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# 4.38: Power

Difficulty Level: At Grade Created by: CK-12
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Did you ever sweep a floor with a broom, like the woman in the picture on the left? It can take a lot of effort to do the job. But if you use an electric vacuum cleaner, like the woman in the picture on the right, you can do the same work more easily and quickly. That’s because the vacuum cleaner provides more power.

### What Is Power?

Power is a measure of the amount of work that can be done in a given amount of time. Power can be represented by the equation:

Power=WorkTime\begin{align*}\mathrm{Power=\frac{Work}{Time}}\end{align*}

In this equation, work is measured in joules (J) and time is measured in seconds (s), so power is expressed in joules per second (J/s). This is the SI unit for power, also known as the watt (W). A watt equals 1 joule of work per second. You’re probably already familiar with watts. Light bulbs and small appliances such as microwave ovens are labeled with the watts of power they provide. For example, the package of light bulbs in the Figure below is labeled “14 watts.”

Q: Assume you have two light bulbs of the same type, such as two compact fluorescent light bulbs like the one pictured in the Figure above. If one light bulb is a 25-watt bulb and the other is a 60-watt bulb, which bulb produces brighter light?

A: The 60-watt bulb is more powerful, so it produces brighter light.

Compared with a less powerful device, a more powerful device can either do more work in the same time or do the same work in less time. For example, compared with a low-power microwave oven, a high-power microwave oven can cook more food in the same time or the same amount of food in less time.

### Calculating Power from Work and Time

Power can be calculated using the formula above if the amount of work and time are known. For example, assume that a microwave oven does 24,000 joules of work in 30 seconds. Then the power of the microwave is:

Power=WorkTime=24000J30s\begin{align*}\mathrm{Power=\frac{Work}{Time}=\frac{24000J}{30s}}\end{align*}=800 J/s, or 800 W

Q: Another microwave oven does 5,000 joules of work in 5 seconds. What is its power?

A: The power of the other microwave oven is:

Power=5000J5s\begin{align*}\mathrm{Power=\frac{5000J}{5s}}\end{align*}=1000 J/s or 1000 W

Q: Which microwave oven will heat the same amount of food in less time?

A: The 1000-watt microwave oven has more power, so it will heat the same amount of food in less time.

### Calculating Work from Power and Time

You can also calculate work if you know power and time by rewriting the power equation above as:

Work = Power x Time

For example, if you use a 1000-watt microwave oven for 20 seconds, how much work does it do? First express 1000 watts in J/s and then substitute this value for power the work equation:

Work = 1000 J/s x 20 s = 20,000 J

You can watch a video about calculating work and power at this URL:

### Horsepower

Sometimes power is measured in a unit called the horsepower. For example, the power of car engines is usually expressed in horsepowers. One horsepower is the amount of work a horse can do in 1 minute. It equals 745 watts of power. Compare the horsepowers in the Figure below to the other Figure below.

This team of six horses provides 6 horsepowers of power.

This big tractor provides 180 horsepowers of power.

Q: If the team of horses and the tractor do the same amount of work plowing a field, which will get the job done faster?

A: The tractor will get the job done faster because it has more power. In fact, because the tractor has 30 times the power of the six-horse team, ideally it can do the same work 30 times faster!

### Summary

• Power is a measure of the amount of work that can be done in a given amount of time. Power equals work (J) divided by time (s).
• The SI unit for power is the watt (W), which equals 1 joule of work per second (J/s).
• Power can be calculated from work and time using the equation: .
• Power may be measured in a unit called the horsepower. One horsepower is the amount of work a horse can do in 1 minute, which equals 745 watts of power.

### Vocabulary

• power: Measure of the amount of work that can be done in a given amount of time.
• watt (W): SI unit for work, equal to 1 joule of work per second.

### Practice

At the following URL, review what power means and how it is calculated. Then do the first four Check Your Understanding problems. Be sure to check your answers and read the explanations. For an extra challenge, try to do the last two Check Your Understanding problems.

### Review

1. What is power? What is the SI unit for power?
2. How much power does a toaster have if it does 21,000 joules of work in 30 seconds?
3. How much work can be done in 30 seconds by a 1000-watt microwave oven?
4. Lamar’s mom has a car with a 182-horsepower engine. How many watts of power is that?

### Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes

### Vocabulary Language: English

power

Measure of the amount of work that can be done in a given amount of time.

watt

(Abbreviation: W) SI unit for work, equal to 1 joule of work per second.

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