Chapter 10.2, Problem 29PP

To determine

The distance by which the end of the lever should be moved to have the efficiency of $88.7$ percent.

Answer to Problem 29PP

  $0.814\text{m}$

Explanation of Solution

Given:

The force exerted on a lever, $F_e=225\text{N}$

The weight of the rock, $F_r=1.25\times {10}^3\text{N}$

The distance by which the rock is raised, $d_r=13\text{}\text{cm = 0}\text{.13 m}$

The efficiency, $e=88.7\%$

Formula used:

The efficiency of a machine is the ratio of real and idea mechanical advantages,

  $e=\frac{MA}{IMA}\times 100=\frac{F_r{d}_r}{F_e{d}_e}\times 100$

Where $F_r$ is the resistance force, $F_e$ is the effort force, $d_r$ and $d_e$ are the distances moved.

Calculation:

Using the given values in above formula, the distance by which the end of the lever ( $d_e$ ) should be moved will be

  $\begin{array}{c}88.7=\frac{\left(1.25\times {10}^3\right)\left(0.13\right)}{\left(225\right)d_e}\times 100\\ d_e=0.814\text{m}\end{array}$

Conclusion:

Thus, the distance by which the end of the lever ( $d_e$ ) should be moved is $0.814\text{m}$ .