Q: Given two vectors $$\vec{A}$$ and $$\vec{B}$$ with an angle $$\theta$$ between them (as shown in the first image), which of the following correctly expresses their dot product?

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

Q: A 5000-kg freight car moving at speed $$v_0$$ compresses a spring with spring constant $$k = 46,000\ \mathrm{N/m} by$$ $$0.46\ \mathrm{m}$$ before coming to rest (see the third image). What is the potential energy stored in the spring at maximum compression?

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

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

$$W = F d \cos \theta = 40.5 \times 1.475 \times \cos 30^\circ$$

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 impulse delivered to the driver by the seatbelt?

$$J = m \Delta v = 65.0 \times 5.50$$

Q: A boy pulls a wagon with a force $$F at an $$angle $$\theta$$ for a distance $$d in $$time $$t. $$What is the average power output?

$$P = \frac{F d \cos \theta}{t}$$

Question 1

Given two vectors $$\vec{A}$$ and $$\vec{B}$$ with an angle $$	heta$$ between them (as shown in the first image), which of the following correctly expresses their dot product?

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 (see 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 moving at speed $$v_0$$ compresses a spring with spring constant $$k = 46,000\ \mathrm{N/m} by$$ $$0.46\ \mathrm{m}$$ before coming to rest (see the third image). What is the potential energy stored in the spring at maximum compression?

Accepted Answer

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

Question 4

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

Accepted Answer

$$W = F d \cos 	heta = 40.5 	imes 1.475 	imes \cos 30^\circ$$

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? (Neglect air resistance.)

Accepted Answer

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

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

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

Question 9

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 impulse delivered to the driver by the seatbelt?

Accepted Answer

$$J = m \Delta v = 65.0 	imes 5.50$$

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 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

$$W = F d \cos 	heta$$

Question 12

A 5000-kg freight car compresses a spring by $$0.46\ \mathrm{m}$$ and comes to rest. If the spring constant is $$46,000\ \mathrm{N/m}$$, what was the car's initial kinetic energy?

Accepted Answer

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

Question 13

A boy pulls a wagon with a force $$F at an $$angle $$	heta$$ for a distance $$d in $$time $$t. $$What is the average power output?

Accepted Answer

$$P = \frac{F d \cos 	heta}{t}$$

Question 14

A car of mass $$m$$ crashes and stops in time $$\Delta t$$ from speed $$v_0. $$What is the magnitude of the average force exerted by the seatbelt?

Accepted Answer

$$F_{avg} = \frac{m v_0$}{\Delta t}$$

Question 15

Which of the following statements about work and energy is correct?

Accepted Answer

Joule is the unit for both work and energy.

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

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