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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!)

Walking is something that we do every day, without thinking about it. Its seems very simple and straight forward. You just put one foot in front of the other and you move. But it is kind of complicated. It has a lot to do with forces. Newton's laws of motion are involved. So what do forces have to do with walking? Newton's third law states that every action has an equal and opposite reaction. This is relevant to walking because when you put your foot on the ground, you are applying a force to it. In doing this, the ground also actually applies an equal force onto your foot, in the opposite direction, pushing you forward. When running, you tend to take longer strides because you are applying a larger force to the ground, so the ground must apply a larger force onto your body. When a larger force is applied to your foot, you go farther, taking a longer step. Another law of motion that is at work is Newton's first law of motion. An object in motion stays moving, and an object at rests stays at rest unless an outside force acts on it. If people didn't apply forces to the ground, they obviously wouldn't move. This is because the ground then doesn't apply a force to the persons foot. They would stay at rest. But also, if it weren't for gravity, we would all float up into space the second we took one step. This is because the ground applies a force onto us, so we are set into motion. Gravity keeps this force from pushing us all the way into space. (there is also centrifugal force that wants to fly people off of the planet, but ehh.)