Question

How is the mechanical advantage related to the velocity ratio for an actual machine? State whether the efficiency of such a machine is equal to 1, less than 1, or more than 1.

Answer 1

Mechanical advantage is a measure of the ratio of output force to input force in a system. It is related to the efficiency of an object and is used to analyse the forces in simple machines like levers and pulleys.

Complete step by step answer
For a machine, its efficiency is determined as
$\eta = \dfrac{{M.A.}}{{V.R.}}$ where M.A. is the mechanical advantage and V.R. is the velocity ratio.
In an actual machine, efficiency is always less than 1. This is because there are always some energy losses associated with the moving parts of the machine. So, forces like friction, sliding, etc can affect the efficiency of the machine and decrease it from the efficiency of an ideal machine which is 1. This means that the output energy will always be lower than the input energy.
Since $\eta = \dfrac{{M.A.}}{{V.R.}} < 1$ , we can write that
$M.A. < V.R.$
So, the mechanical advantage is always less than the velocity ratio for an actual machine. As discussed in the solution, the efficiency of an actual machine will be less than 1 due to different losses.

Note
Typically, the mechanical advantage is expressed in ideal terms, where there are no losses in energy between the input and output. This corresponds to $100\%$ efficiency and is the case for ideal machines. Simple machines use mechanical advantage for their functionality by helping humans perform tasks that would require more force than a person could produce on their own. While the velocity ratio will be constant for a mechanical system, the mechanical advantage depends on how efficiently the machine is designed.