Chapter 4.1, Problem 9PP

To determine

To calculate: the output force from the machine.

Answer to Problem 9PP

The output force from the machine needed to lift the weight is $\underset{\_}{45000\text{ N}}$ .

Explanation of Solution

Given data:

Input force (weight), $F_{in}=3000\text{ N }$

Mechanical Advantage of the machine, $MA=15$

Formula used:

Mechanical Advantage Equation:

  $MA=\frac{F_{out}}{F_{in}}$

Where $MA$ is the mechanical advantage of the machine, $F_{in}$ is the input force in newton and $F_{out}$ is the output force in newton.

Calculation:

As per the problem,

  $\begin{array}{l}{F}_{in}=3000\text{ N}\\ MA=15\end{array}$

Substitute the values of mechanical advantage and input force in the rearranged mechanical advantage equation to get output force:

  $\begin{array}{l}MA=\frac{F_{out}}{F_{in}}\\ F_{out}=MA\times F_{in}\\ F_{out}=(15)(3000\text{ N)}\\ F_{out}=45000\text{ N}\end{array}$

Conclusion:

The output force from the machine needed to lift the weight is $\underset{\_}{45000\text{ N}}$