Q: A 2 kg book is lifted from the floor to a shelf 1.5 m high. What is the change in gravitational potential energy?

$$\Delta U_g = 2 \times 9.8 \times 1.5 = 29.4 J$$

Q: A 3 kg object is moving at 4 m/s. What is its kinetic energy?

$$K = \frac{1}{2} \times 3 \times 4^2$ = 24 J$$

Q: A force acts at an angle $$\theta to $$the direction of displacement. Which expression gives the work done?

$$W = F \cos(\theta) \Delta r$$

Q: A 5 kg object is dropped from a height of 10 m. What is the work done by gravity as it falls?

$$W = 5 \times 9.8 \times 10 = 490 J$$

Question 1

Which of the following best describes the result of the dot product of two vectors $$\vec{a}$$ and $$\vec{b}$$?

Accepted Answer

A scalar quantity given by $$\vec{a} \cdot \vec{b} = ab \cos(	heta)$$

Question 2

If a force $$\vec{F}$$ acts on an object moving from position $$\vec{r}_i to$$ $$\vec{r}_f$$, which integral represents the work done by the force?

Accepted Answer

$$\displaystyle W = \$$int_{\vec{r}$$_i}^{\vec{r}_f} \vec{F} \cdot d\vec{r}$$

Question 3

Which scenario results in zero work being done by a force $$\vec{F} on an $$object?

Accepted Answer

The force is perpendicular to the velocity of the object

Question 4

A 2 kg book is lifted from the floor to a shelf 1.5 m high. What is the change in gravitational potential energy?

Accepted Answer

$$\Delta U_g = 2 	imes 9.8 	imes 1.5 = 29.4 J$$

Question 5

Which of the following statements about conservative forces is TRUE?

Accepted Answer

The work done by a conservative force is equal to the negative change in potential energy

Question 6

A block slides down a rough incline. Which expression correctly represents the work done by kinetic friction?

Accepted Answer

$$W_f = -f_k d$$

Question 7

If the net work done on an object is positive, what happens to its kinetic energy?

Accepted Answer

It increases

Question 8

Which formula gives the kinetic energy of an object of mass $$m$$ moving at speed $$v$$?

Accepted Answer

$$K = \frac{1}{2} m v^2$

Question 9

A 3 kg object is moving at 4 m/s. What is its kinetic energy?

Accepted Answer

$$K = \frac{1}{2} 	imes 3 	imes 4^2$ = 24 J$$

Question 10

Which of the following is NOT a property of work?

Accepted Answer

Work always increases the energy of a system

Question 11

An object is moved from the ground to a shelf of height $$h$$ along three different paths. What is the work done by gravity in each case?

Accepted Answer

$$W = -mgh$$

Question 12

Which equation correctly relates the net work done on an object to its change in kinetic energy?

Accepted Answer

$$\Delta K = W_{net}$$

Question 13

A force acts at an angle $$	heta to $$the direction of displacement. Which expression gives the work done?

Accepted Answer

$$W = F \cos(	heta) \Delta r$$

Question 14

Which of the following is a correct expression for the mechanical energy of a system?

Accepted Answer

$$E_{mech} = U + K$$

Question 15

If the work done by a force depends on the path taken, what type of force is it?

Accepted Answer

Nonconservative force

Question 16

Which of the following forces is NOT considered conservative?

Accepted Answer

Kinetic friction

Question 17

A student pushes a box horizontally across a floor with a constant force. If the box moves 5 m and the force is 10 N, what is the work done?

Accepted Answer

$$W = 10 	imes 5 = 50 J$$

Question 18

Which of the following best describes the change in gravitational potential energy when an object is lowered from a height $$y_i to$$ $$y_f$$?

Accepted Answer

$$\Delta U_g = m g (y_f - y_i)$$

Question 19

If two objects involved in a conservative force are both included in your system, what is the work done by that force on the system?

Accepted Answer

It is zero

Question 20

A 5 kg object is dropped from a height of 10 m. What is the work done by gravity as it falls?

Accepted Answer

$$W = 5 	imes 9.8 	imes 10 = 490 J$$

Work, Energy, and the Dot Product in Physics with Calculus

Study Guide - Practice Questions

Study Guide - Flashcards