Question

How powerful is an engine that can do 400 J of work in 10 seconds?
(Provide your answer in both "Watts" and "horsepower".)

Answer 1

Answer:

$P=40 \ W$

Conceptual:

What is work?

Work is simply the transfer of work over a displacement. Work is a Newton-meter which is called a Joule, J. Work can be calculated using the following formulas.

$\boxed{\left\begin{array}{ccc}\text{\underline{Equations for Work:}}\\W=F \Delta rcos(\theta) \ \text{(Constant} \ \vec F) \\W= \int\limits^{r_2}_{r_1} {Fcos(\theta)} \, dr \ \text{(Varible} \ \vec F) \end{array}\right }$

The angle "θ" is the angle between the force applied and the direction of displacement.

What is power?

Power is the amount work done per second, which is a J/s, and this is clumped together to create a Watt, W. Power can be calculated using the following formula.

$\boxed{\left\begin{array}{ccc}\text{\underline{Formula for Power:}}\\\\P=\frac{W}{t} \end{array}\right}$

Explanation:

Given that an engine does 400 J of work in 10 seconds. Find the power of the engine.

$W=400 \ J\\t=10 \ s$

Plug these values into the formula for power.

$P=\frac{W}{t} \\\\\Longrightarrow P=\frac{400}{10}\\\\\therefore \boxed{P=40 \ W}$

Thus, the engines power is calculated.