Potential Elastic and Mechanical Energy Gravitational Potential Energy

Potential, Elastic, and Mechanical Energy

Gravitational Potential Energy � It takes work to lift a mass against the pull (force) of gravity � The force of gravity is m·g, where m is the mass, and g is the gravitational acceleration � F = mg (note similarity to F = ma) � g = 9. 81 m/s 2 on the surface of the earth � Lifting a height h against the gravitational force requires an energy input (work) of: E = W = F ·h = mgh ∴ PE=mgh UCSD: Physics 8; 2005 Spring 2005 2

First Example of Energy Exchange �When the boulder falls off the cliff, it picks up speed, and therefore gains kinetic energy �Where does this energy come from? ? from the gravitational potential energy �The higher the cliff, the more kinetic energy the boulder will have when it reaches the ground mgh h becomes Energy is conserved, so ½mv 2 = mgh Can even figure out v, since v 2 = 2 gh ½mv 2 UCSD: Physics 8; 2005 Spring 2005 3

Examples of Gravitational Potential Energy �How much gravitational potential energy does a 70 kg high- diver have on the 10 meter platform? mgh = (70 kg) (10 m/s 2) (10 m) = 7, 000 kg·m 2/s 2 = 7 k. J �How massive would a book have to be to have a potential energy of 40 J sitting on a shelf two meters off the floor? mgh = m (10 m/s 2) (2 m) = 40 J so m must be 2 kg UCSD: Physics 8; 2005 Spring 2005 4

Springs �Hooke’s Law: The force exerted by a spring is proportional to the distance the spring is stretched or compressed from its relaxed position. Ø FX = - k x Ø x = displacement from the relaxed position (m) Ø Spring stretched or compressed Ø k = the constant of proportionality. It is best known as the spring constant (N/m)

Relaxed Position

Simple Harmonic Motion �occurs when the force F acting on an object is directly proportional to the displacement x of the object, but in the opposite direction.

Examples of Simple Harmonic Motion

Elastic Potential Energy 2 PE =½kx elastic Ø x = displacement from the relaxed position (m) Ø k = the spring constant. (N/m) Ø PEelastic = Elastic Potential Energy or work stored in the spring. (J)

Sample Problem 5 D The spring constant of a car’s front coil spring is 1. 8 X 10 5 N/m. When a front tire of the car rolls over a rock, the spring is compressed 15 cm from its equilibrium position. How much potential energy is store in the spring at the point of maximum compression?

Law of Conservation of Energy �It cannot be created nor destroyed. �It can change form �The total amount of energy in an isolated system does not change �Mechanical Energy ME= KE + PEg (all forms of PE) �MEi = MEf

Sample 5 E A cliff diver dives from a height of 15 m above the water surface. How far is he from the water when his speed is 12 m/s? Neglect air resistance. http: //mycollegeroadtrip. com /spring-break/mazatlanmexico