Q: A 10 kg block is pushed by a 100 N force over a distance of 5 m on an inclined surface at $$20^\circ to $$the horizontal. The coefficient of friction is $$\mu = 0.4. $$What is the work done by the friction force?

$$W_f = -\mu m g \cos 20^\circ \times 5$$

Q: A block of mass $$m is $$pulled by a force $$F at an $$angle $$\theta to $$the horizontal over a distance $$d on a $$rough surface with friction coefficient $$\mu. $$What is the net work done on the block?

$$W_{net} = F d \cos \theta - \mu m g d$$

Question 1

Which of the following best describes kinetic energy?

Accepted Answer

Kinetic energy is the energy associated with the state of motion of an object.

Question 2

A block of mass $$m is $$moving with velocity $$v. $$What is its kinetic energy?

Accepted Answer

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

Question 3

Which of the following statements about work is correct?

Accepted Answer

Work is energy transferred to or from an object by means of a force acting on the object.

Question 4

A force $$\vec{F}$$ acts at an angle $$	heta to $$the displacement $$\vec{d}. $$What is the formula for the work done by this force?

Accepted Answer

$$W = F d \cos 	heta$$

Question 5

If a force is perpendicular to the displacement of an object, what is the work done by the force?

Accepted Answer

Zero work is done.

Question 6

A 10 kg block is pushed by a 100 N force over a distance of 5 m on an inclined surface at $$20^\circ to $$the horizontal. The coefficient of friction is $$\mu = 0.4. $$What is the work done by the friction force?

Accepted Answer

$$W_f = -\mu m g \cos 20^\circ 	imes 5$$

Question 7

Which of the following is the correct SI unit for work?

Accepted Answer

Joule ($$J)$$

Question 8

According to the work-kinetic energy theorem, what is the relationship between the net work $$W$$ done on a particle and its change in kinetic energy $$\Delta K$$?

Accepted Answer

$$\Delta K = K_f - K_i = W$$

Question 9

A crate is sliding across a parking lot with a force $$\vec{F} = (2.0 \hat{i} - 6.0 \hat{j}) N $$acting on it over a displacement $$\vec{d} = (-3.0 \hat{j}) m. $$What is the work done by the force?

Accepted Answer

$$W = (-6.0)(-3.0)$$

Question 10

A spring with force constant $$k is $$compressed by a distance $$x. $$What is the work done by the spring force as the block moves from $$x_i to$$ $$x_f$$?

Accepted Answer

$$W_s = \frac{1}{2} k x_f^2$ - \frac{1}{2} k x_i^2$

Question 11

A block of mass $$m is $$lifted vertically by a distance $$d at $$constant speed. What is the work done by the gravitational force?

Accepted Answer

$$W_g = -m g d$$

Question 12

Which of the following integrals represents the work done by a variable force $$F(x) as a $$particle moves from $$x_1 to$$ $$x_2$$?

Accepted Answer

$$W = \int_{x_1$}^{x_2$} F(x) dx$$

Question 13

A block of mass $$m is $$attached to a spring with force constant $$k$$ and compressed by $$x. If $$released from rest, what is its speed as it passes through the equilibrium position ($$x = 0) on a $$frictionless surface?

Accepted Answer

$$v = \sqrt{\frac{k x^2$}{m}}$$

Question 14

A block of mass $$m$$ slides on a frictionless floor under a force $$F(x)$$ that varies with position as shown in a graph. How can you determine the work done by the force over a given interval?

Accepted Answer

By calculating the area under the $$F(x)$$ curve between the interval limits.

Question 15

A block of mass $$m is $$pulled by a force $$F at an $$angle $$	heta to $$the horizontal over a distance $$d on a $$rough surface with friction coefficient $$\mu. $$What is the net work done on the block?

Accepted Answer

$$W_{net} = F d \cos 	heta - \mu m g d$$

Question 16

Which of the following is true about the scalar product of two vectors $$\vec{A}$$ and $$\vec{B}$$?

Accepted Answer

It is a scalar quantity.

Question 17

A block of mass $$m is $$attached to a spring and compressed by $$x. If a $$constant friction force $$f$$ acts as the block moves to equilibrium, what is the final speed $$v of $$the block?

Accepted Answer

$$v = \sqrt{\frac{k x^2$ - 2 f x}{m}}$$

Question 18

Which of the following best describes negative work?

Accepted Answer

Energy is transferred from the object.

Kinetic Energy and Work: Concepts, Theorems, and Applications

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