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

`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=(W)/(t) \end{array}\right}`

Step-by-step 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=(W)/(t) \\\\\Longrightarrow P=(400)/(10)\\\\\therefore \boxed{P=40 \ W}`

Thus, the engines power is calculated.