Q: A 5 kg object is pushed with a constant force of 20 N over a displacement of 3 m in the same direction as the force. What is the work done on the object?

$$W = 20 \times 3 = 60\ \text{J}$$

Q: A 2 kg object moves at 4 m/s. What is its kinetic energy?

$$K = \frac{1}{2} \times 2 \times 4^2$ = 16\ \text{J}$$

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

$$U_{elastic} = \frac{1}{2} \times 200 \times (0.1)^2$ = 1\ \text{J}$$

Q: A 3 kg object is lifted to a height of 5 m. What is its gravitational potential energy relative to the ground? (Take $$g = 9.8\ \text{m/s}^2)$$

$$U_{grav} = 3 \times 9.8 \times 5 = 147\ \text{J}$$

Q: A spring is stretched by 0.2 m and exerts a force of 40 N. What is the spring constant?

$$k = \frac{F_x}{x} = \frac{40}{0.2} = 200\ \text{N/m}$$

Q: Two cars, one of mass 1000 kg moving at 10 m/s and another of mass 1500 kg moving at 5 m/s, collide and stick together. What is their final velocity?

$$v_f = \frac{1000 \times 10 + 1500 \times 5}{1000 + 1500} = 7\ \text{m/s}$$

Q: A 0.5 kg ball is dropped from a height of 2 m. What is its speed just before hitting the ground? (Ignore air resistance, $$g = 9.8\ \text{m/s}^2)$$

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 2} = 6.26\ \text{m/s}$$

Q: A 1 kg object moving at 3 m/s collides elastically with a stationary 2 kg object. What is the velocity of the 1 kg object after the collision?

$$v_{1f} = \frac{(1-2)\times3}{1+2} = -1\ \text{m/s}$$

Q: A 0.2 kg mass attached to a spring oscillates with a maximum displacement of 0.05 m. If the spring constant is 100 N/m, what is the maximum elastic potential energy?

$$U_{elastic} = \frac{1}{2} \times 100 \times (0.05)^2$ = 0.125\ \text{J}$$

Question 1

A 5 kg object is pushed with a constant force of 20 N over a displacement of 3 m in the same direction as the force. What is the work done on the object?

Accepted Answer

$$W = 20 	imes 3 = 60\ 	ext{J}$$

Question 2

Which equation best describes the momentum of a moving object?

Accepted Answer

$$\vec{p} = m \vec{v}$$

Question 3

Two objects collide and stick together. Which equation must always be satisfied for their momenta?

Accepted Answer

$$\vec{p}_i = \vec{p}_f$$

Question 4

A 2 kg object moves at 4 m/s. What is its kinetic energy?

Accepted Answer

$$K = \frac{1}{2} 	imes 2 	imes 4^2$ = 16\ 	ext{J}$$

Question 5

Which formula represents the work-energy theorem?

Accepted Answer

$$W_{total} = \Delta K$$

Question 6

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

Accepted Answer

$$U_{elastic} = \frac{1}{2} 	imes 200 	imes (0.1)^2$ = 1\ 	ext{J}$$

Question 7

What is the escape velocity from Earth, given $$G = 6.674 	imes 10$$^{-11}$$\ 	ext{m}^3	ext{kg}^{-1}	ext{s}^{-2}$$, $$M_E = 5.972 	imes 10$$^{24}$$\ 	ext{kg}$$, and $$R_E = 6.371 	imes 10^6$\ 	ext{m}$$?

Accepted Answer

$$v_{escape} = \sqrt{\frac{2GM_E}{R_E}}$$

Question 8

A 3 kg object is lifted to a height of 5 m. What is its gravitational potential energy relative to the ground? (Take $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$U_{grav} = 3 	imes 9.8 	imes 5 = 147\ 	ext{J}$$

Question 9

A spring is stretched by 0.2 m and exerts a force of 40 N. What is the spring constant?

Accepted Answer

$$k = \frac{F_x}{x} = \frac{40}{0.2} = 200\ 	ext{N/m}$$

Question 10

Two cars, one of mass 1000 kg moving at 10 m/s and another of mass 1500 kg moving at 5 m/s, collide and stick together. What is their final velocity?

Accepted Answer

$$v_f = \frac{1000 	imes 10 + 1500 	imes 5}{1000 + 1500} = 7\ 	ext{m/s}$$

Question 11

In a perfectly elastic collision, which quantity is conserved in addition to momentum?

Accepted Answer

Kinetic energy

Question 12

A 0.5 kg ball is dropped from a height of 2 m. What is its speed just before hitting the ground? (Ignore air resistance, $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 2} = 6.26\ 	ext{m/s}$$

Question 13

A 1 kg object moving at 3 m/s collides elastically with a stationary 2 kg object. What is the velocity of the 1 kg object after the collision?

Accepted Answer

$$v_{1f} = \frac{(1-2)	imes3}{1+2} = -1\ 	ext{m/s}$$

Question 14

A 0.2 kg mass attached to a spring oscillates with a maximum displacement of 0.05 m. If the spring constant is 100 N/m, what is the maximum elastic potential energy?

Accepted Answer

$$U_{elastic} = \frac{1}{2} 	imes 100 	imes (0.05)^2$ = 0.125\ 	ext{J}$$

Question 15

A 4 kg object is moving at 2 m/s. What is its momentum?

Accepted Answer

$$p = m v = 4 	imes 2 = 8\ 	ext{kg}\cdot	ext{m/s}$$

Question 16

A 2 kg object is dropped from a height of 10 m. What is its kinetic energy just before it hits the ground?

Accepted Answer

$$K = mgh = 2 	imes 9.8 	imes 10 = 196\ 	ext{J}$$

Question 17

A 1 kg object is attached to a spring with $$k = 50\ 	ext{N/m}$$ and is stretched by 0.2 m. What is the restoring force?

Accepted Answer

$$F_x = -k x = -50 	imes 0.2 = -10\ 	ext{N}$$

Question 18

A 0.5 kg object is moving at 6 m/s. What is its kinetic energy?

Accepted Answer

$$K = \frac{1}{2} 	imes 0.5 	imes 6^2$ = 9\ 	ext{J}$$

Work, Energy, and Momentum in Classical Mechanics

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