The relationship between the load lifted (W) and the effort required (P) to lift the load often called the law of the machine is _______.  

Explanation:

Lifting machines are those machines that are used for lifting loads. The force (or effort) is applied at one point of the machine and weight (or load) is lifted at the other point of the machine.

Pulleys used to lift water from a well and screw jacks used to lift buses are some of the common examples of lifting machines. 

Let P be the effort applied, W be the load lifted, y be the distance moved by the effort, x be the distance moved by the load. Then, 

• The input of machine = Py
• The output of machine = Wx 

Efficiency: It is the ratio of output to input. In a simple mechanism, it is also defined as the ratio of mechanical advantage to the velocity ratio.

\(η = \frac{{Output}}{{Input}} = \frac{{Wx}}{{Py}}=\frac{{\frac{{W}}{{P}}}}{{\frac{{y}}{{x}}}}=\frac{{\frac{{Load}}{{Effort}}}}{{\frac{{Dist.~moved~by~effort}}{{Dist.~moved~by~load}}}}\) = \(Mechanical ~advantage\over Velocity~ratio\)

Law of machine: It is the relation between the load lifted (W) and the effort applied (P). 

It is given by the equation:

P = a.W + C

where a = coefficient of friction which is equal to the slope of line AB in fig., C = constant represent machine friction

η = \(Mechanical ~advantage\over Velocity~ratio\) = \(M.A.\over V.R.\)

for maximum efficiency, mechanical advantage must be maximum which is given by M.A. = \(1\over m\)

∴ ηmax = \(Mechanical ~advantage\over Velocity~ratio\) = \(\frac{1}{m~\times ~V.R.}\)