Machines make work easier, otherwise we wouldn't use them as often as we do. From opening a jar to sweeping the floor, people use simple machines every day. One of the measures of how much "easier" the work is done is called mechanical advantage. Mechanical advantage simply compares the output force to the input force.
Mechanical Advantage
\(\large\mathsf{ M.A. = \frac{F_{out}}{F_{in}} }\)
The mechanical advantage is greater than one if the output force is larger than the input force. Regardless of the mechanical advantage, if you ignore friction, the work done by the input force must be equal to the work done by the output force. So, the output force is usually greater than the input force, but it takes a greater distance to do the same amount of work. The distance in a lever is the lever arm. For an incline plane, it is the distance of the plane versus how tall the incline is. For a screw, it is the distance of the "wrap" versus the vertical height of the screen.
Another way to measure a machine is by efficiency. Efficiency takes into consideration the friction forces and compares the work put in to the output work.
Efficiency
\(\large\mathsf{ eff. = \frac{W_{out}}{W_{in}} }\)
The work that you put in is greater than the output work due to friction and other "losses", so the efficiency is always less than 100%. The goal is creating a machine is to get the efficiency close to 100% while maintaining a high mechanical advantage.
Question
If the load force is 120 N and the input force is 60 N, what is the mechanical advantage of the simple machine?
\(\mathsf{ M.A. = \frac{F_{out}}{F_{in}} = \frac{120 \text{ N}}{60 \text{ N}} }\)
Question
If it takes 102 Nm of work to push a 10.0-kg box up an incline that is 1.00 meter high, what is the efficiency of the ramp?
First, find the work done to lift the 10.0 kg box up 1 meter by taking its weight in Newtons and multiplying by the distance of 1 meter. Then, use the efficiency equation.
\(\mathsf{ eff = \frac{W_{out}}{W_{in}} = \frac{98.1 \text{ Nm}}{102 \text{ Nm}} = 0.962 }\)
The ramp's efficiency is 96.2%.
