Work Power Energy

W, P, E – Machines: Study Guide
Work
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Work is a force applied to an object that causes displacement
W = FΔd
o Measured in Newton-meters (Nm) or Joules (J)
o Kg m2 / s2 is also called a Joule
 Remember: F = m a; or F (weight) = m g
 Fnet = μ m a
 Fnet = μ m g
W = F d cos Θ
o If angle Θ is 90o (straight upwards), cosine = 0
o If angle Θ is flat (180o), cosine = 1
W = KE + PE
Wnet = μ F d cos Θ
o Wnet = μ m g d (cos Θ)
Power
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Power is the rate at which work is being done
Measured in Joules per Second or Watts (W)
o I J/s = 1 W
o 1 hp = 750 W
Power (P) = Work / Time
o P = W/t = Fd/t
o Since d / t is the same as velocity: P = F v
o P = mgh/t
o t = .5 m Δv / P
o F = P/v
o v = P/F
P = KE + PE / t
o P = (.5 m v2) x (m g h) / t
Energy
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Potential Energy
o The stored energy of position, inertia, or ability to do work
o PE = m g h
o PEelastic = .5 k x2
Kinetic Energy
o Energy of motion
o KE = .5 m v2
o KE = F d
Mechanical Energy
o ME = PE + KE
o Measured in Newtons
W, P, E – Machines: Study Guide
Simple Machines
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Efficiency = Woutput / Winput x 100 to make it a percentage
Mechanical Advantage (MA)
o MA = Foutput / Finput
o Actual MA (AMA) = FR / Fe
o Ideal MA (IMA) = Se / SR
Types of Simple Machines
o Inclined Plane (ramp)
 IMA = Length of ramp (L) / Height of ramp (H)
o Wedge
 IMA = Length of side (L) / Width of top (T)
o Screw
 An inclined plane wrapped around a wedge
 Pitch = distance between threads
 IMA = Circumference / Pitch
 Example:
P = .83
C = π d = 2πr = 3.14 x 1 = 3.14
IMA = C / P = 3.14 / .83 = 37.83
o Lever
 Finput x dA = Foutput x dR
 IMA = d from fulcrum to Finput / d from fulcrum to F output
 IMA = di / do
 3 Classes
 1st Class – as applied force goes down, resistant force moves up; fulcrum
in between the two forces
FA
FR
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2nd Class – fulcrum is on end, resistance is in middle moving upwards in
same direction as applied force at end of lever
FA
FR
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3rd Class – Resistant force is on end, applied force in middle and both in
upwards direction with fulcrum at end of lever
FR
FA
W, P, E – Machines: Study Guide
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Wheel and Axle
 IMA = radiuswheel / radiusaxle
 IMA = SpeedinputAxlediameter / SpeedOutputWheeldiameter
o IMA = SiDA / SoDW
Pulley
 IMA = # of sections supporting mass
Gear System
 Gear Ration (gr)
 gr = πd / πD = π small gear diameter / π large gear diameter
Torque τ
o τ = rF
o τ = F d (sin Θ)
Θ
τ
d
d sin Θ
F
FYI:
Hypotenuse (c)
Opposite (b)
of Angle
Θ
Adjacent (a) to Angle
C2 = a2 + b2
Sin Θ = Opposite / Hypotenuse
Cos Θ = Adjacent / Hypotenuse
Tan Θ = Opposite/Adjacent

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