1. Conservation of Energy

2. Forms of Energy Mechanical Energy Thermal Energy Other forms include

3. Law of Conservation of Energy What you put in is what you get out Total energy is conserved

4. Practical Applications Gasoline converts to energy which moves the car A battery converts stored chemical energy to electrical energy Dams convert the kinetic energy of falling water into electrical energy

5. Example : step 1

6. Example : step 2

7. Example : step 3

8. Example : last step

9. Conservation of Mechanical Energy Total Energy Potential Energy Kinetic Energy m = mass v = velocity g = gravitational acceleration h = height ILYA, did you know that even though it was a bumpy ride, our energy remained constant!

10. Conservation of Mechanical Energy We denote the total mechanical energy by Since The total mechanical energy is conserved and remains the same at all times

11. A block projected up a incline Point A (initial state): Point B (final state):

12. Trucks with the noted masses moving at the noted speeds crash into barriers that bring them to rest with a constant force. Which truck compresses the barrier by the largest distance? Questions :

13. 2 Types of Forces Conservative forces  Work and energy associated with the force can be recovered  Examples: Gravity, Spring Force, EM forces Nonconservative forces  The forces are generally dissipative and work done against it cannot easily be recovered  Examples: Kinetic friction, air drag forces, normal forces, tension forces, applied forces …

14. The work done by a conservative force is independent of the path, and depends only on the starting and ending points. Closed path, W=0. Pick any starting and ending points. A B A B W1W1 W2W2 W 1 = W AB W 2 = W BA W 1 + W 2 = 0 W3 W 1 + W 3 = 0 So, all paths from B to A take the same amount of work. W1W1

15. Path doesn’t matter! InitialFinal

16. Conservative Forces A force is conservative if the work it does on an object moving between two points is independent of the path the objects take between the points  The work depends only upon the initial and final positions of the object  Any conservative force can have a potential energy function associated with it  Work done by gravity  Work done by spring force

17. Ex n.1: Block-Spring Collision A block having a mass of 0.8 kg is given an initial velocity v A = 1.2 m/s to the right and collides with a spring whose mass is negligible and whose force constant is k = 50 N/m as shown in figure. Assuming the surface to be frictionless, calculate the maximum compression of the spring after the collision.

18. Nonconservative Forces A force is nonconservative if the work it does on an object depends on the path taken by the object between its final and starting points.  The work depends upon the movement path  For a non-conservative force, potential energy can NOT be defined  Work done by a nonconservative force  It is generally dissipative. The dispersal of energy takes the form of heat or sound

19. Problem-Solving Strategy Define the system to see if it includes non-conservative forces (especially friction, drag force …) Without non-conservative forces With non-conservative forces Select the location of zero potential energy  Do not change this location while solving the problem Identify two points the object of interest moves between  One point should be where information is given  The other point should be where you want to find out something

20. Ex n 2:Block-Spring Collision A block having a mass of 0.8 kg is given an initial velocity v A = 1.2 m/s to the right and collides with a spring whose mass is negligible and whose force constant is k = 50 N/m as shown in figure. Suppose a constant force of kinetic friction acts between the block and the surface, with µ k = 0.5, what is the maximum compression x c in the spring.

21. Connected Blocks in Motion Two blocks are connected by a light string that passes over a frictionless pulley. The block of mass m 1 lies on a horizontal surface and is connected to a spring of force constant k. The system is released from rest when the spring is unstretched. If the hanging block of mass m 2 falls a distance h before coming to rest, calculate the coefficient of kinetic friction between the block of mass m 1 and the surface.

22. To stay on loop, the normal force, N, must be greater than zero. Ex n. 3 :Block on wheel of death

23.  Mass must start higher than top of loop h

24. h h = 5/2 R V max = V max V fin V fin =

25. Potential Energy vs. Force