A pulley system with 75% efficiency is set up to lift a 21kg bag of nails. The bag is lifted to a height of 2.3m by a person pulling on the rope with a force of 91.5N. What is the ideal mechanical advantage of this pulley system?

Dec 3, 2015

$I M A = 3$

Explanation:

The mechanical advantage (MA) of a machine is a measure of how much the force is multiplied. It is the ratio of load/effort:

$M A = \frac{L}{E}$

Because energy is conserved, this is done as a trade - off against the distance the effort moves compared with the load.

The ideal mechanical advantage (IMA) is the ratio of the distance moved by the effort/distance moved by the load.

$I M A = {D}_{e} / {D}_{l}$

If we divide MA by IMA we get:

$\frac{L \times {D}_{l}}{E \times {D}_{e}}$ = Work done on the load / Work done by the effort.

In an ideal world this ratio would equal 1. However there are energy losses due to friction etc. We usually express this ratio in terms of efficiency $E$:

$E = \frac{M A}{I M A} \times 100$

In this case:

$M A = \frac{L}{E} = \frac{21 \times 9.8}{91.5} = 2.25$

$\frac{M A}{I M A} \times 100 = 75$

$\therefore I M A = \frac{M A \times 100}{75} = \frac{225}{75} = 3$