Mechanical Work
Sub Unit 2.1
Objectives
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Define work done by a force or torque in a mechanical system.
Explain the relationship between work, force applied, and the
distance an object moves.
Solve work problems, given force and distance information in English
and SI units.
Explain how efficiency relates to input work and output work for a
mechanical system.
Define radian measure of angles.
Explain the relationship between work, torque applied, and the angle
(in radians) through which and object moves.
Solve work problems, given torque and angle information in English
and SI units.
Work
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Linear
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When a force moves something a distance
(like a pushing a car, moving a desk, lifting
weights, etc.)
Rotational
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When a torque causes rotational
movement (like gears, pulleys,
wheels, etc.)
Work done by a force
Work (W) = Force (F) x Distance (d)
Work Units
English
foot • pounds (ft•lb)
SI
newton • meters (N•m)
=
Force Units
English
pounds
SI
newtons
Distance Units
x
English
feet
1 Newton meter (N•m) = 1 Joule (J)
SI
meters
Work
Uses magnitude of
force and displacement
(both are vectors)
 Can be positive (if both force and
displacement are in same direction)
 Can be negative (if force and
displacement are in opposite direction)
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Change in Potential /
Kinetic Energy?
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Work equals change in energy
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Like when the barbell gains gravitational
potential energy due to the work done to lift
it.
Or when braking, the kinetic
energy of vehicle decreases
due to the work done by the
brakes.
Efficiency
Machines convert work input to useful work
output.
 Theoretically, “work in” equals “work out.”
 Realistically, “work in” is always greater
than “work out.” Why? – Losses
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Efficiency =
output work
input work
To get percentage,
multiply by 100%
“Rotational Work”
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Work done by a torque
“” must be in radians
Work (W) = torque () x angle moved ()
=Fxl
1 rev = 360º = 2 rad
=
Arc length
r
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Summary
Mechanical systems use force and torque to cause desired
movement and do useful work.
Work is done when a force or torque moves an object. Work is
done only while the force or torque is applied in the direction of
movement.
Work equals force times displacement or torque times angle.
Work is measured in ft•lb or N•m (J= N•m). W=Fd; W= 
The displacement used to calculate work is the distance the object
moves while the force is applied.
Efficiency describes how well a machine performs work.
Efficiency is the ration of output work to input work
(Eff = Wout / Win)
Angles can be measured in either radians or degrees. The radian is
a dimensionless unit and is used in most calculations involving
angles.