Work, Power & Energy

1. Work, Power & Energy How does it relate? (Adapted From Mrs. Stone)

4. Work • Work is the product of the force on an object and the distance through which the object is moved. • Work = Force ´ Distance • W = F x d • So… F = ? d = ? • The unit for work is the Newton-meter (N·m) which is also called a Joule (J).

5. x W F d =

6. Work is measured in joules (J). 1 joule is equal to a force of 1 N exerted over a distance of 1 m.

7. How can I tell if work was done? • A) Was the object moved by a force AND a distance? • B) Is there work done by another force • C) Are you forcing something to move against the influence of an opposing force? (gravity or friction) • D) Are you changing speed? • E) Are you transferring energy to another object?

8. Work & Energy • Positive work = • Force and distance same direction • You Gain Energy • Ex?? • Negative work = • Force and distance are in opposite directions • You lose energy • Ex ??

9. Work or No Work

10. ……………………. Is the boulder working???? A boulder falls off a cliff. It drops 2 m. It has a mass of 2 kg.

11. M= 10kg In this case, the weight does (positive) work d = 2 m Work = Mgd = (100N)(2m) Work = 200 Nm =200J M= 10kg Mg = 100N

12. Practice Makes Perfect Questions: a)How much work is done when a weight lifter lifts a barbell weighing 1000 Newtons 1.5 meters above the ground? b)How much work is done when a weight lifter pushes on a stationary wall with a force of 1000 Newtons for 15 seconds?

13. Power • Power equals the amount of work done divided by the time interval during which the work was done. • The unit for power is the Joule/second which is also called a Watt. • Ex: Twice the power means twice an engine can do twice the work in the same amount of time.

14. What is horsepower? 1 horsepower = 746 Watts A horse exerting 1 horsepower can raise 330 pounds of coal 100 feet in a minute, or 33 pounds of coal 1,000 feet in one minute, or 1,000 pounds 33 feet in one minute.

15. More on horsepower... 1 horsepower (over the course of an hour) is equivalent to 2,545 BTU (British thermal units). If you took that 746 watts and ran it through an electric heater for an hour, it would produce 2,545 BTU (where a BTU is the amount of energy needed to raise the temperature of 1 pound of water 1 degree F). One BTU is equal to 1,055 joules, or 252 gram-calories or 0.252 food Calories. Presumably, a horse producing 1 horsepower would burn 641 Calories in one hour if it were 100-percent efficient.

16. Power Problems 1) It takes 2 s for a car to drive down the street. If it takes 100,000 J of work for the engine to move the car, how much power is used? 2) A man sprints 400 m in 20s. If it takes 500 W of power to do this, how much force does he use? (Hint: 2 steps needed.) 3) A women pushes a box across the floor with a force of 600 N in 3 s. The displacement is 30 m. How much power does she use?

17. Energy • Universe is made up of matter and energy. • Energy is the mover of matter. • Energy has several forms: • Kinetic • Potential • Electrical • Heat • etc.

18. Energy • Universe is made up of Energy and Matter • There are many forms of energy • Conversions from one form of energy to another continually occur. • Law of Conservation of Energy: Energy cannot be created nor destroyed. It just transforms from one form into another but the total amount never changes.

19. Mechanical Energy • When work is done on an object, the object generally has acquired the ability to do work. • This "ability to do work" is called energy and it has the same units as work….Joules. • Two Types of Mechanical Energy • Potential Energy and Kinetic Energy

20. Potential Energy • The energy that is stored is called potential energy. • An object’s ability to do work by virtue of its position. I’m learning through osmosis!

21. 3 Types of Potential Energy (PE) • Elastic PE • Chemical PE • Gravitational PE • What are they? Examples of each? How are they converted? To what?

22. Gravitational Potential Energy • PE = Weight ´ height • PE = m g h • Question: • How much potential energy does a 10kg mass have relative to the ground if it is 5 meter above the ground?

23. Kinetic Energy • The energy of motion or the ability objects have to do work because they are moving. • Kinetic Energy = ½ mass ´ velocity2 KE = ½ mv² m = v =

24. Check for Understanding Determine the kinetic energy of a 1000-kg roller coaster car that is moving with a speed of 20.0 m/s. If the roller coaster car in the last problem were moving with twice the speed, then what would be its new kinetic energy?

