# Simple Machines

```In Physics, work is defined to be the amount of energy that is added to or removed from a system.
Mathematically, the work done on a system is equal to the amount of force that acts on the system
times the distance across which the force acted.
Work = Force  Distance
since energy is measured in Joules
1J=1N1m
A simple machine is a device that changes the amount of force or direction of force needed to do
work on another object.
A simple machine does not do work for you, this would violate the 1st Law of Thermodynamics,
which states that energy can never be created or destroyed. It simply makes work easier to do by
allowing you to spread the same amount of work out over a longer distance, thereby using a
smaller force.
The amount of energy you put into a machine (work input) is equal to the amount of work done
by the machine (work output). Remember, work = energy and energy is always conserved.
Work input = energy put into the machine
Work output = energy transferred by machine to some other object
It is useful to imagine an ideal situation where the machine loses no energy to heat or other forms
(this is of course impossible due to the 2nd Law of Thermodynamics). Such a machine could be
described by the following equation:
Work input = Work output
(f  d)input = (f  d)output
Example: A machine is used to lift a 880 N anvil 0.50 meters. If the person using the machine
needs to apply a force through a distance of 2.0 meters to do this, how much input
force is required?
(f  d)input = (f  d)output
f input  2.0 m = 880 N  0.50 m
f input = 440Nm /2.0 m
f input = 220 N
A simple machine can make work easier to do by trading force for distance. In other words, a
machine lets you use less force by putting that force through a greater distance. In the case
above, the machine let you lift an 880N object by using only 220N of input force (¼ the output
force) , but in order to do this you had to apply the input force four times further than the object
was lifted.
Since the machine magnified your input force 4 times, we say it has a mechanical advantage of 4.
Mechanical advantage is the degree to which a machine magnifies your force.
A machine with a mechanical advantage of 5 multiplies your force by 5, so that an input force of
100 N will produce an output force of 500 N (but you’ll have to apply the input force 5 times
further)
A machine with a mechanical advantage of 0.5 multiplies your force by 0.5, so that an input force
of 100 N will only produce an output force of 50 N (but you’ll only have to apply the input force
half as far as the object is lifted)
We can predict the mechanical advantage of a machine by dividing the input distance by the
output distance (if you input distance is twice the output distance the output force will be twice
the input force and the machine will have a mechanical advantage of 2)
When we determine a predicted mechanical advantage by comparing the input and output
distances, we call this the ideal mechanical advantage or IMA.
The following equation allows you to find the IMA of any simple machine:
IMA = input distance
output distance
Examples:
What is the IMA of a lever if you move your hand 6.4 cm in order to lift an object 1.8 cm?
6.4 cm / 1.4 cm = 4.6 (notice that the centimeters cancel, so there are no units)
What is the IMA of a pulley system that lifts an object 2.0 meters when you pull down on 14 m of
rope? 14 m / 2.0 m = 7
If an lever has an IMA of 4.6, how far could you lift an object if your moved your end 1.4
meters?
output distance = input distance / IMA
= 1.4 m/ 4.6
= 0.30 m
Any time the input distance of a machine exceeds the output distance, the machine will have an
IMA that is greater than one, and the machine will make you “stronger”. You want an IMA that
is greater than one when you need to apply more force to an object than your muscles will permit.
Any time the input distance is less than the output distance, the machine will have an IMA that is
less than one. The machine’s output force will be less than the input force (it will make you
“weaker”), but the output distance will be greater. You want an IMA that is less than one when
you want to increase the velocity of an object.
Example: a bicycle has a small input distance (the pedal’s motion) and a large output distance
(the motion of the wheel).
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