A trampoline appears as nothing more than simple fun, but it is actually a complex array of the most basic laws of physics. Jumping up and down is a classic example of the conservation of energy, from potential into kinetic. It also showcases Hooke's laws and the spring constant. Furthermore, it verifies and illustrates each of Newton's three laws of motion.
Kinetic energy is created when an object with some amount of mass is moving with a given velocity. In other words, all moving objects have kinetic energy. The formula for kinetic energy is as follows: KE = (1/2)mv^2, where m is mass, and v is velocity. When you jump on a trampoline, your body has kinetic energy that changes over time. As you jump up and down, your kinetic energy increases and decreases with your velocity. Your kinetic energy is greatest, just before you hit the trampoline on the way down and when you leave the trampoline surface on the way up. Your kinetic energy is 0 when you reach the height of your jump and begin to descend and when are on the trampoline, about to propel upwards.
Potential energy changes along with kinetic energy. At any time, your total energy is equal to your potential energy plus your kinetic energy. Potential energy is a function of height and the equation is as follows: PE = mgh where m is mass, g is the gravity constant and h is height. The higher you are the more potential energy you have. As you leave the trampoline and you begin traveling upward, your kinetic energy decreases the higher up you go. In other words, you slow down. As you slow down and gain height your kinetic energy is transferred into potential energy. Likewise, as you fall, your height decreases which decreases your potential energy. This energy decrease exists because your energy is changing from potential energy into kinetic energy. The transfer of energy is a classic example of the conservation of energy, which states that total energy is constant over time.
Hooke's law deals with springs and equilibrium. A trampoline is basically an elastic disc that is connected to several springs. As you land on the trampoline the springs and the trampoline surface stretches as a result of the force of your body landing on it. Hooke's law states that the springs will work to return to equilibrium. In other words, the springs will pull back against the weight of your body as you land. The magnitude of this force is equal to that which you exert on the trampoline when you land. Hooke's law is stated in the following equation: F = -kx where F is force, k is the spring constant and x is the displacement of the spring. Hooke's law is merely another form of potential energy. Just as the trampoline is about to propel you up, your kinetic energy is 0 but your potential energy is maximized, even though you are at a minimum height. This is because your potential energy is related to the spring constant and Hooke's Law.
Newton's Laws of Motion
Jumping on a trampoline is an excellent way to illustrate all three of Newton's Laws of Motion. The first law, which states that an object will continue its motion unless acted upon by an outside force, is illustrated by the fact that you don't soar into the sky when you jump up and that you don't fly through the bottom of the trampoline when you come down. Gravity and the springs of the trampoline keep you bouncing. Newton's second law illustrates how your velocity changes with the basic equation of F = ma, or force equals mass multiplied by acceleration. This simple equation is used to find the equations for kinetic energy, where acceleration is simply gravity. Newton's third law states than for every action there is an equal an opposite reaction. This is illustrated by Hooke's law. When the springs are stretched they exhibit an equal and opposite force, compressing back into equilibrium and propelling you up in the air.