Try This: Prove that work, Potential Energy, and Kinetic energy are the same for the following: A block sitting at 0meters is slide up a frictionless inclined plane to a height of 80 meters. The block is then held in place for 50 minutes. The block is then released.
Elastic Potential Energy in Springs If you pull on a spring and stretch it out, you do work on the spring. W = Fd Since work is a transfer of energy, then energy must be transferred into the spring.
Work becomes stored in the spring as potential energy. When you stretch a spring, it has the potential to “spring” back. This is stored energy. When you compress a spring, it has the potential to “spring” forwards. This is stored energy.
Work & Elastic Potential Energy: E e = ½ k x 2 E e = elastic potential energy in J (joules) k = spring constant N/m (newtons per meters) x = length of extension m (meters)
Energy Stored in a Spring If a spring’s stretch/compression is directly proportional to the the amount of force applied to it then the elastic potential energy stored in a spring is given by: Where x is the DISTANCE the spring is stretched or compressed K is called a “spring constant”.
Hookes Law: The force exerted by a spring is proportional to the distance the spring is stretched or compressed from its relaxed position. F X = -k x Where x is the displacement from the relaxed position and k is the constant of proportionality. (often called “spring constant”) x > 0
Conservation of Energy: m y y=0 m x x=0 E total = 1/2 mv 2 + 1/2 kx 2 = constant KE PE
Hooke’s Law Investigation: Start Hooke’s Law Investigation