Work, Energy, and Machines

Today in class we looked into the connection between work/energy and how machines work. 
We started off analyzing an inclined plane; its purpose is to lift an object to a greater height and change the object's GPE.  Either lifting the object straight up or sliding it up a ramp accomplish the same task, the same net change in energy, and (ideally) the same work is done in either case. 
(F*d input = F*d output)  if friction is ignored... so the ramp allows you to exert less force, but over a greater distance.  The ratio of input and output distance and force is explained by the term Mechanical Advantage (MA) and is given by two equations:
MA= input distance  / output distance              and   MA = Output Force / Input Force

Today in class we just looked at input and output distances; they're easier to measure than force.  A ramp that is 3m long and 1m tall has mechanical advantage:    3m/1m = 3   (no units)
This means it is 3 times easier to use the ramp, or you must apply 1/3 as much force to roll an object up the ramp that you would to just lift it.

I provided demonstrations of other devices with mechanical advantage; a bolt cutter's handle moves 50cm while the "cutting wedges" move about 1/2cm.     50cm / 0.5cm = 100, and that's not even considering the mechanical advantage of the cutting wedges.  Using the handles makes it 100x easier to cut a bolt thann shoving the wedges together by hand. 
Other examples:   shears for trimming trees - use the handles at the end vs. close to the fulcrum for higher MA,   jacks for lifting a car have MAs in the hundreds as well, making it possible for any adult to lift a car. 

**What about if the input and output distances are equal?  Then the MA would be 1, and the input and output forces would match.  This is the case for some levers and pulleys if they only change the direction of a force. 

Finally, a MA less than one means that the input side of a machine moves less than the output end, and the input force is greater.  The easiest example of this is a bicycle; starting out you use gears with a high MA, but at top speed, you want to apply a large force over a small distance relative to how fast your bike wheels are spinning.  Examples exist within your body as well; muscles can't always be placed in convenient locations, and they don't have the greatest range of motion, so most of our joints and muscles work with MAs less than one. 

Percent efficiency relates the input and output work of a machine in the real world (friction and thermal E included).  %eff = work output / work input       or   %eff = E out / E input. 
Because of friction and thermal E, 100% efficiency is possible, and although people have tried to make free energy for centuries, nobody's ever made a >100% efficient machine that generates useful energy. 
There's no such thing as a free lunch.