Examples involving instantaneous power

First, we'll do an example involving linear motion -- then, one with rotational motion.

Joe is driving his Toyota Corolla one day when it runs out of gas. "Oh well," sighs Joe, "I guess I'll have to push it to the gas station."

He knows there's a gas station about one mile ahead, along a nice, straight, level road. In order to get there before night falls and the ice weasels come, he'll need to maintain a speed of v = 3 m/s.

As he pushes the car at this speed, air resistance exerts a drag force of F = 600 N. Clearly, Joe must push forward with this same force in order to prevent the car from slowing down.

1. How much power must Joe exert to keep the car moving?
2. Will he make it to the gas station in time?

Not sure? Look at a paper by Davies and Sandstrom, Eur. J. Appl. Physiol. 58, 838 (1989)

Figure 1 taken from Maximal mechanical power output and capacity of cyclists and young adults by Davies and Sandstrom, Eur. J. Appl. Physiol. 58, 838 (1989)

Instantaneous power in rotational motion

Image courtesy of Miami Herald

Back in 1934, Pan Am built a big globe as the centerpiece of its Dinner Key airboat terminal in Florida. The hollow globe has a radius of R = 1.524 m and a mass M = 3000 kg.

1. What is the moment of inertia of this globe as it spins around its central axis?

A motor spins the globe at 10 RPM.

2. What is the kinetic energy of the globe?

Little Billy sticks his hand out and presses his finger against the equator with a force of F = 60 N. The coefficient of kinetic friction between finger and globe is μ_k = 0.25.

3. Assume that all the energy dissipated by friction turns into heat in Billy's finger. How much power is his finger absorbing?
4. If Billy keeps pressing with the same force, how long will it take to stop the rotation of the globe?

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.