Potential And Kinetic Energy Worksheet Page 20
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9.2 Mechanical Advantage of Simple Machines
9.2
We use simple machines to make tasks easier. While the output work of a simple machine can never be greater
than the input work, a simple machine can multiply input forces OR multiply input distances (but never both at
the same time). You can use this skill sheet to practice calculating mechanical advantage (MA) for two common
simple machines: levers and ramps.
The general formula for the mechanical advantage (MA) of levers:
F (output force)
o
MA
=
lever
F (input force)
i
L (length of input arm)
Or you can use the ratio of the input arm length to the output arm
i
MA
=
lever
L (length of output arm)
length:
o
Most of the time, levers are used to multiply force to lift heavy objects.
ramp length
The general formula for the mechanical advantage (MA) of ramps:
MA
=
ramp
ramp height
A ramp makes it possible to move a heavy load to a new height using less force
(but over a longer distance).
Example 1: A construction worker uses a board and log as a lever to lift a
heavy rock. If the input arm is 3 meters long and the output arm is 0.75 meters
long, what is the mechanical advantage of the lever?
3 meters
MA =
= 4
0.75 meter
Example 2: Sometimes levers are used to multiply distance. For a broom, your
upper hand is the fulcrum and your lower hand provides the input force: Notice
the input arm is shorter than the output arm. The mechanical advantage of this
broom is:
0.3 meter
MA =
= 0.25
1.2 meters
A mechanical advantage less than one doesn’t mean a machine isn’t useful. It just
means that instead of multiplying force, the machine multiplies distance. A broom
doesn’t push the dust with as much force as you use to push the broom, but a small
movement of your arm pushes the dust a large distance.
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