Power Problems in Physics

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:

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

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:

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

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:

      

   2. Plug in the numbers:

      

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

      

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

      

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

      

   3. Therefore, the power is

      

   4. Plug in the numbers:

      

2. 360 W

   1. The equation for power is

      

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

      

   3. Therefore, the power is

      

   4. Plug in the numbers:

      

3. 4,500 W

   1. The equation for power is

      

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

      

   3. Therefore, the power is

      

   4. Plug in the numbers:

      

4. 7.5 x 10³ W

   1. The equation for power is

      

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

      

   3. Therefore, the power is

      

   4. Plug in the numbers: