Chapter 2 - Work
Section 1 – Work in Mechanical
Systems
Objectives
• Define work by a force or torque in a
mechanical system.
• Explain the relationship between work,
force and distance.
• Solve work problems given force and
distance in English or SI units.
• Explain efficiency in terms of work in &
work out
Objectives – cont.
• Define radian measure of angles.
• Explain the relationship between work,
torque and angle moved.
• Solve work problems given torque and
angle in English or SI units.
Work done by a force
• Work = force times distance
• W = Fd
• If the object does not move, no work is
done.
Units
• English units are foot-pounds (ft-lb) or inch
pounds (in-lb)
• SI units are newton-meters (N-m).
• 1N-m = 1 Joule (J).
• Work can be positive or negative
depending upon the direction of the
displacement.
Work changes energy
• Work changes the kinetic or potential
energy of an object.
• The amount of work done equals the
change in the energy of an object.
• W = DKE + DPE
Efficiency
• Efficiency equals the output work divided
by the input work, usually expressed as a
percentage.
• Eff= (Wout / Win ) x 100%
Measuring angles in radians
Radians
• The angle, q is defined as the ratio of the
arc length, s to the radius, r. q = s / r.
• Since both the radius and the arc length
are measured in meters, the units of the
angle cancel out. The “unit” for the angle
is called radians (rad).
• One radian is the angle marked out by an
arc length equal to the radius of the circle.
Converting to Radians
• The circumference of a circle is 2pr. The
angle marked out by going the entire
circumference would be 2pr / r or 2p rad.
• Thus 2p rad = 360o or p rad = 180o
• 1 rad = 360o / 2p rad = 57.3o
• 1o = 2p rad / 360o = 0.017 rad
• 1 revolution (rev) = 360o = 2p rad
Convert the following
•
•
•
•
•
90o to radians
20 radians to revolutions
45o to revolutions
10 revolutions to radians
5 radians to degrees
Work done by a torque
• Torque = force times
lever arm t = Fr
• Thus F=t / r
• W = Fd = (t/r)d
• W = t (d/r) where d = arc
length
• Thus work = torque times
the angle (in radians)
through it moves.
• W = tq
Example – work done to turn a
crank
• 20 lb of force is
• Now compute the
needed to turn a 1.5 ft
work
crank 5 revolutions.
• W =tq = 30 ft-lb x 10p
Calculate the work
rad = 944 ft-lb
• First, find the torque –
t = Fl = 20 lb x 1.5 ft =
30 ft-lb
• Convert the angle to
radians – 5 rev X 2p
rad/rev = 10p rad
Summary
• Mechanical systems use force and torque
to cause movement and do work.
• Work is done when a force or torque
moves an object. Work is done when the
force or torque is applied in the direction of
motion.
• Work equals force times distance (W = fd)
or torque times angle (W = tq) . Units are
ft-lb or N-m.
Summary - cont
• Efficiency is the ratio of output work to
input work. Eff = Wout / Win . This is
usually expressed as a percentage.
• In calculations of work, angles must be in
radians. A radian is a dimensionless ratio
and thus not a unit.
• 1 revolution = 360o = 2p rad.