Power Problems in Physics - dummies

By Steven Holzner

When it comes to work in physics, you’re sure to see problems involving power, which is the amount of work being done in a certain amount of time. Here’s the equation for power, P:

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W equals force along the direction of travel times distance, so you could write the equation for power this way:

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where theta is the angle between the force and the direction of travel. On the other hand, the object’s speed, v, is just s/t (displacement over time), so the equation breaks down further to:

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In the special case where the force acts along the direction of travel, you have the simplified formula:

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So in this simplest case, power equals force times speed. You use this equation when you need to apply a force to keep something moving at constant speed.

Sample question

  1. You’re riding a toboggan down an icy run to a frozen lake, and you accelerate the 80.0-kg combination of you and the toboggan from 1.0 m/s to 2.0 m/s in 2.0 s. How much power does that require?

    The correct answer is 60 watts.

    1. Assuming that there’s no friction on the ice, you use this equation for the total work:

      image4.jpg

    2. Plug in the numbers:

      image5.jpg

    3. Because this work is done in 2 s, the power involved is

      image6.jpg

Practice questions

  1. 1.A 1,000-kg car accelerates from 88 m/s to 100 m/s in 30 s. How much power does that require?

  2. A 60.0-kg person is running and accelerates from 5.0 m/s to 7.0 m/s in 2.0 s. How much power does that require?

  3. 3.A 120-kg linebacker accelerates from 5.0 m/s to 10.0 m/s in 1.0 s. How much power does that require?

  4. 4.You’re driving a snowmobile that accelerates from 10 m/s to 20 m/s over a time interval of 10.0 s. If you and the snowmobile together have a mass of 500 kg, how much power is used?

Following are answers to the practice questions:

  1. 3.8 x 104 watts

    1. The equation for power is

      image7.jpg

    2. The amount of work done is the difference in kinetic energy:

      image8.jpg

    3. Therefore, the power is

      image9.jpg

    4. Plug in the numbers:

      image10.jpg

  2. 360 W

    1. The equation for power is

      image11.jpg

    2. The amount of work done is the difference in kinetic energy:

      image12.jpg

    3. Therefore, the power is

      image13.jpg

    4. Plug in the numbers:

      image14.jpg

  3. 4,500 W

    1. The equation for power is

      image15.jpg

    2. The amount of work done is the difference in kinetic energy:

      image16.jpg

    3. Therefore, the power is

      image17.jpg

    4. Plug in the numbers:

      image18.jpg

  4. 7.5 x 103 W

    1. The equation for power is

      image19.jpg

    2. The amount of work done is the difference in kinetic energy:

      image20.jpg

    3. Therefore, the power is

      image21.jpg

    4. Plug in the numbers:

      image22.jpg