1. Work and Energy
AP Physics I

2. Warm-Up: December 1, 2014
Write down everything you remember about work and energy.

4. Warm-Up: December 2, 2014
A ball of mass 1.00 kg is thrown directly upward from a height of 1.00 m above the ground. Its initial speed is m/s.
How high above the ground does the ball go?
When does the ball hit the ground?

5. Energy Energy is the ability to do work.
One of the most important concepts in physics.
The total amount of energy in the universe is constant

6. Conservation of Energy
Energy can not be created nor destroyed.
Mass is a form of energy.
Einstein’s equation E=mc2
Numerous experimental tests support the principle of conservation of energy.

7. Vector Multiplication
There are two ways to multiply vectors.
Dot product (also called scalar product)
The result is a scalar
Cross product (also called vector product)
The result is a vector, perpendicular to both original vectors
The directions is found using the right-hand rule

8. Work: The Scientific Definition
AP Physics I
OpenStax section 7.1

9. Work
For work to be done, a force must be exerted and there must be displacement in the direction of the force.
Work is the dot product of force and displacement.
Work is measured in Joules (J).

10. Joule A Joule is equal to a Newton times a meter.
1 Joule is not much energy; it would lift a small 100-gram apple a distance of about 1 meter.

11. Examples of Work

12. Examples of No Work

13. Example of Negative Work

14. Review Questions Is work a scalar or a vector?
What are the possible values of work?
What is the formula to calculate work?
What is the SI (mks) unit for work?

15. Example
How much work is done on the lawn mower (from a few slides ago) if he exerts a constant force of 75.0 N at an angle 35° below the horizontal and pushes the mower 25.0 m on level ground?
If the person’s average daily intake of food energy is about 10,000 kJ (about 2400 kcal), what percent of his daily intake is required to push the lawn mower in part (a)?

16. Biology (yuck!)
Very little of the energy released in the consumption of food is used to do work.
Even when we “work” all day, less than 10% of our food energy intake is used to do work and more than 90% is converted to thermal energy or stored as chemical energy in fat.

19. Warm-Up: December 3, 2014
How much work is done by the boy pulling his sister 30.0 m, with a force of 50.0 N, as shown?

20. Questions on Work?

21. Kinetic Energy and the Work-Energy Theorem
AP Physics 1
OpenStax section 7.2

22. Work Transfers Energy Pushing a lawnmower transfers energy to it.
The energy goes to moving the lawnmower (kinetic energy).
Friction within the lawnmower and between the lawnmower and the ground also transfers energy.
Thermal energy leaves as heat.

23. Net Work

24. Net Work
If net force and displacement are in the same direction (which is a common occurrence), then

25. Kinetic Energy Energy of motion Represented by K or KE
Measured in Joules

26. Work-Energy Theorem
Applies even for forces that vary and for forces that are not parallel to displacement.

27. Diagram for the next 4 problems

28. You-Try 7.2
A 30.0 kg package on a roller belt conveyor system is moving at m/s. What is its kinetic energy?

29. You-Try 7.3 Calculate the net work done on the package.
Find the work done by each force, and show that the total work is equal to the net work found in part a.

30. You-Try 7.3 Calculate the net work done on the package.
Find the work done by each force, and show that the total work is equal to the net work found in part a.

31. You-Try 7.4
Find the speed of the package at the end of the push. Its initial speed was given in You-Try 7.2

32. Warm-Up: December 4, 2014 You-Try 7.5
How far does the package coast after the push, assuming friction remains constant?

33. Questions on Work-Energy Theorem?

34. Gravitational Potential Energy
AP Physics 1
OpenStax section 7.3

35. Work Done Against Gravity
Lifting an object is work done against the gravitational force.
The work done goes into an important form of stored energy, called gravitational potential energy.

36. Gravitational Potential Energy
h is a change in height, even though Δ is not written
Applies for any path that has a change in height of h, not just for vertical motion.

37. Converting Between PE and KE
If an object is dropped from a height h, gravitational force will do work on the object.
This work increases its kinetic energy.
This can be expressed as:
This equation is valid when no force besides gravity is acting on the object (or when all other forces are negligible).

38. Other Forms of the Equation

39. You-Try 7.6
A 60.0 kg person jumps onto the floor from a height of 3.00 m. If he lands stiffly, with his knee joints compressing by cm, calculate the force on the knee joints.

40. Biology (yuck!)
Such a large force (500 times more than a person’s weight) over a short impact time is enough to break bones.

41. You-Try 7.7
What is the final speed of the roller coaster shown if it starts from rest and work done by frictional forces is negligible?
What is its final speed (again assuming negligible friction) if its initial speed is 5.00 m/s?

42. You-Try 7.7
What is the final speed of the roller coaster shown if it starts from rest and work done by frictional forces is negligible?
What is its final speed (again assuming negligible friction) if its initial speed is 5.00 m/s?

43. Review Questions
How does the mass of an object impact the conversion between gravitational potential energy and kinetic energy?
Where else did mass not matter?
How did the dip at the bottom of the first hill affect the final kinetic energy?
True or False: If two objects at the same initial height have speeds that differ by K, then their final speeds at another height will also differ by K.

44. Questions on PE and KE?

45. Experimental Design
With your group (assigned on the next slide), design an experiment that can demonstrate the conversion between gravitational potential energy and kinetic energy.
Materials allowed:
Rulers
Meter stick
Marble
Physics book
Stopwatch
Write detailed procedures in your lab notebook, along with lab name, group members, materials used, and discussion of how your experiment demonstrates conservation of energy.

46. Groups Group # 1 Mark Christina Jocelyn Wesley 2 Elroi Isabel Peter
Foster 3
Karla
Tong
Hector
Jeremy 4
Justin
Diana
Shane
Erin 5
Tiffany
Shelby
Frank
Phat 6
Kevin
Joseph
Regge 7
Courtney
Angela
Paul

49. Lab Idea Work Done in Stretching a Spring (GI) [CR6b]
To determine the work done on the spring from force-versus-distance graph of the collected data.