Chapter SH, Problem 4.8APP

To determine

To calculate: Force needed to lift a rock.

Answer to Problem 4.8APP

Force needed to lift the rock is $\underset{\_}{196\text{ N}}$ .

Explanation of Solution

Given:

Mechanical advantage = $5$

Mass of rock = $\text{100 kg}$

Formula used:

Mechanical advantage is given by,

  $MA=\frac{F_{\text{out}}}{F_{\text{in}}}$

Where $F_{\text{out}}$ is output force and $F_{\text{in}}$ is input force.

Force is given by,

  $F=mg$

Where m is mass and $g=9.8\text{ N/kg}$ is acceleration due to gravity.

Calculation:

Output force is calculated as:

  $\begin{array}{l}{F}_{\text{out}}=mg\\ F_{\text{out}}=\left(\text{100 kg}\right)\left(9.8\text{ N/kg}\right)\\ F_{\text{out}}=980\text{ N}\end{array}$

Input force is calculated as:

  $\begin{array}{l}MA=\frac{F_{\text{out}}}{F_{\text{in}}}\\ 5=\frac{\text{980 N}}{F_{\text{in}}}\\ F_{in}=\frac{980\text{ N}}{5}\\ F_{in}=196\text{ N}\end{array}$

Conclusion:

Force needed to lift the rock is $\underset{\_}{196\text{ N}}$ .