CK-12-Physics - Intermediate

http://www.ck12.org Chapter 6. Work and Energy

(

240

km

h

)(

1000 m

1 km

)(

1 h

3600 s

)

= 66. 666 = 66 .7 m/s

The power the engine develops isP=F v= (4600N)( 66 .7m/s) = 307 , 820 = 308 ,000 W

Converting to horsepower:

(

308 ,000 W

1

)(

1 hp

746 W

)

= 411. 287 =411 hp

Illustrative Example 3

1a. If you look at your utility bill, you’ll see that you’re charged, typically, between 8 and 12 cents per kilowatt-hour
(kWh). Are you being charged for your power consumption or the energy you use?

1b. What is the cost to run a 100-Watt light bulb for 24 hours at 12 cents per kWh?

Answers:

1a. You’re charged for the energy you use. Since a kilowatt is a unit of power (1000 W = 1000 J/s), multiplying
energy/time by time results in just units of energy (joules).

Note: 1. 00 kW h=

(

1000 Js

)(

(^3600) hs

)

= 3 , 600 , 000 = 3. 60 × 106 J

1b. We first convert 100 W into kW and then multiple by the number of hours, 24.

100 W= 0. 100 kW, therefore,( 0. 100 kW)( 24 h) = 2. 4 kW h→( 2. 4 kW h)

(

$0. 12

kW h

)

= 0. 288 =$0.29 or 29 cents.

• Work is defined asW=Fxx= (Fcosθ)x, the product of the component of the force along the line of motion
  and displacement.


• Work has units of N*m, or(kg·m^2 /s^2 ), also known as Joules (J).


• Energy comes in two forms: kinetic and potential

Kinetic energy is the energy of motion and potential energy is the energy of position. Potential energy can also have
many forms. For example: gravitational potential energy, elastic potential energy, chemical potential energy, and
nuclear potential energy to name a few.

• Energy is the ability to do work and has units of joules, J.


• Kinetic energy has the form:KE=^12 mv^2


• Gravitational potential energy has the form:PE=mgh


• The potential energy stored in a spring has the form:PE=^12 kx^2


• The relationship between the applied force and the distance a spring is stretched or compressed is:F=kx
  (Hooke’s Law)


• The Work-Energy principle isW=∆KE


• Dissipative forces such as friction are considered non-conservative forces. Mechanical energy is not conserved
  in the presence of non-conservative forces.