Question

A worker lifts a load of 200 N with the help of a lever by applying an effort of 50 N. The load is
kept at a distance of 20 cm and the effort is applied at a distance of im from the fulcram. Find the
mechanical advantage, velocity ratio, and efficiency of the lever used.​

Answer 1

a) The mechanical advantage is 4

b) The velocity ratio is 5

c) The efficiency is 80%

Explanation:

a)

The mechanical advantage of a lever (or any other machine) is given by

$MA=\frac{Load}{Effort}$

Where

$Eff$ is the effort (the force applied in input)

$Load$ is the load (the force in output to the lever)

For the lever in this problem, we have:

$Eff = 50 N$

$Load = 200 N$

Substituting into the equation, we find the mechanical advantage of the lever:

$MA=\frac{200}{50}=4$

b)

The velocity ratio of a lever (or any other machine) is given by the equation

$vr=\frac{d_{res}}{d_{eff}}$

where

$d_{res}$ is the length of the resistance arm

$d_{eff}$ is the length of the effort arm

For the lever in this problem, we have

$d_{res} = 20 cm$

$d_{eff}=1 m = 100 cm$

Therefore, the velocity ratio is

$vr=\frac{100}{20}=5$

The velocity ratio represents the ideal mechanical advantage of the machine, i.e. the mechanical advantage in absence of friction, or the maximum theoretical mechanical advantage.

c)

The efficiency of the lever is given by the following ratio:

$\eta = \frac{MA}{vr}$

where

MA is the mechanical advantage

vr is the velocity ratio

For the lever in this problem, we have

MA = 4 (calculated in part a)

vr = 5 (calculated in part b)

Therefore, the efficiency of the lever is

$\eta = \frac{4}{5}=0.80$

Which means an efficiency of 80%.

Learn more about levers:

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