Kinetic Energy Kinetic energy is energy of motion. Kinetic energy is a scalar quantity. KE = ½ mv 2 kinetic energy = ½ mass x (speed) 2 Units for KE are in Joules (J)

Kinetic Energy So: W net = FΔx = maΔx And remember that: v f 2 = v i 2 + 2aΔx Rearrange: aΔx = (v f 2 - v i 2 )/2 Then substitute back into work equation: W net = ½ mv f 2 – ½ mv i 2

Kinetic Energy Kinetic energy depends on both an object’s speed and it’s mass. Ex: if a bowling ball and a tennis ball are traveling at the same speed, which has more kinetic energy? The bowling ball because it has a greater mass.

Kinetic Energy The net work done on an object equals its change in kinetic energy. This is known as the Work-Kinetic Energy Theorem W net = ΔKE Net work = change in kinetic energy

Kinetic Energy The speed of an object increases if the net work done on it is positive, because the final KE is greater than the initial KE. The object’s speed decreases if the net work is negative, because the final KE is less than the initial KE.

Kinetic Energy Ex: A student wearing frictionless in-line skates on a horizontal surface is pushed by a friend with a constant force of 45 N. How far must the student be pushed, starting from rest, so that her final kinetic energy is 352 J? G: F net = 45 NE: W net = KE f – KE i KE final = 352 J W net = F net d KE i = 0 JS: d = (KE f – KE i )/ F net U: d d = (352 J – 0 J)/45 N S: 7.8 m

Potential Energy Potential energy is stored energy. PE is associated with an object that has the potential to move because of its position relative to some other location. It depends on the object’s interaction with the environment. (ex: a spring, falling object, arrow pulled back)

Potential Energy Gravitational potential energy is the energy associated with an object due to its position relative to the ground. PE g = mgh Gravitational PE = mass x acceleration due to gravity x height Units are in Joules (J)

Elastic Potential Energy Depends on distance compressed or stretched (mostly used with springs or other stretched strings) The length of a spring when no external forces are acting on it is called the relaxed length of the spring. When an external force compresses or stretches the spring, elastic PE is stored in the spring.

Elastic Potential Energy PE elastic = ½ kx 2 k = spring constant, or force constant. For a flexible spring, k is large, for a stiff spring, k is small. Units are N/m x = distance stretched or compressed

KE and PE example The staples inside a stapler are kept in place by a spring with a relaxed length of m. If the spring constant is 51.0 N/m, how much elastic potential energy is stored in the spring when its length is m? G: k = 51.0 N/mE: PE elastic = ½ kx 2 x = m – m S: PE=½(51.0 N/m)(0.35 m) 2 x = mS: PE = 3.1 x J U: PE