Q: Given the vectors $$\vec{A}$$ and $$\vec{B}$$ shown in the first image, which of the following correctly expresses the dot product $$\vec{A} \cdot \vec{B} in $$terms of their magnitudes and the angle $$\theta$$ between them?

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

Q: A 5000-kg freight car (see third image) compresses a spring with spring constant $$k = 46,000\ \mathrm{N/m} by$$ $$0.46\ \mathrm{m}. $$What is the potential energy stored in the spring at maximum compression?

$$U = \frac{1}{2} k x^2$ = \frac{1}{2} \times 46,000 \times (0.46)^2$ = 4,873\ \mathrm{J}$$

Q: In the fourth image, a boy pulls a wagon with a force $$F = 40.5\ \mathrm{N} at an $$angle of $$30^\circ$$ over a distance of $$1.475\ \mathrm{m}. $$What is the work done by the boy?

$$W = Fd \cos \theta = 40.5 \times 1.475 \times \cos 30^\circ = 51.7\ \mathrm{J}$$

Q: A basketball player throws a 1.00 kg ball straight up with an initial speed of $$6.50\ \mathrm{m/s}$$ from a height of $$1.80\ \mathrm{m}. $$What is the maximum height (above the ground) the ball reaches? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$h_{max} = 1.80 + \frac{(6.50)^2$}{2 \times 9.8} = 4.96\ \mathrm{m}$$

Q: A car of mass $$65.0\ \mathrm{kg}$$ crashes into a tree and stops in $$0.24\ \mathrm{s}$$ from an initial speed of $$5.50\ \mathrm{m/s}. $$What is the magnitude of the average force exerted by the seatbelt on the driver?

$$F_{avg} = \frac{m \Delta v}{\Delta t} = \frac{65.0 \times 5.50}{0.24} = 1,489.6\ \mathrm{N}$$

Q: During an ice show, a $$62.5\ \mathrm{kg}$$ skater moving at $$4.75\ \mathrm{m/s}$$ collides with and is caught by a stationary $$75.0\ \mathrm{kg}$$ skater. What is their final speed after the collision?

$$v_f = \frac{m_1$ v_1$}{m_1$ + m_2$} = \frac{62.5 \times 4.75}{62.5 + 75.0} = 2.13\ \mathrm{m/s}$$

Q: A 1.00 kg basketball is thrown straight up with an initial speed of $$6.50\ \mathrm{m/s}$$ from a height of $$1.80\ \mathrm{m}. $$What is the gravitational potential energy at the maximum height? (Let $$U = 0 at $$ground level, $$g = 9.8\ \mathrm{m/s^2$})$$

$$U = mgh = 1.00 \times 9.8 \times 4.96 = 48.6\ \mathrm{J}$$

Q: A car of mass $$65.0\ \mathrm{kg}$$ crashes into a tree and stops in $$0.24\ \mathrm{s}$$ from an initial speed of $$5.50\ \mathrm{m/s}. $$What is the change in momentum of the driver?

$$\Delta p = m(v_f - v_i) = 65.0 \times (0 - 5.50) = -357.5\ \mathrm{kg\cdot m/s}$$

Question 1

Given the vectors $$\vec{A}$$ and $$\vec{B}$$ shown in the first image, which of the following correctly expresses the dot product $$\vec{A} \cdot \vec{B} in $$terms of their magnitudes and the angle $$	heta$$ between them?

Accepted Answer

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

Question 2

A box is being pushed in the negative x-direction on a horizontal floor, as shown in the second image. What is the work done by the normal force on the box as it moves?

Accepted Answer

The work is zero.

Question 3

A 5000-kg freight car (see third image) compresses a spring with spring constant $$k = 46,000\ \mathrm{N/m} by$$ $$0.46\ \mathrm{m}. $$What is the potential energy stored in the spring at maximum compression?

Accepted Answer

$$U = \frac{1}{2} k x^2$ = \frac{1}{2} 	imes 46,000 	imes (0.46)^2$ = 4,873\ \mathrm{J}$$

Question 4

In the fourth image, a boy pulls a wagon with a force $$F = 40.5\ \mathrm{N} at an $$angle of $$30^\circ$$ over a distance of $$1.475\ \mathrm{m}. $$What is the work done by the boy?

