1. Work and Energy

2. Work and Energy Question- Guess Now
You push very hard on a heavy desk, trying to move it. You do work on the desk
Whether or not it moves, as long as you are exerting a force.
Only if it starts moving
Only if it doesn’t move
Never—it does work on you
None of the above

3. Topics that will be discussed
Work Done by a Constant Force
Work Done by a Varying Force
Kinetic Energy, and the Work-Energy Principle
Potential Energy
Conservative and Nonconservative Forces
Mechanical Energy and Its Conservation
Problem Solving Using Conservation of Mechanical Energy
Other Forms of Energy; Energy Transformations and the Law of Conservation of Energy
Energy Conservation with Dissipative Forces: Solving Problems
Power

4. Work Work = Force ● Distance Work = Force ● ∆X
Don’t forget force is a vector quantity and can be broken into components.
Work = Force ● D●Cosθ

5. WORK W = f ∙d ∙ COS θ W = f ∙d ∙ COS θ so the COS 180 = 1 W= F x D
Force is perpendicular to the motion (angle)

6. Work Done by a Constant Force
The work done by a constant force is defined as the distance moved multiplied by the component of the force in the direction of displacement:

7. Work Done by a Constant Force
In the SI system, the units of work are joules:
As long as this person does not lift or lower the bag of groceries, he is doing no work on it. The force he exerts has no component in the direction of motion.
No work is done on the bag as the man carries it. Only when he picked it up.

9. NET WORK
The work done is the algebraic sum of the work done by each force, since work is a scalar (no components) Worknet = Wgravity + Wfriction + WN + W applied force + Work object is speeding up - Work object is slowing down

10. Work Done by a Constant Force
Solving work problems:
Draw a free-body diagram.
Choose a coordinate system.
Apply Newton’s laws to determine any unknown forces.
Find the work done by a specific force.
To find the net work, either
find the net force and then find the work it does, or
find the work done by each force and add.

11. PROBLEM 1

12. Problem 2
A box is dragged across a floor by a force, which makes an angle θ with the horizontal. If the magnitude of the force is held constant, but the angle is increased, would the work increase, decrease, first increase then decrease, or remain the same?

13. Problem 3

14. Problem 3

15. Problem 3

16. Work Done by a Constant Force
Work done by forces that oppose the direction of motion, such as friction, will be negative.
The moon revolves around the earth in a nearly circular orbit, kept there by the gravitational force exerted by the earth. Does gravity do (a) positive work, (b) negative work, or (c) no work?

17. Work Done by a Constant Force
Work done by forces that oppose the direction of motion, such as friction, will be negative.
Centripetal forces do no work, as they are always perpendicular to the direction of motion.

18. Work Done by a Varying Force
For a force that varies, the work can be approximated by dividing the distance up into small pieces, finding the work done during each, and adding them up. As the pieces become very narrow, the work done is the area under the force vs. distance curve.
work

19. Kinetic Energy, and the Work-Energy Principle
Energy was traditionally defined as the ability to do work. We now know that not all forces are able to do work; however, we are dealing in these chapters with mechanical energy, which does follow this definition.
Energy0 = Energyf K.E.o + P.E.0 = K.E.f + P.E.f
½ mv2o + mgho = ½ mv2f + mghf

20. Kinetic Energy, and the Work-Energy Principle
If we write the acceleration in terms of the velocity and the distance, we find that the work done here is
We define the kinetic energy:
(6-2)
(6-3)

21. Kinetic Energy, and the Work-Energy Principle
This means that the work done is equal to the change in the kinetic energy:
(6-4)
If the net work is positive, the kinetic energy increases.
If the net work is negative, the kinetic energy decreases.
Work energy principle
Work = ½ mv2

22. Kinetic Energy, and the Work-Energy Principle
Because work and kinetic energy can be equated, they must have the same units: kinetic energy is measured in joules.

23. Problem 4
A 145 g baseball is thrown so that it acquires a speed of 25 m/s. (a) What is its kinetic energy? (b) What was the net work done on the ball to make it reach this speed, it starts from rest.

24. Problem 5
How much net work is required to accelerate a 1000 kg car from 20 m/s to 30 m/s?

25. Problem 6

26. Potential Energy
An object can have potential energy by virtue of its surroundings.
Familiar examples of potential energy:
A wound-up spring
A stretched elastic band
An object at some height above the ground

27. Potential Energy
In raising a mass m to a height h, the work done by the external force is
We therefore define the gravitational potential energy:
(6-5a)
(6-6)

28. Potential Energy
This potential energy can become kinetic energy if the object is dropped.
Potential energy is a property of a system as a whole, not just of the object (because it depends on external forces).
If , where do we measure y from?
It turns out not to matter, as long as we are consistent about where we choose y = 0. Only changes in potential energy can be measured.

