$m^2$$), what is her new RPM?

Accepted Answer

$$\omega_f = \omega_i \frac{I_i}{I_f} = 120 	imes \frac{6}{4} = 180\ 	ext{RPM}$$

Chapter 9: Momentum and Angular Momentum – Study Notes

Guida di studio - Domande di pratica

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