Question

gedananken-experiment. explain thebehavior of a yo-yo in terms of conservation of mechanical energy

Answer 1

A yo-yo might look like a toy, but it's also an energy converting machine. Understanding how it constantly changes energy from one kind into another is the key to figuring out how it works. If you're not familiar with scientific terms like potential energy and kinetic energy, you might want to browse through our energy article before you go any further.

When you hold a yo-yo in your hand, it has potential energy: it stores energy because it's high above the floor. When you release it, the potential energy is gradually converted into kinetic energy (the energy something has because it's moving). When a yo-yo is spinning at the bottom of its string, virtually all the potential energy it had originally has been converted into kinetic energy. As a yo-yo climbs up and down its string, it is constantly exchanging potential and kinetic energy—much like a rollercoaster car.

A spinning yo-yo actually has two different kinds of kinetic energy: one kind because it's moving up and down the string and another kind because it's spinning around. When you release the yo-yo from your hand, it falls toward the ground just like a stone, and it picks up speed because it's falling. But a yo-yo is different from a stone because it has string wrapped around its axle. As it falls, it starts to spin. That's why a yo-yo falls much more slowly than a stone: some of the energy that should be making it fall quickly is actually being used to make it spin around at the same time.

Whatever it's doing, and wherever it is on the string, a yo-yo usually has a mixture of three different kinds of energy:

1. Potential energy—because it's a certain height above the floor.
2. Kinetic energy of movement—because it's moving up or down relative to the floor.
3. Kinetic energy of rotation—because it's spinning around

In a perfect world, a yo-yo could rise and fall on its string forever. But as the string spins on the plastic axle, friction (the rubbing force between two things that are in contact and moving past one another) uses up some of its energy. Although you can't see it happening, the spinning yo-yo wheels also rub against the air that surrounds them. This air resistance also eats away at the yo-yo's energy supply. If you don't keep giving the yo-yo more energy, by pumping the string up and down, it slows down very quickly and grinds to a halt. Every time you tug the string, you jerk the yo-yo so it keeps on spinning. In effect, you are recharging its energy batteries with each tug.