A child jumps on a trampoline. He stretches the trampoline downward when he lands on it. He comes to a short stop when the trampoline can't stretch any farther. He then bounces upward again. What is happening to his kinetic energy as the trampoline stretches and slows him? His gravitational potential energy? The elastic potential energy of the trampoline? What is happening to the total of these three?

Explanation:

Everyone likes trampolines. But how do they even work? It's all about energy, and at the same time, proves Newton's laws of motion.

Potential energy (PE) and kinetic energy (KE) are the reason trampolines allow you to jump higher than you can on flat ground. One type of potential energy that is involved with trampolines is the potential energy stored in springs. Another type of energy is gravitational potential energy. There is also kinetic energy because you are moving. The equation that connects potential and kinetic energy to find total energy (E) is:

E=PE+KE+Q

The total energy of the person jumping on a trampoline equals all of the potential energy (both the spring and gravitational potential), plus the kinetic energy. Q is internal energy, which isn't really important here.

Other equations needed to understand the forces and energy of trampolines are:

PE=mgh

This used to find the potential energy due to gravity. You multiply the mass of the object (or person in this case), by the height they are from the ground, by g, acceleration due to gravity. Which is always 9.81 m/s^2.

People with larger masses have a greater potential energy due to gravity if they are at the same height as someone with a smaller mass. However, it is harder for people with larger masses to reach the same heights as people with small masses, because gravity is pulling them down more.

PE=(1/2)kx^2

The potential energy stored in a spring: "x" is how much the spring stretches, and "k" is the spring constant. Hooke's law goes along with this: F=kx. The force of the spring is the constant multiplied by the change in the spring length. This demonstrates Newton's third law; every action has an equal and opposite reaction. When the springs are stretched by the person, they have to compress again, making the person jump higher as the trampoline returns to its original position.

Because of gravity, larger masses allow the spring to be stretched out more. This can be shown by the equation F=ma, which is Newton's second law of motion."F" is the force of gravity, "m" is mass, and "a" here is also g, acceleration due to gravity. So when mass increases, so does the force of gravity. This means the object/person is being pulled down harder by gravity. This stretches the springs of the trampoline more, creating a higher spring potential energy. But the mass is usually too heavy for the spring to move you if you just stand there, which is why you don't move unless you start jumping first.

Smaller kids usually jump higher than adults, even though they have a lower potential energy due to gravity, because the trampoline can more easily spring them back up, since they are being pulled down by gravity slightly less.

This is all a great example of Newton's first law: objects in motion will keep moving, and objects at rest will not move, until acted upon by an outside force. The outside forces that keep you on the trampoline are both gravity, which keeps you down, and the trampoline itself, which keeps you up. You also wont move until you begin jumping. Pushing your feet down makes you go up. (Newton's third law!)

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