Q: Which of the following correctly represents the dot product between vectors $$\vec{A}$$ and $$\vec{B} as $$shown in the first image?

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

Q: A 5000-kg freight car rolls along frictionless rails and compresses a spring with spring constant $$k = 46{,}000\ \text{N/m} by$$ $$0.46\ \text{m}$$, as shown in the third image. What is the potential energy stored in the spring when the car is at rest?

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

Q: A basketball player throws a 1.00 kg ball straight up with an initial speed of $$6.50\ \text{m/s}$$ from a height of $$1.80\ \text{m}. $$What is the maximum height reached by the ball above the ground?

$$h_{\text{max}} = 1.80 + \frac{v_0$^2}{2g}$$

Q: A 62.5 kg skater leaps into the air and is caught by a stationary 75.0 kg skater. If the initial speed of the first skater is $$4.75\ \text{m/s}$$, what is the magnitude of her initial momentum?

$$p = m_1$ v_1$ = 62.5 \times 4.75$$

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

$$\Delta p = m \Delta v = 65.0 \times (0 - 5.50)$$

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

$$F_{\text{avg}} = \frac{\Delta p}{\Delta t}$$

Question 1

Which of the following correctly represents the dot product between vectors $$\vec{A}$$ and $$\vec{B} as $$shown in the first image?

Accepted Answer

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

Question 2

A box is being pushed in the negative x-direction on the 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 rolls along frictionless rails and compresses a spring with spring constant $$k = 46{,}000\ 	ext{N/m} by$$ $$0.46\ 	ext{m}$$, as shown in the third image. What is the potential energy stored in the spring when the car is at rest?

Accepted Answer

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

Question 4

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

Accepted Answer

$$W = Fd \cos 	heta$$

Question 5

Which of the following statements about potential energy is correct?

Accepted Answer

Potential energy can be negative depending on the reference point.

Question 6

A basketball player throws a 1.00 kg ball straight up with an initial speed of $$6.50\ 	ext{m/s}$$ from a height of $$1.80\ 	ext{m}. $$What is the maximum height reached by the ball above the ground?

Accepted Answer

$$h_{	ext{max}} = 1.80 + \frac{v_0$^2}{2g}$$

Question 7

What is the value of gravitational potential energy at the maximum height for the basketball in the previous question, assuming zero at ground level?

Accepted Answer

$$U = mgh_{	ext{max}}$$

Question 8

A 62.5 kg skater leaps into the air and is caught by a stationary 75.0 kg skater. If the initial speed of the first skater is $$4.75\ 	ext{m/s}$$, what is the magnitude of her initial momentum?

Accepted Answer

$$p = m_1$ v_1$ = 62.5 	imes 4.75$$

Question 9

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

Accepted Answer

$$v_f = \frac{m_1$ v_1$}{m_1$ + m_2$}$$

Question 10

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

Accepted Answer

$$\Delta p = m \Delta v = 65.0 	imes (0 - 5.50)$$

Question 11

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

Accepted Answer

$$J = \Delta p = m \Delta v$$

Question 12

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

Accepted Answer

$$F_{	ext{avg}} = \frac{\Delta p}{\Delta t}$$

Question 13

Which of the following is the correct unit for both work and energy?

Accepted Answer

Joule

Question 14

A freight car compresses a spring and comes to rest. What was the car's kinetic energy before it compressed the spring?

Accepted Answer

$$KE = \frac{1}{2} k x^2$

Question 15

A boy pulls a wagon for $$1.475\ 	ext{m} in $$one minute. If the work done is $$W$$, what is the boy’s power output?

Accepted Answer

$$P = \frac{W}{t}$$

Question 16

Which scenario best illustrates the conservation of mechanical energy?

Accepted Answer

A basketball thrown straight up, reaching maximum height and then falling back down.

Question 17

Which equation best describes the relationship between impulse and momentum?

Accepted Answer

$$J = \Delta p$$

Question 18

In a perfectly inelastic collision, which quantity is conserved?

Accepted Answer

Momentum

Question 19

A spring with constant $$k is $$compressed by $$x. $$What is the force exerted by the spring?

Accepted Answer

$$F = -kx$$

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

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