29. Potential Energy
Potential energy can also be stored in a spring when it is compressed; the figure below shows potential energy yielding kinetic energy.

30. Potential Energy
The force required to compress or stretch a spring is:
where k is called the spring constant, and needs to be measured for each spring.
(6-8)

31. Potential Energy
The force increases as the spring is stretched or compressed further. We find that the potential energy of the compressed or stretched spring, measured from its equilibrium position, can be written:
(6-9)

32. Problem 7

33. Problem 7

34. Problem 7

35. Conservative and Nonconservative Forces
Conservative Forces - do not depend on the path taken only on the original and final positions.
Ex. Spring force gravity
potential energy
An object that starts at a given point and returns that same point under the action of conservative force has no net work done on it because the potential energy is the same at the start and finish of the round trip.
Nonconservative Forces – depend on the path taken
Ex. Friction

36. Conservative and Nonconservative Forces
If friction is present, the work done depends not only on the starting and ending points, but also on the path taken. Friction is called a nonconservative force.

37. Conservative and Nonconservative Forces
An object acted on by a constant force F moves from point 1 to point 2 and back again. The work done by the force F in this round trip is 60 J. Can you determine if this is a conservative or nonconservtive force?

38. Conservative and Nonconservative Forces
Potential energy can only be defined for conservative forces.

39. Conservative and Nonconservative Forces
Therefore, we distinguish between the work done by conservative forces and the work done by nonconservative forces.
We find that the work done by nonconservative forces is equal to the total change in kinetic and potential energies:
(6-10)

40. Mechanical Energy and Its Conservation
If there are no nonconservative forces, the sum of the changes in the kinetic energy and in the potential energy is zero – the kinetic and potential energy changes are equal but opposite in sign.
This allows us to define the total mechanical energy:
And its conservation:

41. Problem Solving Using Conservation of Mechanical Energy
In the image on the left, the total mechanical energy is:
The energy buckets (right) show how the energy moves from all potential to all kinetic.

42. Problem 8
If the original height of the stone is h = 3.0 m, calculate ht stone’s speed when it has fallen to 1.0 m above the ground.

43. Problem Solving Using Conservation of Mechanical Energy
If there is no friction, the speed of a roller coaster will depend only on its height compared to its starting height.

44. Problem 9

45. Problem 10

46. Problem 11

47. Problem Solving Using Conservation of Mechanical Energy
For an elastic force, conservation of energy tells us:
(6-14)

48. Problem 12

49. Problem 13

50. Problem 14

51. Other Forms of Energy; Energy Transformations and the Conservation of Energy
Some other forms of energy:
Electric energy, nuclear energy, thermal energy, chemical energy.
Work is done when energy is transferred from one object to another.
Accounting for all forms of energy, we find that the total energy neither increases nor decreases. Energy as a whole is conserved.

52. Law of Conservation of Energy
The total energy is neither increased nor decreased in any process. Energy can be transformed from one form to another, and transferred from one object to another, but the total amount remains

53. Energy Conservation with Dissipative Processes; Solving Problems
If there is a nonconservative force such as friction, where do the kinetic and potential energies go?
They become heat; the actual temperature rise of the materials involved can be calculated.

54. Energy Conservation with Dissipative Processes; Solving Problems
Problem Solving:
Draw a picture.
Determine the system for which energy will be conserved.
Figure out what you are looking for, and decide on the initial and final positions.
Choose a logical reference frame.
Apply conservation of energy.
Solve.

55. Power Power is the rate at which work is done –
(6-17)
In the SI system, the units of power are watts:
The difference between walking and running up these stairs is power – the change in gravitational potential energy is the same.

57. Power Power is the rate at which work is done – Power = work/time
(6-17)
Power = work/time
Power = Fd/time
Power = FdCosθ/time
Power = F d/time so Power = F v
(b/c v = d/t)
In the SI system, the units of power are watts:
The difference between walking and running up these stairs is power – the change in gravitational potential energy is the same.

58. Power Problem 15

59. Power
Power is also needed for acceleration and for moving against the force of gravity.
The average power can be written in terms of the force and the average velocity:
(6-17)

60. Problem 15

61. Power and Efficiency
Efficiency = Power output/Power input e = Pout /Pin

62. Summary of Work: Kinetic energy is energy of motion:
Potential energy is energy associated with forces that depend on the position or configuration of objects.
The net work done on an object equals the change in its kinetic energy.
If only conservative forces are acting, mechanical energy is conserved.
Power is the rate at which work is done.
W = ½ mv b/c W = ∆ K.E.