Question

An effort of 21 kgf is applied on a machine for the movement of a load of 120 kgf. Find the mechanical advantage of the machine.

Answer 1

Hint:Mechanical advantage refers to the ability of a simple machine in amplifying the applied force. It is defined as the ratio of the output force to the input force or the ratio of the load to the effort applied in lifting the load.

Formula used:
The mechanical advantage of a machine is given by, $MA = \dfrac{L}{E}$ where $L$ refers to the load which is to be lifted and $E$ refers to the effort applied to lift the load.

Complete step by step answer.
Step 1: List the parameters known from the question.
The problem at hand describes the lifting of a load by applying some effort to a machine. We are to determine the mechanical advantage of the machine.
The effort applied to the machine is given to be $E = {\text{21kgf}}$ .
The load which is to be lifted is given as $L = 120{\text{kgf}}$ .

Step 2: Express the relation for the mechanical advantage.
The mechanical advantage of the given machine can be expressed as $MA = \dfrac{L}{E}$ ------- (1)
Substituting for $E = {\text{21kgf}}$ and $L = 120{\text{kgf}}$ in equation (1) we get, $MA = \dfrac{{120}}{{21}} = 5 \cdot 7$
Thus the mechanical advantage of the given machine is obtained as $MA = 5 \cdot 7$ .

Additional information:The machine can be a lever, a wedge, an inclined plane, a pulley system, a jackscrew or a wheel and axle. The theoretical value of the mechanical advantage is determined under the assumption that friction is not present. In practice, the mechanical advantage will be less than that of the theoretical value. The amount of decrease will be in correspondence with the amount of friction present.

Note:Here load and effort represent the output force and the input force of the machine respectively. As they are ultimately forces they will have the same unit as that of force. The given unit of the load and the effort - kgf refers to kilogram-force. Since mechanical advantage is a dimensionless number, conversion of the unit kgf to Newtons is not necessary. We neglected frictional forces while determining the mechanical advantage.