Wheel and Axle Question

Question

A wheel and axle arrangement is used to raise a 150-kg load of bricks with a 140-newtom effort. If the axle's radius is 4.00 cm and the wheel's radius is 44.0 cm, calculate:

a) Actual mechanical advantage

b) theoretical mechanical advantage

c) efficiency

Answer 1

Let

g = 9.81 m/s² be gravitational acceleration

F_in = 140 N be the force going into the mechanism,

F_out = g × 150 kg = 9.81 m/s² × 150 kg = 1471.5 N be the force coming out of the mechanism.

a)

Actual mechanical advantage is defined as

F_out/F_in = 1471.5/140 = 10.51

b)

Theoretical mechanical advantage is defined as the ratio of force out and force in,

which could be observed under the ideal conditions of the mechanism dissipating

or storing no energy.

In the case of wheel and axle mechanism, the theoretical mechanical advantage

is the ration between the two radii:

44 cm / 4 cm = 11

c)

Efficiency is defined as the ratio of the two mechanical advantages:

10.51/11 = 0.95

There are several reasons why it might be less than 1:

- energy dissipated into friction,

- energy dissipated into bending the axle,

- energy stored into kinetic energy of the bricks in case the 140 N force

is sufficient to actually cause acceleration of the load.