Answer to Question #129946 in Mechanics | Relativity for Demola

Question

Show the efficiency E the force ratio (MA)and the velocity of a machine are related to the equation
E= MA/VR × 100

Answer 1

Energy conservation demands that the total energy output of a machine must equal its energy input. However, when we measure the energy output as work done on the load by a machine, we find it is less than the energy input.

The work done by a machine against its load (moving, lifting, cutting it etc.) is called its useful work or useful energy output. In a simple mechanical machine we can measure this useful energy output as the load * the distance the load is moved by the machine.

The machine also does work against frictional forces and sometimes does work in moving itself. The work done against friction converts input energy into wasted heat energy and a little noise energy (which also eventually becomes heat energy). The energy equation now looks like this:

energy input = useful energy output + wasted energy output

As a machine wastes some of its input energy it is not completely efficient at converting the input energy onto the desired output form. We measure the efficiency of a machine, usually stated as a percentage, by the ratio:

$efficiency = \frac{useful energy output}{energy input} \times 100$

The efficiency of a mechanical machine can be calculated from the input and output work done:

useful output work = load $\times$ distance load is moved,

the input work = effort $\times$ distance effort moves,

so that $efficiency = \frac{load}{effort} \times\frac{distance load is moved}{distance effort moves} \times 100$

Looking at this formula we can see that it contains the relations for MA and $\frac{1}{VR}$ . It is often useful to be able to calculate the efficiency of a machine from values of its MA and VR. So we have the ratio for the efficiency of a machine:

$$E = \frac {MA}{VR}\times100$$