Question

The efforts required for lifting various loads by a lifting machine are tabulated below:

Load lifted in N	100	100	100	100	100	100
Effort required in N	16.0	22.5	28.0	34.0	40.5	46.5

Determine the law of machine. If the velocity ratio is 25, calculate efficiency at each load and plot efficiency versus load curve. From this curve, determine the maximum efficiency.

Answer 1

Figure  shows the graph of effort versus load. From this figure, C = 10 N and slope

m = \(\frac{30}{500}\) = 0.06

∴ The law of machine is

P = 0.06 W + 10

η = \(\frac{MA}{VR}\) = \(\frac WP\) x \(\frac{1}{VR}\) = \(\frac WP\) x \(\frac{1}{25}\) = \(\frac W{25P}\)

Table below shows the calculation of efficiency for various loads:

Load in N	100	200	300	400	500	600
Effort in N	16.0	22.5	28.0	34.0	40.5	46.5
Efficiency in %	25	36.56	42.86	47.06	49.38	51.61

From the graph maximum efficiency is seen as 57%. Actually if it is plotted for infinitely large load, maximum efficiency will be equal to

\(\frac1m\) x \(\frac1{VR}\) = \(\frac1{0.06}\) x \(\frac1{25}\) = 0.6667 = 66.67%