Q: A man pulls a vacuum cleaner with a force of magnitude $$F = 30.0\ \mathrm{N} at an $$angle of $$60.0^\circ$$ with the horizontal. If the vacuum cleaner is displaced $$4.00\ \mathrm{m} to $$the right, what is the work done by the force on the vacuum cleaner?

$$W = 30.0 \times 4.00 \times \cos 60.0^\circ = 60.0\ \mathrm{J}$$

Q: A $$0.50\ \mathrm{kg}$$ book is lifted from the floor to a shelf $$2.0\ \mathrm{m}$$ above the ground. What is the change in gravitational potential energy of the book? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$\Delta U = mgh = 0.50 \times 9.8 \times 2.0 = 9.8\ \mathrm{J}$$

Q: A block is attached to a spring and pulled so that the spring is stretched by $$0.10\ \mathrm{m}. If $$the spring constant is $$k = 200\ \mathrm{N/m}$$, what is the work done by the spring force as the block returns to equilibrium?

$$W = \frac{1}{2} k x^2$ = \frac{1}{2} \times 200 \times (0.10)^2$ = 1.0\ \mathrm{J}$$

Q: A $$0.35\ \mathrm{kg}$$ mass stretches a spring by $$2.0\ \mathrm{cm}. $$What is the force constant $$k of $$the spring? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$k = \frac{mg}{d} = \frac{0.35 \times 9.8}{0.020} = 171.5\ \mathrm{N/m}$$

Q: Which of the following best describes the relationship between the force and displacement vectors for maximum positive work?

The force and displacement are in the same direction ($$\theta = 0^\circ).$$

Q: A force $$F$$ acts on a box, causing a displacement $$\Delta r. In $$which case is the work done by the force most negative?

When the force is directly opposite to the displacement ($$\theta = 180^\circ).$$

Question 1

A man pulls a vacuum cleaner with a force of magnitude $$F = 30.0\ \mathrm{N} at an $$angle of $$60.0^\circ$$ with the horizontal. If the vacuum cleaner is displaced $$4.00\ \mathrm{m} to $$the right, what is the work done by the force on the vacuum cleaner?

Accepted Answer

$$W = 30.0 	imes 4.00 	imes \cos 60.0^\circ = 60.0\ \mathrm{J}$$

Question 2

Which of the following best describes the work done by the gravitational force on the Earth as it moves in a perfectly circular orbit around the Sun?

Accepted Answer

The work is zero because the force is perpendicular to the displacement.

Question 3

A box is pushed across a rough floor and comes to a stop due to friction. Which statement is true about the work done by friction?

Accepted Answer

The work done by friction is negative and equal in magnitude to the initial kinetic energy of the box.

Question 4

Which of the following forces is considered nonconservative?

Accepted Answer

Friction

Question 5

A spring with force constant $$k is $$stretched a distance $$x$$ from equilibrium. What is the elastic potential energy stored in the spring?

Accepted Answer

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

Question 6

A $$0.50\ \mathrm{kg}$$ book is lifted from the floor to a shelf $$2.0\ \mathrm{m}$$ above the ground. What is the change in gravitational potential energy of the book? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$\Delta U = mgh = 0.50 	imes 9.8 	imes 2.0 = 9.8\ \mathrm{J}$$

Question 7

Which of the following statements about conservative forces is correct?

Accepted Answer

The work done by a conservative force is independent of the path taken.

Question 8

A block is attached to a spring and pulled so that the spring is stretched by $$0.10\ \mathrm{m}. If $$the spring constant is $$k = 200\ \mathrm{N/m}$$, what is the work done by the spring force as the block returns to equilibrium?

Accepted Answer

$$W = \frac{1}{2} k x^2$ = \frac{1}{2} 	imes 200 	imes (0.10)^2$ = 1.0\ \mathrm{J}$$

Question 9

Which energy transformation occurs when a book is lifted from the floor and placed on a shelf?

Accepted Answer

Work is done against gravity and stored as gravitational potential energy.

Question 10

A $$0.35\ \mathrm{kg}$$ mass stretches a spring by $$2.0\ \mathrm{cm}. $$What is the force constant $$k of $$the spring? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$k = \frac{mg}{d} = \frac{0.35 	imes 9.8}{0.020} = 171.5\ \mathrm{N/m}$$

Question 11

Which of the following best describes the relationship between the force and displacement vectors for maximum positive work?

Accepted Answer

The force and displacement are in the same direction ($$	heta = 0^\circ).$$

Question 12

A force $$F$$ acts on a box, causing a displacement $$\Delta r. In $$which case is the work done by the force most negative?

Accepted Answer

When the force is directly opposite to the displacement ($$	heta = 180^\circ).$$

Question 13

The area under the force vs. displacement curve represents:

Accepted Answer

The work done by the force.

Question 14

A block slides down a frictionless incline. Which of the following statements is true?

Accepted Answer

The gravitational force does positive work, increasing the block's kinetic energy.

Question 15

Which of the following is a correct statement of the work-kinetic energy theorem?

Accepted Answer

$$K_f = K_i + W_{ext}$$

Question 16

A ball is thrown vertically upward. At the highest point, which of the following is true?

Accepted Answer

The kinetic energy is zero and the potential energy is maximum.

Question 17

Which of the following best describes a stable equilibrium in an energy diagram?

Accepted Answer

A position where the potential energy is at a minimum and small displacements result in restoring forces.

Question 18

Which of the following is true about the elastic potential energy of a spring?

Accepted Answer

It is always positive and zero at equilibrium.

Work, Energy, and Systems: Physics with Algebra Study Notes (Chapter 7)

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