Delivering Power to the People

Students are asked to consider the work and power required to pedal a bike up two identical hills. The first question asks which hill requires more work. (In this scenario, the rider took 1 minute to climb the first hill and 2 minutes to climb the second). The second question asks which hill required the most power.

Give students a moment to answer the first multiple-choice question (about work) before reading on to the provided answer.

Have students talk to their partner and agree on an answer for the second multiple-choice question (about power). Read the "reveal" paragraph that explains that more power was used on the first hill.

Students are first reminded the unit of measure for work is a joule. The amount of work to ride up the hill is estimated in context of the work of lifting an apple onto a shelf. The estimate is 10,000 joules.

Students are then asked to think about the work involved for both hill-climbing situations. The ratio of work to time is discussed. The ratio is first written using the word “to” and then as a fraction. Ask students to recall what a rate that has 1 in the denominator is called (unit rate). Ratio, rate, and unit rate are generally 6th and 7th grade concepts so they should be understood in this context.

Emphasize that by dividing numerator by denominator the answers will have a 1 in the denominator, so the unit rates can be compared. The goal is to determine which is greatest. Before calculating the unit rate, ask students to estimate their answers and choose which number will be greater.

The calculations to determine which climb required the greatest power are shown at the top of this page. The two resulting unit rates can be compared because both have 1 in the denominator.

• 10,000 joules / 60 seconds or 166.67 joules / 1 second is greater than 10,000 joules / 120 seconds or 83.33 joules / 1 second. Therefore it takes twice as much power to ascend the first hill.

Pause to clarify any questions. Reiterate that a watt is a unit of measure of power, and that watt is a unit rate (1 watt = 1 joule per 1 second).

Before reading the second slide, ask students if they know how many watts are in a typical light bulb. This wattage will provide a point of reference for the definition and size of the units. Consider asking, if a windmill generates 1,000,000 watts, how many typical light bulbs could it light up?

Ask:

Think of other examples that use the concept of power.

Sample answers:

• weightlifters, car engines, sports, various sized batteries, etc.

Ask:

How would you calculate power for each example listed?

Note that some examples the students list will be the everyday use of the word "power" rather than the scientific.