Lesson 13.3: Power is the rate at which work is done

Lesson Focus

This lesson explores power, the rate at which work is done or energy is transferred. We'll see how doing the same work faster requires more power and discover how this concept applies to everyday machines and activities.

Learning Objectives

• Explain the relationship between power, work, and time.
• Understand how power also measures the rate of energy transfer over time.
• Describe common uses of power, measured in watts and horsepower.
• Apply your knowledge to measure the power required to move an object.

Doing work quickly requires more power. Power is the rate at which work is done, found using P = W/t, where P is power in Watts, W is work in Joules, and t is time in seconds. A high-power engine accomplishes the same work as a low-power one, but much faster.

When work is hard to measure, like in a TV, power is seen as the rate of energy transfer. We use the formula P = E/t, where E is energy in Joules. A 60-Watt light bulb, for example, converts 60 Joules of electrical energy into light and heat each second.

The standard scientific unit for power is the Watt (W), equal to one Joule per second. For powerful machines like car engines, the larger, historical unit of horsepower (hp) is common. One horsepower equals about 745 Watts, allowing us to compare the power of different engines and motors.

Home appliances show power at work. A hair dryer's wattage indicates how much energy it uses per second. A higher power setting makes the fan and heater work faster, drying hair more quickly. This demonstrates the direct link between an appliance's power rating and its performance speed.

A swimmer can increase her power by pushing with more force or moving at a greater speed. Since Power = Work / time and Work = Force × distance, we can also see that Power = Force × (distance / time). This means Power = Force × speed, a useful shortcut for analyzing moving objects.