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
𝛕 = dFsinθ
𝛕 = 2.4 ft 116 lb sin90°
𝛕 = 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
𝑟𝑒𝑣 1 𝑚𝑖𝑛 2𝜋 𝑟𝑎𝑑
ω = 42
𝑚𝑖𝑛 60 𝑠
1 𝑟𝑒𝑣
𝑟𝑎𝑑
ω = 4.40
𝑠
P =𝛕ω
𝑟𝑎𝑑
P = 278 ft − lb 4.40
𝑠
ft − lb
P = 1,222
Convert hp
𝑠
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