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Chapter 2: Problem 87

Use your understanding of work and power to answer the following question. Two teammates, Randy and Aaron, are in the weight-lifting room. Randy lifts the 100-pound barbell over his head 10 times in 5 minutes; Aaron lifts the same 100-pound barbell over his head 10 times in 3 minutes. Which teammate delivers the most power?

Short Answer

Expert verified
Aaron delivers more power.

Step by step solution

01

- Understand the Problem

We need to determine which of the two teammates delivers the most power while lifting the 100-pound barbell. Power is the rate at which work is done.
02

- Convert Weight to Newtons

Convert the weight from pounds to Newtons: 1 pound ≈ 4.44822 Newtons. Therefore, a 100-pound barbell is approximately 445 Newtons.
03

- Calculate the Work Done

The work done in lifting the barbell is given by the formula: Work = Force × Distance. Assuming the height to which the barbell is lifted is the same for Randy and Aaron, the work done by both is: Work = 445 N * Distance. This step doesn't need specific height as it cancels out later.
04

- Calculate the Time in Seconds

Convert the time from minutes to seconds for both teammates. Randy: 5 minutes = 5 * 60 = 300 seconds. Aaron: 3 minutes = 3 * 60 = 180 seconds.
05

- Calculate Power

Power is calculated using the formula: Power = \( \frac{Work}{Time} \). Therefore, calculate the power for both teammates: Randy’s Power = \( \frac{445 * Distance}{300} \) Aaron’s Power = \( \frac{445 * Distance}{180} \)
06

- Compare the Power

Comparing the power of both: Since the work (445 * Distance) for both is identical, the teammate with the lesser time will have more power. Since 180 seconds < 300 seconds, Aaron has more power than Randy.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Calculating Power
Power is an essential concept in physics that tells us how quickly work is done. It’s the rate at which energy is expended or converted. To calculate power, you need to know two things: the amount of work done and the time it takes to do that work. The formula to calculate power is:
  • Power = \( \frac{Work}{Time} \)

Work is measured in Joules and time is measured in seconds. So, power is measured in Watts (W), where 1 Watt equals 1 Joule per second.
Work Formula
Work refers to the amount of energy transferred when a force is applied over a distance. The formula for calculating work is:
  • Work = Force × Distance

Here, force is often measured in Newtons (N) and distance in meters (m). The product of these two gives you work in Joules (J). Whenever you lift an object, you do work against gravity, and lifting a heavier object or lifting it higher requires more work.
Conversion to Newtons
In everyday life, we often measure weight in pounds. However, for scientific calculations, we usually need this weight in Newtons. Here’s how to convert from pounds to Newtons:
  • 1 pound ≈ 4.44822 Newtons.

For example, in the exercise, the 100-pound barbell was converted to Newtons:
  • 100 pounds * 4.44822 ≈ 445 Newtons.

This conversion allows us to use the proper units for calculations involving work and force.
Rate of Work
The rate at which work is done is crucial to understanding power. In simple terms, it’s about how quickly or slowly the work is completed. Here’s how to factor time into your calculations:
  • Power = \( \frac{Work}{Time} \)

In the exercise, time was converted from minutes to seconds because power is measured in Joules per second. For instance, Randy's 5 minutes is converted to:
  • 5 minutes * 60 seconds/minute = 300 seconds.
The same method applies to Aaron's 3 minutes:
  • 3 minutes * 60 seconds/minute = 180 seconds.

By comparing how long each person takes to do the same amount of work, we can determine who delivers the most power.

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