Elements of PowerTypes and Calculations

© 2013 Project Lead The Way, Inc.Computer Integrated Manufacturing

What is Work and Power?

• Work is the energy transferred when a force displaces a mass

• Power is the rate at which work is done

• Typically mechanical, electrical, or fluid

Mechanical CalculationsW = work,

measured as ft-lbP = power

measured as ft-lb/st = time

measured as s1 hp = 550 ft-lb/s

t

WP

W  = F∥ ∙  d

slb-ft

550

PPhp

ExampleIf Jessica moves her 112 pound (lb) body up 8 feet (ft) of stairs in 2.3 seconds (s), how much work did she perform? How much power did she use?W = W = 112 lb (8 ft)W = 896 ft-lb

P 896 ft-lb

2.3 sft-lbsP = 390

ft-lbs390

Php = 0.71 hp

Php = 550 ft-lb

s

=

1 hp( )P = W

t

Your Turn

An escalator moves 84 people per minute from one floor of a mall to the second floor. The mall’s floors are 24 ft apart, and the average passenger weighs 154 lb.

How much power does the escalator need?

Solution Available from Teacher

Torque

• Torque, , is a twisting force on a shaft• Torque measured as in.-lb or ft-lb• = dFsinθ• A force applied at 90 degrees allows the

formula to be simplified to = dF

= 90r

F

Finding Torque

116 pounds of force is applied at the end of a lever 2.4 feet long. The force is applied at an angle of 90° to the lever. What is the torque produced?

90

116 lb

2.4 ft

pivot

Torque Calculation

𝛕=dFsinθ𝛕=2.4 ft (116 lb ) sin 90 °𝛕=278 ft− lb

d=3 ftF=100 lb

90

116 lb

2.4 ft

pivot

Power Calculations

Using the previous problem, how much power will be generated if the force is applied at a rate of 42 rpm?

P=278 ft− lb(4.40𝑟𝑎𝑑𝑠 )P=1,222

ft− lbsec ( 1hp

550ft −lbs )

P=1,222ft− lb𝑠

2.2 hp

ω=42𝑟𝑒𝑣𝑚𝑖𝑛 (1𝑚𝑖𝑛

60 𝑠 )( 2𝜋𝑟𝑎𝑑1𝑟𝑒𝑣 )

Convert rpm to rad/s

ω=4.40𝑟𝑎𝑑𝑠

Convert hp

P =

Your TurnA shaft has a force of 32 pounds applied 5.2 feet from the pivot point. What is the resulting torque?

How much power is generated if the torque is produced at 2,850 rpm?

Solution Available from Teacher

Electrical Work and Power

• Commonly measured as watt (W)

• Also measured as joule or horsepower

Electrical Calculations

Electrical power is determined by the formula P = IV

V = voltage measured as volt (V)

P = powerMeasured aswatt (W) andhorsepower (hp)

I = current measured as ampere (A)

1 hp = 745.7 W1 W = 0.00134 hp

Electrical CalculationsA house is wired such that a typical circuit can allow 15 A. Which two appliances can be used simultaneously without blowing a circuit? Hair dryer (1500 W, 110 V)

Microwave (1600 W, 120 V)

Toaster (400 W, 110 V)

Coffee maker (250 W, 120 V)

Dishwasher (1300 W, 120 V)

Flat iron (72 W, 110 V)

13.6 A

13.3 A

3.6 A

2.1 A

10.8 A

0.65 A

The hairdryer and microwave must be used alone. All other combination of two appliances would work.

P = IV

Your TurnAssume that a shop is wired so that a typicalcircuit is 20 amps. Which appliances can be usedsimultaneously?

A. Band saw (1 hp, 110 V motor)B. CNC laser (200 W, 120 V)C. Laser engraver (3500 W, 220 V)D. Light (each) (400 W, 120 V)E. Computer (250 W, 120 V)F. 3D printer (1600 W, 220 V)

Solution Available from Teacher

Fluid Power

• Operated by compressed fluid

• Low load-carrying capacity

• Requires mechanical stops if not used with servomotors

Fluid Power Definitions

Fluid PowerThe use of a fluid to transmit power from one location to another

HydraulicsThe use of a liquid flowing under pressure to transmit power from one location to another

PneumaticsThe use of a gas flowing under pressure to transmit power from one location to another

Fluid Calculationsp = Pressure, measured in pounds per square inch (psi)F = Force, measured in poundsA = Area of the base of the fluid container

F

A

p=FA

A piston has the geometric shape of a circle so how is area calculated?

If the piston diameter is 4 in. then what is the area?

F = Force being applied

A = Area to which force is being applied

Your Turn

62 pounds of force is applied to a ¾ inch pneumatic cylinder. How much pressure is created in the cylinder?

Solution Available from Teacher

Your TurnA hydraulic pressure of 175 psi is applied to a piston that has a 3.75 inch diameter and 8 inch stroke. What is the power produced by the piston that moves its full stroke in 2.25 s?

Solution Available from Teacher

Image ResourcesMicrosoft, Inc. (2012). Clip art. Retrieved from http://office.

microsoft.com/en-us/clipart/default.aspx