Chapter 10, Problem 84A

To determine

Ways to increase the ideal mechanical advantage of a machine.

Explanation of Solution

Introduction:

The mechanical advantage is mathematically defined as the ratio of force experienced by the load ( $F_L$ ) to the force applied i.e. the effort ( $F_E$ ) .

  $\text{Machine advantage (}MA\text{)}=\frac{F_L}{F_E}$

The machine advantage can also be represented in terms of distance of load $\left(x_L\right)$ and fulcrum $\left(x_E\right)$ with the help of conservation of energy.

According to the law of conservation of energy, the energy at load will always be equal to the energy applied at effort.

Therefore,

  $\begin{array}{l}{E}_L=E_E\\ F_L{x}_L=F_E{x}_E\end{array}$

  $\begin{array}{l}{E}_L=E\\ \frac{F_L}{F_E}=\frac{x_E}{x_L}\end{array}$

Thus, $MA=\frac{x_E}{x_L}$

With increase of mechanical advantage, more power can be transferred to load.

The ways to increase the ideal mechanical advantage are as follows:

1. The $MA$ is directly proportional to $x_E$ keeping $x_L$ constant, so with increase in the value of $x_E$, the mechanical advantage can be increased.
2. With decrease of length of the arm load keeping effort arm fixed.
3. The third way is to move the effort point from the fulcrum and simultaneously moving the load closer to the fulcrum.