Question

A boy uses a single fixed pulley to lift a load of 50kgf to some height, another boy using a single movable pulley to lift the same load to the same height. Compare the effort applied by them. Give reason to support your answer.

Answer 1

We will use the mechanical advantage of pulley to determine the height of the load raised by the effort. Mechanical advantage is the amplification of forces achieved while using a particular tool. We must know that the mechanical advantage of a pulley system is directly proportional to the number of movable pulleys.

Formula used:
$MA = \dfrac{L}{E}$
Here MA is the mechanical advantage, L is the load and E is the effort applied.

Complete step by step answer:
We know that the mechanical advantage of a single fixed pulley is 1.
We know that the mechanical advantage of a movable pulley is 2.

For a single fixed pulley,
$MA1 = \dfrac{L}{{E1}}$
Here MA1 is the mechanical advantage of single fixed pulley and E1 is the effort for single fixed pulley.
We will now substitute MA1=1 and L=50kgf to determine E1.
$\Rightarrow 1 = \dfrac{{50\;{\rm{kgf}}}}{{E1}}$
$\Rightarrow E1 = 50\;{\rm{kgf}}$
For a movable pulley:
$MA2 = \dfrac{L}{{E2}}$
Here, MA2 is the mechanical advantage of single movable pulley and E2 is the effort for single movable pulley.
We will now substitute MA2=2 and L=50kgf to determine E2.
$\Rightarrow 2 = \dfrac{{50\;{\rm{kgf}}}}{{E2}}$
$\Rightarrow E2 = 25\;{\rm{kgf}}$
We will now divide E2 by E1 and we will get,
$\Rightarrow \dfrac{{E2}}{{E1}} = \dfrac{{25\;{\rm{kgf}}}}{{50\;{\rm{kgf}}}}$
$\Rightarrow E 2 = \dfrac{{E1}}{2}$

Hence we can see that the effort required in the case of a movable pulley is half that of a fixed pulley.

Note: The effort is the amount of work done on an object. And we know that work is given by force required to move an object from one place to another. Hence here pulley may reduce the force we are applying but it changes the direction and so the displacement, which is the distance will get increased and the effort will be the same.