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Elements of Power Types and Calculations Computer Integrated Manufacturing © 2013 Project Lead The Way, Inc. 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 Calculations W = F∥ ∙ d W P t P Php ft - lb 550 s W = work, measured as ft-lb P = power measured as ft-lb/s t = time measured as s 1 hp = 550 ft-lb/s Example If 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 = F∥ ∙ d W = 112 lb (8 ft) W = 896 ft-lb W t 896 ft-lb P= 2.3 s ft-lb P = 390 s P = ft-lb Php = 390 s Php = 0.71 hp ( 1 hp 550 ft-lb s ) 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 r = 90 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? 116 lb 2.4 ft pivot 90 Torque Calculation 116 lb 2.4 ft pivot = dFsinθ = 2.4 ft 116 lb sin90° = 278 ft − lb 90 d = 3 ft F = 100 lb Power Calculations Using the previous problem, how much power will be generated if the force is applied at a rate of 42 rpm? Convert rpm to rad/s 1 2 ω = 42 60 1 ω = 4.40 P =ω P = 278 ft − lb 4.40 ft − lb P = 1,222 Convert hp ft − lb 1 hp P = 1,222 ft − lb sec 550 s P = 2.2 hp Your Turn A 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 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 (1500 W, 110 V) 13.6 A P = IV Microwave (1600 W, 120 V) 13.3 A Toaster (400 W, 110 V) 3.6 A Coffee maker (250 W, 120 V) 2.1 A Dishwasher (1300 W, 120 V) 10.8 A Flat iron (72 W, 110 V) 0.65 A The hairdryer and microwave must be used alone. All 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? 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) 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 Power The use of a fluid to transmit power from one location to another Hydraulics The use of a liquid flowing under pressure to transmit power from one location to another Pneumatics The use of a gas flowing under pressure to transmit power from one location to another 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 p= A F A 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 Turn A 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 Resources Microsoft, Inc. (2012). Clip art. Retrieved from http://office. microsoft.com/en-us/clipart/default.aspx