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

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

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?

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

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?

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

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 the ball reaches above the ground? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

$$h_{max} = 1.80 + \frac{(6.50)^2$}{2 \times 9.8} = 3.96\ \mathrm{m}$$

Q: A 62.5 kg skater moving at $$4.75\ \mathrm{m/s}$$ collides with a stationary 75.0 kg skater. After the collision, they move together. What is the final speed of both skaters?

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

Q: A car of mass $$65.0\ \mathrm{kg}$$ crashes into a tree at $$5.50\ \mathrm{m/s}$$ and stops in $$0.24\ \mathrm{s}. $$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: A car moving at $$5.50\ \mathrm{m/s}$$ comes to rest in $$0.24\ \mathrm{s}. $$What is the change in momentum of a $$65.0\ \mathrm{kg}$$ driver?

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

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, $$g = 9.8\ \mathrm{m/s^2$})$$

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

Question 1

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

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 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

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

Question 4

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

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

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 the ball reaches above the ground? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$h_{max} = 1.80 + \frac{(6.50)^2$}{2 	imes 9.8} = 3.96\ \mathrm{m}$$

Question 6

Is it possible for a system to have negative potential energy?

Accepted Answer

Yes, because potential energy is defined relative to a chosen reference point.

Question 7

An elevator is moving upwards. What is the work done by gravity on the elevator?

Accepted Answer

Negative

Question 8

A 62.5 kg skater moving at $$4.75\ \mathrm{m/s}$$ collides with a stationary 75.0 kg skater. After the collision, they move together. What is the final speed of both skaters?

Accepted Answer

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

Question 9

A car of mass $$65.0\ \mathrm{kg}$$ crashes into a tree at $$5.50\ \mathrm{m/s}$$ and stops in $$0.24\ \mathrm{s}. $$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 10

Which of the following best describes the type of collision when two skaters stick together after colliding?

Accepted Answer

Perfectly inelastic collision

Question 11

A car moving at $$5.50\ \mathrm{m/s}$$ comes to rest in $$0.24\ \mathrm{s}. $$What is the change in momentum of a $$65.0\ \mathrm{kg}$$ driver?

Accepted Answer

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

Question 12

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

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

Question 13

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

Accepted Answer

$$KE = \frac{1}{2} k x^2$ = 4,873.4\ \mathrm{J}$$

Question 14

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

Accepted Answer

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

Question 15

What is the magnitude of the impulse delivered to a $$65.0\ \mathrm{kg}$$ driver by the seatbelt if the car stops from $$5.50\ \mathrm{m/s} to $$rest?

Accepted Answer

$$J = m \Delta v = 65.0 	imes 5.50 = 357.5\ \mathrm{kg\cdot m/s}$$

Question 16

A 5000-kg freight car compresses a spring by $$0.46\ \mathrm{m}. $$What was its initial speed before hitting the spring? ($$k = 46,000\ \mathrm{N/m})$$

Accepted Answer

$$v_0$$ = \sqrt{\frac{k $$x^2$$}{m}} = \sqrt{\frac{46,000 	imes $$(0.46)^2$$}{5,000}} = 0.99\ \mathrm{m/s}$$

Question 17

What is the work done by gravity on a basketball thrown straight up from a height of $$1.80\ \mathrm{m} to $$its maximum height $$3.96\ \mathrm{m}$$?

Accepted Answer

$$W_g = -m g (h_{max} - h_{initial}) = -1.00 	imes 9.8 	imes (3.96 - 1.80) = -21.2\ \mathrm{J}$$

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

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