Q: A box is pushed 5 meters across a horizontal floor by a constant force of 20 N, directed at an angle of $$30^\circ$$ below the horizontal. What is the work done by the force on the box? (Assume no friction.)

$$W = 20 \times 5 \times \cos(30^\circ) = 86.6\ \mathrm{J}$$

Q: Which of the following best describes the dot product of two vectors $$\vec{A}$$ and $$\vec{B}$$?

$$\vec{A} \cdot \vec{B} = |\vec{A}| |\vec{B}| \cos\theta$$

Q: A 2 kg object is dropped from a height of 10 m. Ignoring air resistance, what is its kinetic energy just before it hits the ground?

$$KE = mgh = 2 \times 9.8 \times 10 = 196\ \mathrm{J}$$

Q: A spring with a spring constant $$k = 400\ \mathrm{N/m} is $$compressed by 0.1 m. What is the elastic potential energy stored in the spring?

$$U = \frac{1}{2} k x^2$ = \frac{1}{2} \times 400 \times (0.1)^2$ = 2\ \mathrm{J}$$

Q: A 1000 kg car accelerates from rest to 20 m/s in 10 seconds. What is the average power delivered to the car during this time?

$$P = \frac{\Delta KE}{\Delta t} = \frac{\frac{1}{2} \times 1000 \times 20^2$}{10} = 20,000\ \mathrm{W}$$

Q: A 2 kg block slides down a frictionless incline of height 5 m. What is its speed at the bottom?

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 5} = 9.9\ \mathrm{m/s}$$

Q: A 0.2 kg hockey puck slides on ice and is stopped by friction after 10 m. If the friction force is 0.1 N, what is the work done by friction?

$$W = -Fd = -0.1 \times 10 = -1\ \mathrm{J}$$

Q: A 0.5 kg ball moving at 6 m/s collides inelastically with a 1 kg ball at rest. After the collision, the balls stick together. What is their final velocity?

$$v_f = \frac{0.5 \times 6 + 1 \times 0}{0.5 + 1} = 2\ \mathrm{m/s}$$

Q: A 2 kg object is acted on by a constant force of 10 N for 3 seconds. What is the impulse delivered to the object?

$$J = F \Delta t = 10 \times 3 = 30\ \mathrm{N\cdot s}$$

Question 1

A box is pushed 5 meters across a horizontal floor by a constant force of 20 N, directed at an angle of $$30^\circ$$ below the horizontal. What is the work done by the force on the box? (Assume no friction.)

Accepted Answer

$$W = 20 	imes 5 	imes \cos(30^\circ) = 86.6\ \mathrm{J}$$

Question 2

Which of the following best describes the dot product of two vectors $$\vec{A}$$ and $$\vec{B}$$?

Accepted Answer

$$\vec{A} \cdot \vec{B} = |\vec{A}| |\vec{B}| \cos	heta$$

Question 3

A 2 kg object is dropped from a height of 10 m. Ignoring air resistance, what is its kinetic energy just before it hits the ground?

Accepted Answer

$$KE = mgh = 2 	imes 9.8 	imes 10 = 196\ \mathrm{J}$$

Question 4

A spring with a spring constant $$k = 400\ \mathrm{N/m} is $$compressed by 0.1 m. What is the elastic potential energy stored in the spring?

Accepted Answer

$$U = \frac{1}{2} k x^2$ = \frac{1}{2} 	imes 400 	imes (0.1)^2$ = 2\ \mathrm{J}$$

Question 5

A 0.5 kg ball moving at 4 m/s collides elastically with a stationary 0.5 kg ball in one dimension. What is the velocity of the first ball after the collision?

Accepted Answer

$$v_1$$' = 0\ \mathrm{m/s}$$

Question 6

A 3 kg object moves with velocity $$\vec{v} = (2\ \mathrm{m/s})\hat{i} + (3\ \mathrm{m/s})\hat{j}. $$What is its momentum vector?

Accepted Answer

$$\vec{p} = (6\ \mathrm{kg\cdot m/s})\hat{i} + (9\ \mathrm{kg\cdot m/s})\hat{j}$$

Question 7

A 1000 kg car accelerates from rest to 20 m/s in 10 seconds. What is the average power delivered to the car during this time?

