14.3: Mechanical Advantage and Efficiency
Machines can take a and create a large output force.
The mechanical advantage of a machine is the that the machine
increases an input force.
There are two ways to calculate the mechanical advantage of a machine: and .
Actual Mechanical Advantage
The actual mechanical advantage ( ) equals the ratio of the output force to the input force.
Ideal Mechanical Advantage
The ideal mechanical advantage ( ) is the mechanical advantage a machine can
have. To have the maximum mechanical advantage, there must be .
If there is no friction, then none of the input force will be lost . So the input force is the same as the force.
In this case, the only thing that matters is the of the forces and the over
which they act.
AMA vs IMA
Since there is always some , AMA is than IMA.
We always want to see how a machine is. Most cars get at least 20 miles per gallon.
This is an example of efficiency. We say that a car that gets 30 miles per gallon is more efficient.
With efficiency, we compare how much we get from the
Because there is always some friction, the efficiency of any machine is always
Critical Thinking Problems
1. A force of 200 newtons is applied to a machine in order to lift a 1,000-newton load. What is the mechanical
advantage of the machine?
2. A force of 30newtons is applied to a machine through a distance of 10meters. The machine is designed to lift
an object to a height of 2meters. If the total work output for the machine is 18 newton-meters (N- m), what is
the mechanical advantage of the machine?
3. A machine is required to produce an output force of 600 newtons. If the machine has a mechanical advantage
of 6, what input force must be applied to the machine?
4. A machine with a mechanical advantage of 10 is used to produce an output force of 250 newtons. What input
force is applied to this machine?
5. Two hundred joules of work is put into a machine over a distance of 20 meters. The machine does
150 joules of work as it lifts a load 10 meters high. What is the mechanical advantage of the machine?
6. A wheelbarrow has a mechanical advantage of 2.2. The output distance extends from the load’s center of
mass to the wheel and the input distance is from the handles to the wheel. For an output distance of 0.45 m,
what is the input distance?
7. Suppose you need to remove a nail from a board by using a claw hammer. What is the input distance for a
claw hammer if the output distance is 2.0 cm and the mechanical advantage is 5.5?
8. An inclined plane allows you to do 280 J of useful work on a refrigerator that you are sliding upward along
the plane. If the work that you have to do is 760 J, what is the efficiency of the plane?
9. A forklift developed in Sweden is able to do 1.8 106 J of useful work in lifting a heavy load. Suppose 7.6
106 J must be done by the lift’s motors on the load in order to accomplish this task. What is the efficiency of the