Elements of Power

Types and Calculations

What is Work and Power?

• Work is the result of force displacing a mass

• Power is the rate at which work is done

• Typically mechanical, electrical, or fluid

Mechanical CalculationsP = power

measured as ft-lb/sW = work,

measured as ft-lbt = time

measured as s1 hp = 550 ft-lb/s

tWP

W  = F∥ ∙  d

ExampleIf Jessica moves her 103 pound (lb) body up 6 feet (ft) of stairs in 2 seconds (s), how much work did she perform? How much power did she use?

Your TurnAn escalator moves 60 people per minute from one floor of a mall to the second floor. The mall’s floors are 20 ft apart, and the average passenger weighs 150 lb.

How much power does the escalator need?

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 (1600 W, 110 V)Microwave (500 W, 100 V)Toaster (450 W, 110 V)Coffee maker (200 W, 120 V)Dishwasher (1800 W, 120 V)Flat iron (72 W, 110 V)

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)

Power CalculationsUsing the previous problem, how much power will be generated if the force is applied at a rate of 200 rpm?

Your Turn

A shaft has a force of 13.5 pounds applied 2 feet from the pivot point. What is the resulting torque?

How much power is generated if the torque is produced at 3200 rpm?

Solution Available from Teacher

Fluid Power

• Operated by compressed fluid

• Low load-carrying capacity

• Requires mechanical stops if not used with servomotors

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

50 pounds of force is applied to a 1 inch pneumatic cylinder. What pressure is created in the cylinder?

Solution Available from Teacher

Your TurnA hydraulic pressure of 150 psi is applied to a piston that has a 4 inch diameter and 9 inch stroke. What is the power produced by the piston that moves its full stroke in 2.5 s?

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

100 pounds of force is applied at the end of a lever 3 feet long. The force is applied at an angle of 90° to the lever. What is the torque produced?

90

100 lb

3 ft

pivot

Torque Calculation

90

100 lb

3 ft

pivot

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

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