Wheel and Axle

A Wheel and Axle is a simple machine that consists of a wheel and axle mounted with the same axis of rotation. The radius of the wheel is always greater than that of the axle.
Consider the diagram below.

Mechanical advantage of Wheel and Axle

      Mechanical advantage (M.A) = Load
                                                         Effort

        M.A = L
                                E

Velocity ratio of Wheel and Axle

      Velocity ratio ( V.R)= radius of wheel (R)
                                             radius of axle (r)

                                  V.R = R
                                              r

Example 1.

A wheel and axle of efficiency 80% is used to raise a load of 2000N. If the radius of the wheel is 50cm, and that of the axle is 2cm, calculate

a)  The velocity ratio and mechanical Advantage of machine

b)  The effort required to overcome the load

Solution

          Data given

          Efficiency (ɛ) = 80%

          Load (L) = 2000N

          Radius of wheel (R)= 50cm

          Radius of axle (r) = 2cm

          Velocity ratio (V.R) =?

          Mechanical advantage (M.A) =?

          Effort (E) =?

a)  Velocity ratio (V.R)

The velocity ratio of the machine = 25

Mechanical advantage (M.A) =?

From

The Mechanical advantage of the machine = 20

b)      Effort (E) =?

From

The effort required to raise the load = 100 N