Question

What is the mechanical advantage of a nail puller—similar to the one shown inFigure\({\rm{9}}{\rm{.23}}\)—where you exert a force \({\rm{45}}\;{\rm{cm}}\)from the pivot and the nail is \({\rm{1}}{\rm{.8}}\;{\rm{cm}}\)on the other side? What minimum force must you exert to apply a force of \({\rm{1250}}\;{\rm{N}}\) to the nail?

Short answer

The mechanical advantage of the nail puller is \({\rm{25}}{\rm{.0}}\) and the minimum force is \({\rm{50}}\;{\rm{N}}\).

Step-by-step solution

Force

A force is an external factor that can change the rest or motion of a body. It has a size and a general direction.

Given data and the free-body diagram

The force is \({\rm{1250}}\;{\rm{N}}\).

You exert a force at a distance of\({\rm{45}}\;{\rm{cm}}\)from the pivot.

The nail is at a distance\({\rm{1}}{\rm{.8}}\;{\rm{cm}}\)from the pivot on the other side.

The diagram of the nail puller is shown below:

Calculation of the Mechanical advantage and the minimum Force

The mechanical advantage is,

\(\begin{align}MA &= \frac{{{l_i}}}{{{l_o}}}\\ &= \frac{{45}}{{1.8}}\\ &= 25.0\end{align}\)

The input force is\({\rm{1250}}\;{\rm{N}}\), the minimum force that one exerts is,

\(\begin{align}{F_o} &= \frac{{{F_i}}}{{MA}}\\ &= \frac{{1250}}{{25.0}}\\ &= 50\;{\rm{N}}\end{align}\)

Thus, the values are \({\rm{25}}{\rm{.0}}\) and \({\rm{50}}\;{\rm{N}}\).