25. The answers • 200,000 J • 800,000 J

26. Kinetic Energy • KE is dependent upon velocity: • Proportional to the square of your velocity : if velocity doubles what happens to KE? (quadruples) • KE is also dependent on mass • If mass doubles what happens to KE? (doubles too)

27. Compare & Contrast? If momentum is mass X velocity, what’s the difference in Momentum and Kinetic Energy ??

28. Compare/Contrast Momentum and Kinetic Energy • Similar? • Both only involve mass and velocity • Different? • velocity is more important to KE • Δ KE actually does work on an object (breaking bones, denting fenders, lifting bookbags)

29. Scalar Versus Vector: • An important difference is that momentum is a vector quantity - it has a direction in space, and momenta combine like forces do. • Kinetic energy is a scalar quantity -it has no direction in space, and kinetic energies combine like "regular numbers

30. A Thought Experiment: • Suppose that you were captured by an evil physicist who gave you the following choice: • You must either: • Stand in front of a 1000 kg. truck moving at 1 m/s, or • Stand in front of a 1 kg. frozen meatball moving at 1000 m/s.

31. Truck: • Truck's momentum = mv = (1000 kg)(1 m/s) = 1000 kg m/s • Truck's kinetic energy = 0.5 mv2 = (0.5)(1000 kg)(1 m/s)2 = 500 Joules • Meatball: • Meatball's momentum = mv = (1 kg)(1000 m/s) = 1000 kg m/s • Meatball's kinetic energy = 0.5 mv2 = (0.5)(1 kg)(1000 m/s)2 = 500 000 Joules

32. Work/Energy Relationship • If you want to move something, you have to do work. • The work done is equal to the change in kinetic energy. • Work = DKE • Work is a transfer of Energy!

33. Work & Energy

34. Foundations of Physics Science Review (pgs 87-90) • What has the ability to create a force? • Why is energy measured in joules? • What does the “potential” in PE mean? • How do we calculate Ep? What are all the variables? • More force means more ____ means more _____ needed. • What 2 things does Ek depend on? • Ek increases as the square of the ______ & if you go twice as fast your energy increases by ___x. • More energy means more ____ is need to ____ to car. • Describe or draw an example of the Law of Conservation of Energy. • What’s the formula for solving for Ek? What are the variables?

35. Law of Conservation of Energy • Energy can change forms but cannot be created nor destroyed. • In a closed, isolated system, the total ME (KE + PE) remains constant. • Examples??

36. Example Question When the brakes of a car going 90 km/h are locked, how much farther will it skid than if the brakes lock at 30 km/h? Answer: 9 times

37. PE = 1000J KE = 0J PE = 800J KE = 200J PE = 400J KE = 600J PE = 0J KE = 1000J

38. PE = 500J KE = 0J PE = 100J PE = 100J KE = 400J PE = 0J KE = 400J KE = 500J • Energy lost due to friction is actually not a loss; it is just a conversion.

39. PE (initial) = KE (final)

41. Example Problem • A 100 kg mass is dropped from rest from a height of 1 meter. • How much potential energy does it have when it is released? • How much kinetic energy does it have just before it hits the ground? • What is its speed just before impact? • How much work could it do if it were to strike a nail before hitting the ground?

42. 100 kg 100 kg 100 kg 1 meter nail

43. Examples to Practice: 1. A 10 lb weight is lifted 5 ft. A 20 lb weight is lifted 2.5 ft. Which lifting required the most work? (a) 10 lb weight (b) 20 lb weight (c) same work for each lifting (d) not enough information is given to work the problem (c) same work for each lifting

44. Examples to Practice: 2. A 50 kg kid rolls down a snow covered hill that is 25 m high. What’s the kid’s speed at the bottom of the hill? (a) 22 m/s (b) 22 m (c) 1250 m/s (d) not enough information is given to work the problem

45. Examples to Practice: • A 4 kg book is sitting on a 2.4 m high shelf. A) How much PE does sit have? B) How fast would it be traveling the moment before it landed if it fell off the shelf?