Energy

1. Energy What is it? Energy is conserved How do we use it in physics

2. An Energy Pathway • We need energy • Where does it come from? • Where does the energy in food come from?

3. An Energy Pathway

4. An Energy Pathway • Where does the Energy of the Sun come from?

5. Energy • Energy can be transformed from one form to another. Nuclear-> Heat and Light Chemical Mechanical • What is conversion rate? • We can account for every bit of energy along the way. ENERGY IS CONSERVED

6. Forms of Energy Mechanical Energy Thermal Energy Other forms include Slide 10-12

7. Energy Transformations Kinetic energy K = energy of motion Potential energy U = energy of position Thermal energy Eth = energy associated with temperature System energy E = K + U + Eth + Echem + ... Energy can be transformed within the system without loss. Energy is a property of a system. Slide 10-14

9. The Law of Conservation of Energy The total energy of the Universe (closed system) is unchanged by any physical process. Energy may be converted from one form to another or transferred between bodies. It never disappears. It cannot be created or destroyed.

10. Does the power generated • affect the speed of the wind? • Would locations behind the • “windmills” have more wind if • the windmills weren’t there? • Yes • No

11. Energy • Energy has a somewhat abstract nature. Try to be concrete. • Energy is the property of a system that enables it to do work. • What is work?

12. Work by a Constant Force Work is an energy transfer by the application of a force. For work to be done there must be a nonzero displacementi.e. the object must be moving. F must have component in direction of motion Work = Force x Distance if F and D are parallel. If F, D not parallel use the component of F that is parallel to displacement The unit of work and energy is the joule (J). 1 J = 1 Nm = 1 kg m2/s2.

13. Is he doing any work against the wall? A) Yes B) No

14. Is her arm doing any work on the briefcase?

15. Work Done by Force at an Angle to Displacement Slide 10-29

16. y F rx rx N  x  w F It is only the force in the direction of the displacement that does work. An FBD for the box at left: The work done by the force F is:

17. The work done by the normal force N is: The normal force is perpendicular to the displacement. The work done by gravity (w) is: The force of gravity is perpendicular to the displacement.

18. The net work done on the box is:

19. In general, the work done by a force F is defined as where F is the magnitude of the force, r is the magnitude of the object’s displacement, and  is the angle between F and r (drawn tail-to-tail).

20. r y x w Example: A ball is tossed straight up. What is the work done by the force of gravity on the ball as it rises? FBD for rising ball: Work can be negative!

21. Question A box with mass m1 is being pulled up a rough incline by a rope-pulley-weight system. How many forces are doing work on the box? A) one force B) two forces C) three forces D) four forces E) no forces are doing work Gravity, friction and tension

22. Fig. 06.10

23. Kinetic Energy • An object that is moving has the ability to do work The faster the ball is moving the more the pins will bounce. The heavier the ball the more the pins will bounce

24. Kinetic Energy is an object’s translational kinetic energy. This is the energy an object has because of its state of motion. It can be shown that, in general

25. Gone with the Wind • 20 mph winds hardly ever do damage • 60 mph almost always do: uproot trees, rip shingles off roofs. Why? • 60 mph winds have 9 times the energy (1/2mv2) and can do 9 times as much (destructive ) work

26. How much work do the brakes do when your car decreases its speed from 25m/s to 20 m/s? Take m= 1,500 kg ΔK = ½mvf2 - ½mvi2 = ½m(vf2 – vi2 )

27. Does it require more energy to slow a car down • from 30 to 25 mph than from 25 to 20 mph? • Yes • No • The same

28. Question Your brakes can apply a constant force, F, to the wheels of your car. If it takes a distance of 30 m to stop when you are traveling 40 km/hr, what distance is required to stop when you are traveling 120 km/hr? A) 10 m B) 90 m C) 110 m D) 270 m

29. Checking Understanding Each of the boxes, with masses noted, is pulled for 10 m across a level, frictionless floor by the noted force. Which box experiences the largest change in kinetic energy? Slide 10-31

30. Answer Each of the boxes, with masses noted, is pulled for 10 m across a level, frictionless floor by the noted force. Which box experiences the largest change in kinetic energy? D. Slide 10-32

31. Potential Energy • Object can store energy because of its position. Examples • A stretched or compressed spring • A drawn bow • Water in an elevated reservoir • Chemical energy because of the position of electrons

32. Gravitational Potential Energy Objects have gravitational potential energy (PE) because of their elevated position.

33. Gravitational Potential Energy Objects have gravitational potential energy (GPE) because of their elevated position. Work is done to lift an object and this is equal to the amount of GPE. Lifting an object up to a height h at constant v requires a Force of mg F We can get this back Work = FΔx = mg Δx =mgh =GPE mg This is minus the work done by gravity -Wg

34. The change in gravitational potential energy (only near the surface of the Earth) is where y is the change in the object’s vertical position with respect to some reference point that you are free to choose.

35. GPE depends only on h not on how it got there

36. Example: What is the change in gravitational potential energy of the box if it is placed on the table? The table is 1.0 m tall and the mass of the box is 1.0 kg. First: Choose the reference level at the floor. U = 0 here.

37. Example continued: Now take the reference level (U = 0) to be on top of the table so that yi = 1.0 m and yf = 0.0 m. The results do not depend on the location of U = 0.

38. Mechanical energy If we can neglect friction, the mechanical energy of a system is conserved. That is Ei = Ef or K = U.

40. Conservation of Mechanical Energy

41. Conservation of Mechanical Energy

43. Example (text problem 6.28): A cart starts from position 4 with v = 15.0 m/s to the left. Find the speed of the cart at positions 1, 2, and 3. Ignore friction.

44. If friction is present The work done by friction.

45. y F rx rx N  x  w F Friction Box is moving with constant v An FBD for the box at left: constant v f f Ftot= ma =0 => Fcosθ –f =0

46. Friction The work done by friction is fxΔx = –FxΔx We cannot “retrieve” this work The work has gone into heating up the box and the ground Friction dissipated this amount of work

47. Work by a Variable Force Work is the area of the graph of Fx (the applied force in the direction of the displacement) versus the displacement. Remember x = vΔt = area under v vs. t graph

48. Question Two forces are applied over a distance x as shown in the graph at right. F1 is constant over the distance, but F2 varies from zero to 2F1. Compare the work done by the two forces. A) W1 > W2 B) W1 = W2 C) W1 < W2

49. ENERGY • Mechanical Energy • Kinetic Energy • Potential Energy • Gravitational • Chemical • Elastic