Accepted Answer

$$P = \frac{\Delta KE}{\Delta t} = \frac{\frac{1}{2} 	imes 1000 	imes 20^2$}{10} = 20,000\ \mathrm{W}$$

Question 8

A 2 kg block slides down a frictionless incline of height 5 m. What is its speed at the bottom?

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 5} = 9.9\ \mathrm{m/s}$$

Question 9

A 0.2 kg hockey puck slides on ice and is stopped by friction after 10 m. If the friction force is 0.1 N, what is the work done by friction?

Accepted Answer

$$W = -Fd = -0.1 	imes 10 = -1\ \mathrm{J}$$

Question 10

A 0.5 kg ball moving at 6 m/s collides inelastically with a 1 kg ball at rest. After the collision, the balls stick together. What is their final velocity?

Accepted Answer

$$v_f = \frac{0.5 	imes 6 + 1 	imes 0}{0.5 + 1} = 2\ \mathrm{m/s}$$

Question 11

A 2 kg object is acted on by a constant force of 10 N for 3 seconds. What is the impulse delivered to the object?

Accepted Answer

$$J = F \Delta t = 10 	imes 3 = 30\ \mathrm{N\cdot s}$$

Question 12

A 1 kg ball moving at 5 m/s explodes into two pieces: one of 0.4 kg moving at 8 m/s in the original direction. What is the velocity of the other piece?

Accepted Answer

$$v = \frac{1 	imes 5 - 0.4 	imes 8}{0.6} = 1\ \mathrm{m/s}$$

Question 13

A 0.3 kg ball is attached to a spring ($$k = 200\ \mathrm{N/m}) $$and pulled 0.05 m from equilibrium, then released from rest. What is its speed as it passes through equilibrium?

Accepted Answer

$$v = \sqrt{\frac{k}{m}} x = \sqrt{\frac{200}{0.3}} 	imes 0.05 = 0.41\ \mathrm{m/s}$$

Question 14

A 5 kg object moving at 2 m/s collides elastically with a 10 kg object at rest. What is the velocity of the 5 kg object after the collision?

Accepted Answer

$$v_1$$' = \frac{$$m_1$$ - $$m_2$$}{$$m_1$$ + $$m_2$$} $$v_1$$ = \frac{5 - 10}{15} 	imes 2 = -0.67\ \mathrm{m/s}$$

Question 15

A 70 kg person runs up a flight of stairs 3 m high in 5 seconds. What is the average power output?

Accepted Answer

$$P = \frac{mgh}{t} = \frac{70 	imes 9.8 	imes 3}{5} = 411.6\ \mathrm{W}$$

Question 16

A 1.5 kg block slides at 4 m/s on a horizontal surface and compresses a spring ($$k = 300\ \mathrm{N/m}) $$until it comes to rest. What is the maximum compression of the spring?

Accepted Answer

$$x = \sqrt{\frac{mv^2$}{k}} = \sqrt{\frac{1.5 	imes 16}{300}} = 0.282\ \mathrm{m}$$

Question 17

A 0.8 kg ball is thrown vertically upward with an initial speed of 10 m/s. What is the maximum height reached? (Ignore air resistance.)

Accepted Answer

$$h = \frac{v^2$}{2g} = \frac{100}{19.6} = 5.1\ \mathrm{m}$$

Question 18

A 2 kg object moving at 3 m/s collides with a 1 kg object moving at -2 m/s. What is the total momentum before the collision?

Accepted Answer

$$p_{total} = 2 	imes 3 + 1 	imes (-2) = 4\ \mathrm{kg\cdot m/s}$$

Question 19

A 0.5 kg ball is dropped from a height of 2 m onto a spring ($$k = 100\ \mathrm{N/m}). $$What is the maximum compression of the spring? (Assume no energy loss.)

Accepted Answer

$$x = \sqrt{\frac{mgH}{0.5k}} = \sqrt{\frac{0.5 	imes 9.8 	imes 2}{0.5 	imes 100}} = 0.44\ \mathrm{m}$$

Work, Energy, and Momentum: Exam 3 Review Notes

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