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, 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). 

 

 

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, 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)

 

A pulley system has an IMA of 7, if you want to use it to lift an object 2.0 meters, how much rope will you need to pull?   7 = input force / 2 meters

                             14 m = input force

 

 

When you use a machine, you will find that the actual mechanical advantage is usually less than what you predicted.  This is because some of the input work is going into things like: stretching the ropes in a pulley system, bending the bar of a lever, friction, etc. 

 

The actual mechanical advantage of a machine or AMA is found by using the following equation:

 

AMA = output force

             Input force

 

Examples:

 

What is the AMA of a pulley system that requires 24 N of effort force to lift a 80 N object?

 

AMA = 80 N / 24 N

AMA =  3.3

 

A lever has an AMA of 2.6.  How much weight could it lift if you gave it 1,200 N of input force?

 

              2.6 = output force / 1,200 N

output force =  460 N