Accepted Answer

$$W = Fd \cos 	heta = 40.5 	imes 1.475 	imes \cos 30^\circ = 51.7\ \mathrm{J}$$

Question 5

A basketball player throws a 1.00 kg ball straight up with an initial speed of $$6.50\ \mathrm{m/s}$$ from a height of $$1.80\ \mathrm{m}. $$What is the maximum height (above the ground) the ball reaches? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$h_{max} = 1.80 + \frac{(6.50)^2$}{2 	imes 9.8} = 4.96\ \mathrm{m}$$

Question 6

A car of mass $$65.0\ \mathrm{kg}$$ crashes into a tree and stops in $$0.24\ \mathrm{s}$$ from an initial speed of $$5.50\ \mathrm{m/s}. $$What is the magnitude of the average force exerted by the seatbelt on the driver?

Accepted Answer

$$F_{avg} = \frac{m \Delta v}{\Delta t} = \frac{65.0 	imes 5.50}{0.24} = 1,489.6\ \mathrm{N}$$

Question 7

During an ice show, a $$62.5\ \mathrm{kg}$$ skater moving at $$4.75\ \mathrm{m/s}$$ collides with and is caught by a stationary $$75.0\ \mathrm{kg}$$ skater. What is their final speed after the collision?

Accepted Answer

$$v_f = \frac{m_1$ v_1$}{m_1$ + m_2$} = \frac{62.5 	imes 4.75}{62.5 + 75.0} = 2.13\ \mathrm{m/s}$$

Question 8

Which of the following statements about potential energy is correct?

Accepted Answer

Potential energy can be negative depending on the choice of reference point.

Question 9

A force $$\vec{F}$$ acts at an angle $$	heta to $$the direction of displacement $$\vec{d}. $$Which formula gives the work done by the force?

Accepted Answer

$$W = Fd \cos 	heta$$

Question 10

A 1.00 kg basketball is thrown straight up with an initial speed of $$6.50\ \mathrm{m/s}$$ from a height of $$1.80\ \mathrm{m}. $$What is the gravitational potential energy at the maximum height? (Let $$U = 0 at $$ground level, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$U = mgh = 1.00 	imes 9.8 	imes 4.96 = 48.6\ \mathrm{J}$$

Question 11

A 5000-kg freight car compresses a spring by $$0.46\ \mathrm{m}$$ and comes to rest. What was the car's initial kinetic energy before hitting the spring?

Accepted Answer

$$KE = \frac{1}{2} k x^2$ = 4,873\ \mathrm{J}$$

Question 12

A car of mass $$65.0\ \mathrm{kg}$$ crashes into a tree and stops in $$0.24\ \mathrm{s}$$ from an initial speed of $$5.50\ \mathrm{m/s}. $$What is the change in momentum of the driver?

Accepted Answer

$$\Delta p = m(v_f - v_i) = 65.0 	imes (0 - 5.50) = -357.5\ \mathrm{kg\cdot m/s}$$

Question 13

A boy pulls a wagon with a force of $$40.5\ \mathrm{N} at$$ $$30^\circ$$ for $$1.475\ \mathrm{m} in$$ $$60\ \mathrm{s}. $$What is his average power output?

Accepted Answer

$$P = \frac{W}{t} = \frac{51.7}{60} = 0.86\ \mathrm{W}$$

Question 14

Which of the following best describes the type of collision when a moving skater is caught by a stationary skater and they move together afterward?

Accepted Answer

Perfectly inelastic collision

Question 15

A force acts perpendicular to the displacement of an object. What is the work done by this force?

Accepted Answer

Zero

Question 16

A 1.00 kg basketball is thrown straight up with an initial speed of $$6.50\ \mathrm{m/s}$$ from a height of $$1.80\ \mathrm{m}. $$What is the work done by gravity as the ball rises to its maximum height?

Accepted Answer

$$W = -mgh = -1.00 	imes 9.8 	imes (4.96 - 1.80) = -31.0\ \mathrm{J}$$

Physics Exam Study Guide: Work, Energy, Momentum, and Collisions

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