Elements of Power Types and Calculations What is

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 Calculations P = power measured as ft-lb/s W = work, measured as ft-lb t = time measured as s 1 hp = 550 ft-lb/s

Example If 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? W t 618 ft-lb P = 2 s ft-lb P = 309 s P = ft-lb Php = 309 s Php = 0. 56 hp ( 1 hp 550 ft-lb s )

Your Turn An 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 F = 150 lb/person 60 people F = 9000 lb W P = t 180, 000 ft-lb P = 60 s P = 3000 ft-lb s ft-lb P (hp) = 3000 s P (hp) = 5. 5 hp ( 1 hp ) 550 ft-lb s

Torque • • Torque, , is a twisting force on a shaft Torque measured as in. -lb or ft-lb = d. Fsinθ A force applied at 90 degrees allows the formula to be simplified to = d. F r = 90 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? 100 lb 3 ft pivot 90

Torque Calculation 100 lb 3 ft 90 pivot

Power Calculations Using the previous problem, how much power will be generated if the force is applied at a rate of 200 rpm? Convert rpm to rad/s Convert hp

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 Convert rpm to rad/s Convert to horsepower

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 P = power Measured as watt (W) and horsepower (hp) 1 hp = 745. 7 W 1 W = 0. 00134 hp V = voltage measured as volt (V) I = current measured as ampere (A)

Electrical Calculations A 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) 14. 5 A P = IV Microwave (500 W, 100 V) 5. 0 A Toaster (450 W, 110 V) 4. 1 A Coffee maker (200 W, 120 V) 1. 7 A Dishwasher (1800 W, 120 V) 15. 0 A Flat iron (72 W, 110 V) 0. 65 A The dishwasher and hairdryer must be used alone. Any other combination of two appliances would work.

Your Turn Assume that a shop is wired so that a typical circuit is 20 amps. Which appliances can be used simultaneously? P = IV 1 hp = 745. 7 W A. B. C. D. E. F. Band saw (1 hp, 110 V motor) CNC laser (200 W, 120 V) Laser engraver (3500 W, 220 V) Light (each) (400 W, 120 V) Computer (250 W, 120 V) 3 D printer (1600 W, 220 V) 7 A 16 A 3. 3 A 2. 1 A 7. 3 A Combination ABDE, ABEF, ADEF, BC, CD, CE or any subset

Fluid Power • Operated by compressed fluid • Low load-carrying capacity • Requires mechanical stops if not used with servomotors

Fluid Calculations p = Pressure, measured in pounds per square inch (psi) F = Force, measured in pounds A = Area of the base of the fluid container F A A piston has the geometric shape of a circle so how is area calculated? The area of a circle is r 2 If the piston diameter is 4 in. then what is the area? 12. 6 in. 2

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 r = ½ D r = ½ (1 in. ) r = 0. 5 in. A = r 2 A = (0. 5 in. )2 A = 0. 785 in. 2

Your Turn A 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?

r = ½ D r = ½ (4 in. ) r = 2 in. Solution 2 A = r A = (2 in. )2 A = 12. 6 in. 2 P = W t 1418 ft-lb 2. 5 s P = 567 ft-lb s ft-lb P (hp) = 567 s P (hp) = 1. 03 hp ( 1 hp 550 ft-lb s )

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