14.3 Mechanical Advantage and
Efficiency
• It is impossible to change a tire using just your
fingers. If you place a jack under the car, that
will help, unless you push the end of the lever
closest to the car.
• Input force and input distance are important.
Mechanical Advantage
• Location and amount of input force is
dependent on the type of machine used and
how it is used.
• For example, a lever can lift a car or entertain
young children on a see-saw.
• The mechanical advantage of a machine is the
number of times that the machine increases
an input force.
• You want the mechanical advantage, MA, to
be large, or what’s the point of using the
machine?
Actual Mechanical Advantage
• Actual mechanical advantage = output
force/input force
• Why does a rough ramp have less MA than a
smooth ramp?
• More input force is needed and less friction is
present
MA Problems
• The output force is 8 N and the input force is 4
N. What is MA?
• 8N/4N =
• 2
• The input force is 4N and the MA is 3. What is
the output force?
• 4N x 3 =
• 12 N
• The output force is 6N and the MA is 2. What
is the input force?
• 6N/2 =
• 3N
Ideal Mechanical Advantage
• What can increase MA?
• Reduce friction.
• Ideal Mechanical Advantage (IMA) assumes
that the world can be made perfect.
• In other words, IMA assumes the absence of
friction.
• Because friction is always present, the actual
mechanical advantage of a machine is always
less than the ideal mechanical advantage
Why IMA when it’s impossible?
• We calculate IMA, even though it can never
happen, because sometimes it is too difficult
to calculate MA.
• We would need to find exactly how much is
lost to friction, and we do not have a machine
that does this.
• Also, in the case of ramps, trigonometry must
be used (sin, cos, tan buttons on the
calculator).
Calculating Mechanical Advantage
• IMA only depends on distances.
• Remember that friction does not play a role in
IMA.
• IMA = input distance/output distance
• Remember the screwdriver (your hand makes
a greater turn than the bit does).
IMA problems
• A woman drives her car up onto wheel ramps
to perform some repairs. If she drives a
distance of 2 m along the ramp to raise the car
0.5 meters, what is the IMA?
• 2m/0.5m=
• 4
• A student working in a grocery store after
school pushes several grocery carts together
along a ramp. The ramp is 3 m long and rises
0.5 m. What is the IMA?
• 3m/0.5m=
• 6
• A construction worker moves a crowbar
through a distance of 0.5 m to lift a load 0.05
m off the ground. What is the IMA?
• 0.5m/0.05m=
• 10
• The IMA of a simple machine is 2.5. If the
output distance is 1 m, what is the input
distance?
• 2.5 x 1 m =
• 2.5 m
• The IMA of a simple machine is 3. The input
distance is 21 m. What is the output distance?
• 21 m/3 =
• 7m
Efficiency
• Because some of the work input is used to
overcome friction, the work output of a
machine is always less than the work input.
• The percentage of the work input that
becomes work output is the efficiency of a
machine.
• Because there is always some friction, the
efficiency of any machine is always less than
100%.
Efficiency Problems
• Wheels are often used, since rolling friction is
less than sliding, and making objects closer to
the center reduces air resistance.
• Efficiency = work output/work input x 100%
• What is the efficiency of a machine that has a
work input of 20 J and a work output of 10 J?
• 10J/20J x 100% =
• 50%
• The efficiency of a machine is 75%. The work
input is 10 J. What is the work output?
• 75% x 10 J =
• 7.5 J
• You know a machine has a 10% efficiency. You
want it to do 4 J of work. How much work will
you have to do?
• 4J/10%=
• 40J