2. 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 Spring 2005 2 UCSD: Physics 8; 2005

3. 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 Spring 2005 3 UCSD: Physics 8; 2005 mgh becomes ½mv 2 Energy is conserved, so ½mv 2 = mgh Can even figure out v, since v 2 = 2gh h

4. 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 kJ 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 Spring 2005 4 UCSD: Physics 8; 2005

5. Hooke’s Law: Hooke’s 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  x = displacement from the relaxed position (m)  Spring stretched or compressed  k = the constant of proportionality. It is best known as the spring constant (N/m)

6. Relaxed Position

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

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

10. 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 15cm from its equilibrium position. How much potential energy is store in the spring at the point of maximum compression?

11. 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 + PE g (all forms of PE) ME i = ME f

12. A cliff diver dives from a height of 15m 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/mazatlan- mexico