Chapter 11.1, Problem 6PP

To determine

The amount of work done to lower a $20.0\text{kg}$ bag of sand by $1.20\text{m}$ .

Answer to Problem 6PP

  $235.2\text{J}$

Explanation of Solution

Given:

The mass of the bag of sand, $m=20.0\text{kg}$

The distance by which the bag is lowered, $d=1.20\text{m}$

Formula used:

The work done is given by,

  $W=Fd\cos \theta$

Where $F$ is the force done, $d$ is the distance, and $\theta$ is the angle between the distance and force.

Calculation:

The force acting on the bag is its weight, and the angle between the force and its displacement is $0°$ . Thus, work done in lowering the bag is,

  $\begin{array}{c}W=Fd\cos \theta \\ =\left(mg\right)d\cos 0°\\ =\left(20\right)\left(9.8\right)\left(1.20\right)\\ =235.2\text{J}\end{array}$

Conclusion:

Thus, the amount of work done to lower a $20.0\text{kg}$ bag of sand is $235.2\text{J}$ .