1. Conservation of Mechanical Energy Chapter 6

2. Energy  As you know, energy comes in many forms. Kinetic Energy Potential Energy  Gravitational Potential Energy (gravity)  Elastic Potential Energy (springs, rubber bands)  Chemical Energy (chemical bonds)  Rest Mass Energy = Nuclear (E = mc 2 )  Electric Potential Energy (ΔU = kq 1 q 2 /r) Thermal Energy (heat = KE of molecules) Sound (waves) Light (waves/photons)  What does it mean to conserve energy?

3. Conservation of Energy  The Law of Conservation of Energy simply states that: 1. The energy of a system is. 2. Energy cannot be nor. 3. Energy can only change (e.g. electrical to kinetic to potential, etc). True for any system with no external forces. E T = KE = Kinetic Energy PE = Potential Energy = [kinetic energy due to the motion of molecules (translational, rotational, vibrational)]

4. Conservation of Energy Energy

5. Conserved Quantities  Other conserved quantities that you may or may not already be familiar with? Conservation of.

6. E T = KE +  PE = Constant The relationship implies that the total mechanical energy of a system is.  If the Potential Energy is at a, then the system will have Kinetic Energy.  If the Kinetic Energy is at a, then the system will have Potential Energy.

7. Conservation of Mechanical Energy E T = KE + PE + = +

8. Conservation of Mechanical Energy – The Roller Coaster www.howstuffworks.com

9. Conservation of Mechanical Energy – Skier Critical points to consider PE max Heat (Q) KE max Total Mechanical Energy = PE + KE

10. Example 1:  A student with a mass of 55 kg goes down a frictionless slide that is 3 meters high. 1. What is the student’s kinetic energy at the bottom of the slide. 2. What is the student’s speed at the bottom of the slide? KE initial + PE initial = KE final + PE final  KE initial =  PE initial =  KE final =  PE final =

11. Example 1 (cont.) 1. = = 2. KE final = = √ √

12. Example 2:  El Toro goes through a vertical drop of 50 meters. Using the conservation of energy, determine the speed at the bottom of the drop. Assume that the initial speed of the coaster is 0 m/s.

13.  The conservation of energy says that the kinetic energy at the bottom of the drop will the gravitational potential energy at the top. =

14. Example 3:  A student with a mass of 55 kg goes down a non-frictionless slide that is 3 meters high. Compared to a frictionless slide the student’s speed will be: a. the same. b. less than. c. more than. Why?  Because energy is to the in the form of due to.

15. Example 3 (cont.) Does this example reflect conservation of mechanical energy?, because of.  Is the law of conservation of energy violated? : as previously stated, some of the “mechanical” energy is to the environment in the form of.

16. Conservation of Mechanical Energy  Mechanical Energy: If Internal Energy(Q) is ignored: E T = KE + GPE + PE s  could be a combination of and energy, or any other form of energy.