Chapter 6, Problem 4PC

Calculate the power expended when a 20 N force pushes a cart 3.5 m in a time of 0.5s .

To determine

The power expended.

Answer to Problem 4PC

The power expended is 140 watt .

Explanation of Solution

Given info: The force is 20 N , the distance is 3.5m and the time interval is 0.5 s .

Write the expression for the work done.

$W=F\times d$

Here,

F is the force

d is the distance

Substitute 20 N for F and 3.5 m for d in the above equation to get w .

$\begin{array}{c}W=20\text{N}\times 3.5\text{m}\\ W=70\text{N}\cdot \text{m}\times \frac{1\text{J}}{1\text{N}\cdot \text{m}}\\ W=70\text{J}\end{array}$

Write the expression for the power.

$P=\frac{W}{t}$

Here,

W is the work done

t is the time interval

Substitute 70 J for W and 0.5 s for t in the above equation to get P .

$\begin{array}{l}P=\frac{\text{70}\text{J}}{0.5\text{s}}\\ P=140\text{J}/\text{s}\times \frac{1\text{watt}}{1\text{J}/\text{s}}\\ P=140\text{watt}\end{array}$

Conclusion:

Therefore, the power is 140 watt .