Q: Given the vectors $$\vec{A}$$ and $$\vec{B}$$ shown in the first image, which of the following correctly expresses the dot product between $$\vec{A}$$ and $$\vec{B}$$?

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

Q: What is the gravitational potential energy of the basketball at its maximum height, if zero potential energy is defined at ground level?

$$U = mgh = 1.00 \times 9.8 \times 3.96 = 38.8\ \mathrm{J}$$

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

$$U = \frac{1}{2} k x^2$ = \frac{1}{2} \times 46,000 \times (0.46)^2$ = 4,873.4\ \mathrm{J}$$

Q: Given the initial kinetic energy and the mass of the freight car, what was its initial speed $$v_0$$ before hitting the spring?

$$v_0$$ = \sqrt{\frac{2 \times 4,873.4}{5,000}} = 1.4\ \mathrm{m/s}$$

Q: A boy pulls his sister in a wagon (see fourth image) with a force $$F = 40.5\ \mathrm{N} at an $$angle of $$30^\circ to $$the horizontal for a distance of $$1.475\ \mathrm{m}. $$How much work does he do?

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

Q: A 62.5 kg skater jumps with a horizontal speed of 4.75 m/s and is caught by a stationary 75.0 kg skater. What is the magnitude of the initial momentum of the 62.5 kg skater?

$$p = m v = 62.5 \times 4.75 = 297\ \mathrm{kg \cdot m/s}$$

Q: A car driver of mass 65.0 kg is moving at 5.50 m/s and comes to a stop in 0.24 s due to a collision. 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 between $$\vec{A}$$ and $$\vec{B}$$?

Accepted Answer

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

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?

Accepted Answer

Zero

Question 3

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

Accepted Answer

$$3.96\ \mathrm{m}$$

Question 4

What is the gravitational potential energy of the basketball at its maximum height, if zero potential energy is defined at ground level?

Accepted Answer

$$U = mgh = 1.00 	imes 9.8 	imes 3.96 = 38.8\ \mathrm{J}$$

Question 5

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

Accepted Answer

$$U = \frac{1}{2} k x^2$ = \frac{1}{2} 	imes 46,000 	imes (0.46)^2$ = 4,873.4\ \mathrm{J}$$

Question 6

What was the initial kinetic energy of the freight car before it compressed the spring?

Accepted Answer

$$4,873.4\ \mathrm{J}$$

Question 7

Given the initial kinetic energy and the mass of the freight car, what was its initial speed $$v_0$$ before hitting the spring?

Accepted Answer

$$v_0$$ = \sqrt{\frac{2 	imes 4,873.4}{5,000}} = 1.4\ \mathrm{m/s}$$

Question 8

A boy pulls his sister in a wagon (see fourth image) with a force $$F = 40.5\ \mathrm{N} at an $$angle of $$30^\circ to $$the horizontal for a distance of $$1.475\ \mathrm{m}. $$How much work does he do?

Accepted Answer

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

Question 9

If the boy pulls the wagon 1.475 m in one minute, what is his average power output?

Accepted Answer

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

Question 10

A 62.5 kg skater jumps with a horizontal speed of 4.75 m/s and is caught by a stationary 75.0 kg skater. What is the magnitude of the initial momentum of the 62.5 kg skater?

Accepted Answer

$$p = m v = 62.5 	imes 4.75 = 297\ \mathrm{kg \cdot m/s}$$

Question 11

After the collision, what is the final speed of both skaters moving together?

Accepted Answer

$$v_f = \frac{297}{62.5 + 75.0} = 2.06\ \mathrm{m/s}$$

Question 12

A car driver of mass 65.0 kg is moving at 5.50 m/s and comes to a stop in 0.24 s due to a collision. 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

What is the magnitude of the impulse delivered to the driver by the seatbelt during the collision?

Accepted Answer

$$J = |\Delta p| = 357.5\ \mathrm{kg \cdot m/s}$$

Question 14

What is the magnitude of the average force exerted by the seatbelt on the driver to bring her to a halt?

Accepted Answer

$$F_{avg} = \frac{J}{\Delta t} = \frac{357.5}{0.24} = 1,489.6\ \mathrm{N}$$

Question 15

Which of the following statements about potential energy is correct?

Accepted Answer

A system can have negative potential energy depending on the reference point.

Question 16

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 17

Which of the following is true about the work done by gravity on an elevator moving upward?

Accepted Answer

The work done by gravity is negative.

Physics I: Work, Energy, Momentum, and Collisions – Guided Study Notes

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