2. ENERGY

3. Objectives: After completing this module, you should be able to: Define kinetic energy and potential energy, along with the appropriate units in each system. Describe the relationship between work and kinetic energy, and apply the WORK-ENERGY THEOREM.

4. Energy What is energy? You can see its effects, but it is a difficult concept to define.

5. Mechanical Energy Energy = ability of an object or a system which enables it to do work Energy is measured in JOULES.

6. MECHANICAL ENERGY is the energy due to the position or the motion of something Mechanical energy may be either kinetic or potential.

7. Potential Energy (PE) Potential energy is energy stored and held in readiness due to position.

8. For example: A boulder sitting atop a hill – has “gravitational potential energy” (GPE) due to its position (height) The higher the rock is sitting, the more GPE it has.

9. To calculate gravitational potential energy: PE = (mass X g) X (height) or PE = m·g·h Units: mass in kg “g” in m/s 2 h in meters

10. Example Problem: What is the potential energy of a 50-kg person in a skyscraper if he is 480 m above the street below? Gravitational Potential Energy What is the P.E. of a 50-kg person at a height of 480 m? PE = mgh = (50 kg)(9.8 m/s 2 )(480 m) PE = 235200 J

11. Kinetic Energy Kinetic energy is the energy of motion

12. To calculate KE: KE = ½ mv 2 Where KE = kinetic energy m = mass (kg) v = velocity (m/s)

13. Examples of Kinetic Energy What is the kinetic energy of a 5-g bullet traveling at 200 m/s? What is the kinetic energy of a 1000-kg car traveling at 14.1 m/s? 5 g 200 m/s KE = 100 J KE = 99405 J

14. Law of Conservation of Energy Energy cannot be created nor destroyed; it can only be transformed. Total energy remains constant.

15. PE transformed to KE

16. At the top of the hill, the cart has only PE. Towards the middle of the hill, the cart has equal amounts of PE and KE. At the bottom of the hill, all of the PE has been transformed into KE.

17. On a pendulum: Can you think of a similar device used in construction or on a playground?

18. On a roller coaster:

19. Conservation of Energy TME Initial = TME Final Neglecting energy loss to friction/heat initial (PE +KE) = final (PE + KE) mgh i + ½ mv i 2 = mgh f + ½mv f 2

20. Conservation of Energy Sample Problem 1 A child with a mass of 18 kg zooms down from the top of a 2.5 m tall slide. What is her speed at the bottom of the slide? m = h i = h f = v i = v f =

21. Conservation of Energy Sample Problem 2 Ivan throws a ball straight upward with an initial velocity of 22 m/s. How high above the release point will the ball rise? g = 10 m/s 2 mgh 1 + ½ mv 1 2 = mgh 2 + ½ mv 2 2 0 0

22. Conservation of Mechanical Energy SP3 A skater has a kinetic energy of 57 J at position 1, the bottom of the ramp. At position, 3, he comes to a stop for just a moment so that he has 57 J of gravitational potential energy. What is his kinetic energy at position 2, if his gravitational potential energy at position 2 is 25.7 J? Mechanical energy = K + GPE E = 57 J PE = 25.7 J KE = ??

24. Work-Energy Theorem- states that whenever work is done, energy changes.

25. Examples Pushing a wagon- the force applied becomes kinetic energy Stretching a spring – your force puts potential energy into the spring Lifting an object – the work you put into raising the object becomes GPE

26. The Work-Kinetic Energy Theorem NET Work done by all forces =  Kinetic Energy W net = ½ mv 2 final – ½ mv 2 initial

27. NET Work =  Kinetic Energy How much more distance is required to stop if a car is going twice as fast (all other things remaining the same)? The work done by the forces stopping the car = the change in the kinetic energy Fd =  ½ mv 2 With TWICE the speed, the car has FOUR times the kinetic energy. Therefore it takes FOUR times the stopping distance. (What FORCE is doing the work??)

28. A car going 25 km/h will skid to a stop over a distance of 7 meters. If the same car was moving at 50 km/h, how many meters would be required for it to come to a stop? The velocity DOUBLED, therefore the stopping distance is FOUR times the original distance: 7 meters x 4 = 28 meters

29. Jacob pushes a Honda with mass 3135 kg from rest to a speed v, doing 5450 J of work. The Honda moves 15 m. Neglecting friction, what is the final speed of the Honda.

30. Find the force with which Jacob pushed the Honda.

31. A 12 g projectile is fired from a cylinder 48.3 cm long to a speed of 736 m/s. Use the work-energy theorem to find average force on the projectile in the cylinder.

32. An ice skater starting from rest is pushed by another skater with a constant force of 48 N. How far must the force be applied in order for her final kinetic energy to be 351 J?

33. A truck with mass 2.29 X 10 3 kg takes 5.2 kJ of work to move from rest to some final speed in 20.7 m. Find the final speed, neglecting friction.

34. Find the net horizontal force to push the truck.

35. Energy Key Terms Energy Kinetic energy Law of Conservation of Energy Mechanical energy Potential energy Work-energy Theorem