Q: A 6.0-kg block is pulled by a constant force of 12 N across a frictionless surface for 3.0 m. What is its final speed?

$$v_f = \sqrt{\frac{2 F \Delta x}{m}} = \sqrt{\frac{2 \times 12 \times 3}{6}} = 3.5\,\mathrm{m/s}$$

Q: A crate of mass 10.0 kg is pulled up a rough incline (angle $$20^\circ) $$with an initial speed of 1.50 m/s. The pulling force is 100 N parallel to the incline, and the kinetic frictional force is 36.8 N. The crate is pulled 5.00 m. What is the total work done by gravity?

$$W_{gravity} = (10 \times 9.80)(5.00) \cos(110^\circ) = -168\,\mathrm{J}$$

Question 1

A 1000-kg car accelerates from 20 m/s to 30 m/s. What is the total work required to achieve this change in speed?

Accepted Answer

$$W = \frac{1}{2} m v_f^2$ - \frac{1}{2} m v_i^2$ = \frac{1}{2} (1000\,\mathrm{kg}) (30^2$ - 20^2$)\,\mathrm{m}^2/\mathrm{s}^2 = 250,000\,\mathrm{J}$$

Question 2

Which of the following statements about kinetic energy is correct?

Accepted Answer

Kinetic energy has units of $$\mathrm{kg} \cdot \mathrm{m}^2/\mathrm{s}^2$$, the same as work.

Question 3

Ball A has half the mass and eight times the kinetic energy of ball B. What is the speed ratio $$v_A/v_B$$?

Accepted Answer

$$4$$

Question 4

A 6.0-kg block is pulled by a constant force of 12 N across a frictionless surface for 3.0 m. What is its final speed?

Accepted Answer

$$v_f = \sqrt{\frac{2 F \Delta x}{m}} = \sqrt{\frac{2 	imes 12 	imes 3}{6}} = 3.5\,\mathrm{m/s}$$

Question 5

A 2.0-kg block is pulled by an 8 N force across a horizontal surface with a coefficient of kinetic friction $$\mu_k = 0.25$$ for 3.0 m. What is the block's final speed?

Accepted Answer

$$v_f = 3.05\,\mathrm{m/s}$$

Question 6

Which box experiences the greatest change in kinetic energy when pulled 10 m across a frictionless floor by the force shown below?
A: 10 N, 1 kg
B: 15 N, 2 kg
C: 5 N, 0.5 kg
D: 20 N, 3 kg
E: 12 N, 0.8 kg

Accepted Answer

Box D

Question 7

A crate of mass 10.0 kg is pulled up a rough incline (angle $$20^\circ) $$with an initial speed of 1.50 m/s. The pulling force is 100 N parallel to the incline, and the kinetic frictional force is 36.8 N. The crate is pulled 5.00 m. What is the total work done by gravity?

Accepted Answer

$$W_{gravity} = (10 	imes 9.80)(5.00) \cos(110^\circ) = -168\,\mathrm{J}$$

Question 8

Which of the following best describes the work-energy theorem?

Accepted Answer

The work done by the net force on a particle equals the change in the particle's kinetic energy: $$W_{net} = K_f - K_i$$

Question 9

A force acting on a particle varies with position as shown in a graph. The total work done by the force as the particle moves from $$x=0 to$$ $$x=6.0 m is$$:

Accepted Answer

$$W = 25\,\mathrm{J}$$

Question 10

The force required to stretch a spring a distance $$x is $$given by:

Accepted Answer

$$F_s = -kx$$

Question 11

The work done by a spring force as it moves from $$x_i to$$ $$x_f is$$:

Accepted Answer

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

Question 12

Which of the following is the correct expression for power in terms of force and velocity?

Accepted Answer

$$P = Fv$$

Question 13

A worker produces 200 W of power to do 10,000 J of work. How long does it take?

Accepted Answer

$$t = \frac{W}{P} = \frac{10,000}{200} = 50\,\mathrm{s}$$

Question 14

Which of the following is the SI unit of power?

Accepted Answer

Watt ($$\mathrm{W})$$

Question 15

A force varies with position. The work done by this force as an object moves from $$x_1 to$$ $$x_2 is $$given by:

Accepted Answer

$$W = \int_{x_1$}^{x_2$} F_x dx$$

Question 16

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

Accepted Answer

It decreases.

Question 17

A small airplane of mass 690 kg has a kinetic energy of 25,000 J during takeoff. If its speed is tripled, by what factor does its kinetic energy change?

Accepted Answer

9

Question 18

Mike applies 10 N of force over 3 m in 10 seconds. Joe applies the same force over the same distance in 1 minute. Who did more work?

Accepted Answer

Both did the same work.

Question 19

Mike performed 5 J of work in 10 seconds, Joe did 3 J of work in 5 seconds. Who produced the greater power?

Accepted Answer

Joe produced more power.

Chapter 6: Work and Kinetic Energy – Study Notes

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