Question

A typical car has an axle with \({\rm{1}}{\rm{.10}}\;{\rm{cm}}\) radius driving a tire with a radius of \({\rm{27}}{\rm{.5}}\;{\rm{cm}}\). What is its mechanical advantage assuming the very simplified model inFigure\({\rm{9}}{\rm{.25}}\)(b)?

Short answer

The mechanical advantage is \({\rm{0}}{\rm{.040}}\).

Step-by-step solution

Radius

The radius is the length of the distance between the circle's center and any point on the circle. The letters 'r' or 'R' stand for it.

Diagram

The diagram of the car axle is shown below:

The distance between the input force and the pivot point is \({I_i} = 1.10\;{\rm{cm}}\)

The distance between the output force and the pivot is \({I_0} = 27.5\;{\rm{cm}}\)

Calculation of the mechanical advantage

The mechanical advantage is,

\(\begin{align}MA &= \frac{{{l_i}}}{{{l_o}}}\\ &= \frac{{1.10}}{{27.5}}\\ &= 0.040\end{align}\)

Thus, the value is \({\rm{0}}{\rm{.040}}\).