Chapter 10, Problem 8STP

To determine

To Calculate: The work done and power required to move the box.

Answer to Problem 8STP

Option D

Explanation of Solution

Given:

Force applied on the box, $F=200.0\text{N}$

Displacement of the box, $s=5.0\text{m}$

Time elapsed, $t=10.0\text{s}$

The force is applied at an angle of $\theta ={45.0}^{\text{o}}$ from the horizontal.

Formula Used:

Power consumed can be obtained by:

  $P=\frac{W}{t}$

Where, W is the work done and t is the time elapsed.

Work done: $W=F\cdot s$

Here, F is the applied force and s is the displacement

Calculations:

Resolve the force into its components. Along the horizontal axis:

  $\begin{array}{c}{F}_x=F\cos \theta \\ =\left(200.0\text{N}\right)\left(\cos {45}^{\text{o}}\right)\\ =141.4\text{N}\end{array}$

The vertical component would not contribute the work done because the vertical component of force and displacement of the box are perpendicular, so their dot product would be zero.

Work done to move the box can be calculated as follows:

  $\begin{array}{c}W=F_x\cdot s\\ W=200.0\text{N}\cdot 5.0\text{m}\\ \text{=1000}\text{J}\end{array}$

Power required to move the box:

  $\begin{array}{c}P=\frac{1000\text{J}}{10.0\text{s}}\\ =10\text{0}\text{W}\end{array}$

Conclusion:

Thus, the work done to move the box is 1000 J and the power required is 100 W.