Q: A box of mass $$5\ \mathrm{kg} is $$pushed across a horizontal floor by a constant force of $$20\ \mathrm{N}$$ over a distance of $$3\ \mathrm{m}. $$What is the work done by the force on the box?

$$W = F \times d = 20 \times 3 = 60\ \mathrm{J}$$

Q: A spring with spring constant $$k = 200\ \mathrm{N/m} is $$compressed by $$0.1\ \mathrm{m}. $$What is the elastic potential energy stored in the spring?

$$U = \frac{1}{2} k x^2$ = \frac{1}{2} \times 200 \times (0.1)^2$ = 1\ \mathrm{J}$$

Q: A $$2\ \mathrm{kg}$$ object is dropped from a height of $$5\ \mathrm{m}. $$Ignoring air resistance, what is its speed just before hitting the ground?

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

Q: Which equation expresses the Work-Energy Theorem?

$$W_{\text{net}} = \Delta K = K_f - K_i$$

Q: A $$1\ \mathrm{kg}$$ object moving at $$3\ \mathrm{m/s}$$ collides with a $$2\ \mathrm{kg}$$ object moving at $$-2\ \mathrm{m/s}. $$What is the total momentum before the collision?

$$p = m_1$ v_1$ + m_2$ v_2$ = 1 \times 3 + 2 \times (-2) = 3 - 4 = -1\ \mathrm{kg\cdot m/s}$$

Q: A $$0.2\ \mathrm{kg}$$ ball is thrown vertically upward with a speed of $$10\ \mathrm{m/s}. $$What is its maximum height?

$$h = \frac{v^2$}{2g} = \frac{10^2$}{2 \times 9.8} \approx 5.1\ \mathrm{m}$$

Question 1

A box of mass $$5\ \mathrm{kg} is $$pushed across a horizontal floor by a constant force of $$20\ \mathrm{N}$$ over a distance of $$3\ \mathrm{m}. $$What is the work done by the force on the box?

Accepted Answer

$$W = F 	imes d = 20 	imes 3 = 60\ \mathrm{J}$$

Question 2

Which of the following best describes the difference between conservative and non-conservative forces?

Accepted Answer

Conservative forces do not change the total mechanical energy of a system, while non-conservative forces do.

Question 3

A spring with spring constant $$k = 200\ \mathrm{N/m} is $$compressed by $$0.1\ \mathrm{m}. $$What is the elastic potential energy stored in the spring?

Accepted Answer

$$U = \frac{1}{2} k x^2$ = \frac{1}{2} 	imes 200 	imes (0.1)^2$ = 1\ \mathrm{J}$$

Question 4

A $$2\ \mathrm{kg}$$ object is dropped from a height of $$5\ \mathrm{m}. $$Ignoring air resistance, what is its speed just before hitting the ground?

Accepted Answer

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

Question 5

Which equation expresses the Work-Energy Theorem?

Accepted Answer

$$W_{	ext{net}} = \Delta K = K_f - K_i$$

Question 6

A $$0.5\ \mathrm{kg}$$ ball moving at $$4\ \mathrm{m/s}$$ collides elastically with a stationary $$0.5\ \mathrm{kg}$$ ball. What is the velocity of the first ball after the collision?

Accepted Answer

$$0\ \mathrm{m/s}$$

Question 7

A $$3\ \mathrm{kg}$$ object moving at $$2\ \mathrm{m/s}$$ collides inelastically with a $$2\ \mathrm{kg}$$ object at rest. What is their final velocity after the collision?

Accepted Answer

$$v_f = \frac{m_1$ v_1$ + m_2$ v_2$}{m_1$ + m_2$} = \frac{3 	imes 2 + 2 	imes 0}{3 + 2} = 1.2\ \mathrm{m/s}$$

Question 8

Which of the following is true about the conservation of momentum in collisions?

Accepted Answer

Momentum of the system is conserved in both elastic and inelastic collisions, provided no external force acts.

Question 9

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

Accepted Answer

$$p = m_1$ v_1$ + m_2$ v_2$ = 1 	imes 3 + 2 	imes (-2) = 3 - 4 = -1\ \mathrm{kg\cdot m/s}$$

Question 10

Which of the following statements about elastic collisions is correct?

Accepted Answer

Both kinetic energy and momentum are conserved in elastic collisions.

Question 11

A $$0.2\ \mathrm{kg}$$ ball is thrown vertically upward with a speed of $$10\ \mathrm{m/s}. $$What is its maximum height?

Accepted Answer

$$h = \frac{v^2$}{2g} = \frac{10^2$}{2 	imes 9.8} \approx 5.1\ \mathrm{m}$$

Question 12

Which of the following is an example of a non-conservative force?

Accepted Answer

Friction

Question 13

A $$1\ \mathrm{kg}$$ cart moving at $$2\ \mathrm{m/s}$$ collides and sticks to a $$2\ \mathrm{kg}$$ cart at rest. What is the final kinetic energy of the system?

Accepted Answer

$$K_f = \frac{1}{2} (m_1$ + m_2$) v_f^2$, where v_f$$ = \frac{$$m_1$$ $$v_1$$}{$$m_1$$ + $$m_2$$} = \frac{1 	imes 2}{3} = 0.67\ \mathrm{m/s}$$, so K_f$$ = \frac{1}{2} 	imes 3 	imes $$(0.67)^2$$ \approx 0.67\ \mathrm{J}$$

Question 14

A $$0.5\ \mathrm{kg}$$ object is attached to a spring and oscillates with amplitude $$0.2\ \mathrm{m}$$ and spring constant $$k = 50\ \mathrm{N/m}. $$What is its maximum kinetic energy?

Accepted Answer

$$K_{	ext{max}} = \frac{1}{2} k A^2$ = \frac{1}{2} 	imes 50 	imes (0.2)^2$ = 1\ \mathrm{J}$$

Question 15

Which of the following best describes impulse in physics?

Accepted Answer

Impulse is the change in momentum of an object, $$J = \Delta p = F_{	ext{avg}} \Delta t$$

Question 16

A $$2\ \mathrm{kg}$$ object is acted on by a force of $$10\ \mathrm{N}$$ for $$0.5\ \mathrm{s}. $$What is the change in velocity of the object?

Accepted Answer

$$\Delta v = \frac{F \Delta t}{m} = \frac{10 	imes 0.5}{2} = 2.5\ \mathrm{m/s}$$

Question 17

A $$1\ \mathrm{kg}$$ ball moving at $$5\ \mathrm{m/s}$$ bounces off a wall and returns at $$-4\ \mathrm{m/s}. $$What is the magnitude of the impulse delivered by the wall?

Accepted Answer

$$J = m (v_f - v_i) = 1 	imes (-4 - 5) = -9\ \mathrm{kg\cdot m/s}$$; magnitude is $$9\ \mathrm{kg\cdot m/s}$$

Question 18

Which of the following is true about the rate at which work is performed (power)?

Accepted Answer

Power is the rate at which work is done, $$P = \frac{W}{t}$$

Question 19

A $$60\ \mathrm{kg}$$ person runs up a $$5\ \mathrm{m}$$ high flight of stairs in $$4\ \mathrm{s}. $$What is the average power output?

Accepted Answer

$$P = \frac{mgh}{t} = \frac{60 	imes 9.8 	imes 5}{4} = 735\ \mathrm{W}$$

Work, Energy, and Momentum: Study Notes for College Physics

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