4.41 Mechanical Advantage
Note that this equation represents theactualmechanical advantage of a machine. The actual mechanical advantage
takes into account the amount of the input force that is used to overcome friction. The equation yields the factor by
which the machine changes the input force when the machine is actually used in the real world.
Ideal Mechanical Advantage
It can be difficult to measure the input and output forces needed to calculate the actual mechanical advantage of
a machine. Generally, an unknown amount of the input force is used to overcome friction. It’s usually easier
to measure the input and output distances than the input and output forces. The distance measurements can then
be used to calculate theidealmechanical advantage. The ideal mechanical advantage represents the change in
input force that would be achieved by the machine if there were no friction to overcome. The ideal mechanical
advantage is always greater than the actual mechanical advantage because all machines have to overcome friction.
Ideal mechanical advantage can be calculated with the equation:
Ideal Mechanical Advantage=Output DistanceInput Distance
You can watch a video about actual and ideal mechanical advantage at this URL:
http://video.google.com/videoplay?docid=8517358537561483069#
A Simple Example
Look at the ramp in theFigure4.81. A ramp is a type of simple machine called an inclined plane. It can be used
to raise an object off the ground. The input distance is the length of the sloped surface of the ramp. This is the
distance over which the input force is applied. The output distance is the height of the ramp, or the vertical distance
the object is raised. For this ramp, the input distance is 6 m and the output distance is 2 meters. Therefore, the ideal
mechanical advantage of this ramp is:
Ideal Mechanical Advantage=Output distanceInput distance =^62 mm= 3
An ideal mechanical advantage of 3 means that the ramp ideally (in the absence of friction) multiplies the input force
by a factor of 3. The trade-off is that the input force must be applied over a greater distance than the object is lifted.
FIGURE 4.81
Q: Assume that another ramp has a sloping surface of 8 m and a vertical height of 4 m. What is the ideal mechanical
advantage of this ramp?
A: The ramp has an ideal mechanical advantage of:
Ideal Mechanical Advantage=^84 mm= 2