1. PHYSICS 103: Lecture 12 Review of Example Problems Energy and Work Agenda for Today:

2. Work is done whenever a force causes motion or a change in motion Work = force. distance (both in same direction) Work Units = N m = Joules

3. Energy Stored Work Work waiting to happen The ability to do work Also measured in Joules

4. Energy comes in different Forms Kinetic Energy(KE) Gravitational Potential Energy Internal Energy - friction, air resistance Also measured in Joules Some common examples: Elastic Potential Energy - springs

5. Kinetic Energy Energy of Motion

6. Gravitational Potential Energy Energy due to height when gravity is present

7. Energy Conservation Energy cannot be created or destroyed; it may be transformed from one form to another but the total amount of energy never changes.

8. h Consider a single pendulum with a ball attached to a string E = PE = m  g  h m E = KE = 1 / 2  m  v 2 v h E = PE = m  g  h

9. Test your understanding: The pendulum bob has a mass of 0.5 kg and is released from a height of 12 cm relative to the low point in the swing. What is the speed of the bob as it passes through the low point? m = 0.5 kg h = 12 cm v = ? Initial Energy is PE = m  g  h = 0.5 kg  9.8 m/s 2  0.12 m = 0.588 J Energy at low point is KE = 0.588 J 1 / 2  m  v 2 = 0.588 J

10. Roller Coasters ~ 80 feet History of the roller coaster - Russian Ice Slides

11. Some current coasters

12. Energy is conserved => Energy at top = Energy at bottom Roller Coaster Design: Some Simple Physics

13. (KE + PE) top = (KE +PE) bottom ( 1 /2)mv 1 2 + mgh = ( 1 /2)mv 2 2 + 0 ( 1 /2)v 1 2 + gh = ( 1 /2)v 2 2 ( 1 /2)(8.8) 2 + 9.8(95) = ( 1 /2)v 2 2 38.72 + 931 = ( 1 /2)v 2 2 969.72 = ( 1 /2)v 2 2 1939.44 = v 2 2 v 2 = 44.04 m /s...at the bottom the the 1st hill. (assuming no friction)

14. Main Points from Today’s Lecture Energy, Work and Energy Conservation You should understand that work is defined as the product of the component of the force along the line of motion and the distance the object moves as a result of the force. You should understand that energy is “stored work”. It comes in different forms and it can never be created or destroyed. It just changes forms. You should be able to solve problems involving these concepts.

15. HW CH6: Q1,Q2,Q4,Q5,Q6,Q7 E1,E2,E3,E4, E5, E7,E10,E11,E13,E15,CP1 Read Ch. 6