Chapter 10.2, Problem 32SSC

To determine

The ideal mechanical advantage of the given compound machine

Answer to Problem 32SSC

  $18.0$

Explanation of Solution

Given:

The radius of the crank, $r_e=45\text{cm}$

The radius of the drum, $r_r=7.5\text{cm}$

Number of revolutions undertaken by crank, $n=3$ to rotate the drum through one revolution.

Formula used:

The idea mechanical advantage is the ratio of the distances moved,

  $IMA=\frac{d_e}{d_r}$

Where $d_e$ is the displacement by the effort force, and $d_r$ is the displacement of the load.

Calculation:

Using the given values in above formula, the ideal mechanical advantage of the given compound machine will be,

  $\begin{array}{c}IMA=\frac{n\times 2\pi r_e}{2\pi r_r}\\ =\frac{3\times 45}{7.5}\\ =18.0\end{array}$

Conclusion:

Thus, the ideal mechanical advantage of the given combined machine is $18.0$ .