Q: A 5 kg box is pulled across a horizontal surface by a rope that makes a $$30^\circ$$ angle with the horizontal. If the tension in the rope is 40 N and the box moves 8 m, how much work is done by the rope on the box?

$$W = 40 \times 8 \times \cos 30^\circ = 277 \text{ J}$$

Q: A 2 kg object is dropped from a height of 10 m. Ignoring air resistance, what is its speed just before hitting the ground? (Use $$g = 9.8 \ \text{m/s}^2)$$

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 10} = 14 \ \text{m/s}$$

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

$$0 \ \text{m/s} (it $$comes to rest)

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

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

Q: A 70 kg astronaut in space throws a 2 kg wrench away from herself at $$3 \ \text{m/s}. $$What is her recoil velocity?

$$v = -\frac{2 \times 3}{70} = -0.086 \ \text{m/s}$$

Q: A car of mass 1000 kg accelerates from rest to $$20 \ \text{m/s} in 10 $$seconds. What is the average power output if the net force is constant?

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

Q: A 3 kg object moves in a straight line under a net force of 12 N for 4 seconds. What is the change in momentum of the object?

$$\Delta p = F \Delta t = 12 \times 4 = 48 \ \text{kg} \cdot \text{m/s}$$

Question 1

A 5 kg box is pulled across a horizontal surface by a rope that makes a $$30^\circ$$ angle with the horizontal. If the tension in the rope is 40 N and the box moves 8 m, how much work is done by the rope on the box?

Accepted Answer

$$W = 40 	imes 8 	imes \cos 30^\circ = 277 	ext{ J}$$

Question 2

Which of the following statements best describes Newton's Third Law of Motion?

Accepted Answer

For every action, there is an equal and opposite reaction.

Question 3

A 2 kg object is dropped from a height of 10 m. Ignoring air resistance, what is its speed just before hitting the ground? (Use $$g = 9.8 \ 	ext{m/s}^2)$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 10} = 14 \ 	ext{m/s}$$

Question 4

Which of the following is a correct statement about conservative and nonconservative forces?

Accepted Answer

Conservative forces have potential energies associated with them, while nonconservative forces do not.

Question 5

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

Accepted Answer

$$0 \ 	ext{m/s} (it $$comes to rest)

Question 6

Which equation correctly expresses the work-energy theorem?

Accepted Answer

$$W_{	ext{net}} = \Delta K$$

Question 7

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

Accepted Answer

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

Question 8

A 70 kg astronaut in space throws a 2 kg wrench away from herself at $$3 \ 	ext{m/s}. $$What is her recoil velocity?

Accepted Answer

$$v = -\frac{2 	imes 3}{70} = -0.086 \ 	ext{m/s}$$

Question 9

Which of the following best describes the relationship between force and potential energy for a conservative force?

Accepted Answer

$$F = -\frac{dU}{dx}$$

Question 10

A car of mass 1000 kg accelerates from rest to $$20 \ 	ext{m/s} in 10 $$seconds. What is the average power output if the net force is constant?

Accepted Answer

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

Question 11

A 3 kg object moves in a straight line under a net force of 12 N for 4 seconds. What is the change in momentum of the object?

Accepted Answer

$$\Delta p = F \Delta t = 12 	imes 4 = 48 \ 	ext{kg} \cdot 	ext{m/s}$$

Question 12

Which of the following is true about the center of mass of a system?

Accepted Answer

The center of mass moves as if all the external forces act on a single particle of mass equal to the total mass.

Question 13

A 0.2 kg ball is thrown vertically upward with a speed of $$10 \ 	ext{m/s}. $$What is the maximum height it reaches? (Ignore air resistance, $$g = 9.8 \ 	ext{m/s}^2)$$

Accepted Answer

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

Question 14

Which of the following best describes the difference between mass and weight?

Accepted Answer

Mass is a measure of the amount of matter in an object, while weight is the force of gravity acting on that mass.

Question 15

A 1.5 kg block slides down a frictionless incline of height 2 m. What is its speed at the bottom?

Accepted Answer

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

Question 16

A 0.3 kg puck slides on ice and comes to rest after traveling 10 m. If the friction force is $$0.15 \ 	ext{N}$$, how much work is done by friction?

Accepted Answer

$$W = -F d = -0.15 	imes 10 = -1.5 \ 	ext{J}$$

Question 17

Which of the following is true for a completely inelastic collision?

Accepted Answer

The colliding objects stick together and move with a common velocity after the collision.

Question 18

A force $$F(x) = 4x (in N) $$acts on a particle moving from $$x = 0 to$$ $$x = 3 m. $$What is the work done by this force?

Accepted Answer

$$W = \$$int_0$$^3 4x \, dx = 2x^2$ \Big|_0^3$ = 18 \ 	ext{J}$$

Question 19

A 2 kg object moving at $$5 \ 	ext{m/s}$$ collides with a 3 kg object at rest. If they stick together after the collision, what is their final velocity?

Accepted Answer

$$v_f = \frac{2 	imes 5 + 3 	imes 0}{2 + 3} = 2 \ 	ext{m/s}$$

PHY 251 Exam 2 Study Guide: Forces, Work & Energy, Momentum

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