2. Work and Energy Salud N. Velasco Ramon Magsaysay (Cubao) High School

3. Lesson Objectives: 1. Determine the relationship between the work done and the energy transferred. 2. Familiarize with the formulas for work done, kinetic and potential energies. 3. Understand real life application of work done, kinetic and potential energies.

4. Read the following statements and determine whether or not they represent work. Click on the puzzle piece to verify your answer. 1. A teacher applies a force to a wall and became exhausted. became exhausted. 2. A book fall off a table and free falls to the ground. ground. 3. A waiter carries a tray full of meals above his head by one arm straight across the his head by one arm straight across the room at constant speed. room at constant speed. 4. A rocket accelerates through space.

5. Explanation: Explanation: Yes. This is an example of work. There is a force (gravity) which acts on the book which causes it to displaced in a downward direction.

6. Answer: Answer: No. This is not an example of work. There is force (the waiter pushes up on the tray) and there is displacement ( the tray is moved horizontally across the room). Yet the force does not causes the displacement. To cause a displacement, there must be a component of force in the direction of the displacement.

7. Answer: Answer: Yes. This is an example of work. There is a force (the expelled gases push on the rocket) which causes the rocket to be displaced through space.

8. Answer: No. This is not an example of work. The wall is not displaced. No. This is not an example of work. The wall is not displaced.

9. The Concept of Work For work to be done, three conditions must be meet; For work to be done, three conditions must be meet; 1. There must be a force acting on the object. 1. There must be a force acting on the object. 2. The object has to move a certain distance. 2. The object has to move a certain distance. 3. There must be a component of the force in the 3. There must be a component of the force in the direction of the motion. direction of the motion. distance force

10. From the three conditions given, express work done mathematically.

11. W = F cosØ d Scenario A: The force and the displacement are in the same direction. d F Ø = 180º

12. W = F cosØ d Scenario B: The force and the displacement are in opposite direction. d F Ø = 0º

13. W = F cosØ d Scenario C: The force and the displacement are right angle to each other. d F Ø = 90º

14. Sample Problem: Marie lift a 5 kg mass from the floor and puts it on a table one meter high. What is the work done? Marie lift a 5 kg mass from the floor and puts it on a table one meter high. What is the work done? Which is the answer? A. 5 Nm A. 5 Nm B. 10 Nm B. 10 Nm C. 25 Nm C. 25 Nm D. 50 Nm D. 50 Nm

15. Congratulations! It’s good to know that you have been paying attention. Solution: Work Done = Force x distance (ma) (d) ( 5 kg) (10 m/s 2 ) (1 m) 50 Nm = 50 J

16. Concept of Energy Energy is the capacity to do work. Energy is the capacity to do work. The release of energy does work - and doing work on something adds energy to it so - energy and work are actually equivalent concepts. The release of energy does work - and doing work on something adds energy to it so - energy and work are actually equivalent concepts. E = W = F x d. E = W = F x d.

17. Unit for Work and Energy In the English system, the unit of energy is the Foot.Pound. In the metric system it’s the Newton-Meter, which is also called the Joule. One joule = The ability to exert a force of one Newton over a distance of one Meter

18. Two forms of Energy Suppose I throw a ball. I do work getting the ball moving. Suppose I throw a ball. I do work getting the ball moving. I exert a force F over a distance d. The ball then has acquired some energy, the energy of motion, or KINETIC energy. I exert a force F over a distance d. The ball then has acquired some energy, the energy of motion, or KINETIC energy. K. E. = 1/2 m v 2. K. E. = 1/2 m v 2.

19. Two forms of Energy A man lift an object to a height. As he exert a force W = object’s weight over a distance h, He do work W x h = mgh. Potential Energy is the energy with respect to position. P.E. = mgh.

20. Sample Problem A 50 kg box falls from a bridge and lands in the water 20 m below. Find its initial PE and maximum KE. A 50 kg box falls from a bridge and lands in the water 20 m below. Find its initial PE and maximum KE. Which is the answer? A. PE = 10000 J KE = 10000 J A. PE = 10000 J KE = 10000 J B. PE = 10000 J KE = 0 B. PE = 10000 J KE = 0 C. PE = 0 KE = 10000 J C. PE = 0 KE = 10000 J D. PE = 500 J KE = 10000 J D. PE = 500 J KE = 10000 J

21. Congratulations! It’s good to know that you have been paying attention. It’s good to know that you have been paying attention.Solution: a. Initial energy is taken from the top. Therefore, PE i = mgh PE i = mgh = (50 kg)(10 m/s 2 )(20 m) = (50 kg)(10 m/s 2 )(20 m) = 10000 J = 10000 J b. The maximum KE is equal to the total PE at the top. Ke max = 10000 J top. Ke max = 10000 J

22. Let’s do more example A package of 5kg is lifted vertically through a distance of 10m at a constant speed. Taking the acceleration due to gravity to be 10m/s 2 What is the gravitational potential energy gained by the package?

23. Congratulations! It’s good to know that you have been paying attention. Solution: PE i = mgh = (5 kg)(10 m/s 2 )(10 m) = 500 J

24. Conservation and Conversion of Energy Potential Energy is potential because it can be gotten back as “real” kinetic energy. To get it back, all I have to do is to let the object fall.

25. Conservation and Conversion of Energy As the object falls faster and faster, its PE is gradually converted into KE. At the bottom, just before impact, its KE is zero. And its original PE has become entirely KE 1/2 m v 2 = m g h.

26. Conservation and Conversion of Energy Conservation of energy tells us that the total energy of the system does not change but maybe converted into other forms What happens to the objects energy when he hits the floor?

27. Conservation and Conversion of energy.

28. Trace the energy conversion in the given situation. POTENTIAL ENERGY

29. Evaluation PEKE Work Done ______ 0 J ______ 15 J ______ 15 J Complete the table.

30. References: http://www.google.comhttp://www.google.com for the pictures http://www.google.com http://www.conceptualphysics.com Physics Matters by Dr Chew et al

32. Sorry. Sorry. You need to revise on the topic.