1. Work and Energy CHAPTER 6

2. A New Perspective on Motion  We have been analyzing motion through the perspective of Newton’s Laws dealing with acceleration, velocity, and displacement.  In this chapter, we will look at motion from a different perspective – that of work and energy.

3. What is Work?  When a force acts upon an object and causes its displacement, it is said that work has been done on the object.  The force MUST cause a displacement! No work is done if the object doesn’t move.

4. Is There Work? 1. A woman pushes a shopping cart across the floor.  YES – Force causing displacement. 2. A man pushes against a wall.  NO – No displacement 3. A book falls off a table to the ground.  YES – Gravity provides the force to cause displacement 4. A child holds a book over her head while she stands on a moving walkway.  NO – The force is not causing the displacement.

5. Calculating Work

7. Units for Work

8. Example #1

9. Example #2

10. Example #3

11. Example #4

12. Energy  Energy (E) – the ability to do work.  Types of energy:  Mechanical – kinetic energy + potential energy  Electrical  Nuclear  Heat  Chemical  Sound

13. Kinetic Energy

14. Kinetic Energy Example

15. Work-Energy Theorem

16. Work-Energy Theorem Example 1

17. Work-Energy Theorem Example 2

18. Work Done by the Force of Gravity

19. Work Done by Gravity Example 1

20. Work Done by Gravity Example 2

21. Gravitational Potential Energy

22. Potential Energy Example

23. Next Class: Quiz on Work and Energy (What we’ve learned so far)  Concepts and problem-solving applications related to:  Work done by forces (including gravity and friction)  Kinetic and potential energy  Work-Energy Theorem

24. Conservative vs. Nonconservative Forces  Conservative force – total Work on a closed path is zero. (ex: gravity)  Nonconservative force – total Work on a closed path is NOT zero. (ex: friction) Energy 24 -W+W -W Gravity- down Motion- up Friction – left Motion - right Friction - right Motion- left Gravity- down Motion- down

25. Conservation of Energy

26. Conservation of Mechanical Energy

28. Conceptual Example 1: Pendulum  Pendulum - Kinetic and Potential Energy Pendulum - Kinetic and Potential Energy  In the absence of air resistance and friction…  the pendulum would swing forever  example of conservation of mechanical energy  Potential → Kinetic → Potential and so on…  In reality, air resistance and friction cause mechanical energy loss, so the pendulum will eventually stop.

29. Conceptual Example 2: Roller Coaster  Roller Coaster - Kinetic and Potential Energy Roller Coaster - Kinetic and Potential Energy

30. Conceptual Example 3: Downhill Skiing  Downhill Skiing - Kinetic and Potential Energy Downhill Skiing - Kinetic and Potential Energy  This animation neglects friction and air resistance until the bottom of the hill.  Friction is provided by the unpacked snow.  Mechanical energy loss (nonconservative force)  Negative work

31. Mousetrap Cars

32. Problem Solving Insights  Determine if non-conservative forces are included.  If yes: ME f = ME 0 + W nc  If no: ME f = ME 0  Eliminate pieces that are zero before solving  Key words: starts from rest (KE 0 = 0), ends on the ground (PE f = 0), etc.

33. Example 1  The Magnum XL-200 at Cedar Point includes a vertical drop of 59.4m. Assume the roller coaster has a speed of nearly zero at the crest of the hill. Neglecting friction, find the speed of the coaster at the bottom of the hill. ME f = ME 0 KE f + PE f = KE 0 + PE 0 ½ mv f 2 + mgh f = ½ mv 0 2 + mgh 0 ½ mv f 2 = mgh 0 (mass cancels!) v f 2 = 2(9.8)(59.4) → v f = 34.1 m/s

34. Example 2  A 55.0 kg skateboarder starts out with a speed of 1.80 m/s. He does +80.0J of work on himself by pushing with his feet against the ground. In addition, friction does -265 J of work on him. The final speed of the skateboarder is 6.00 m/s.  a) Calculate the change in gravitational potential energy.  b) How much has the vertical height of the skater changed, and is the skater above or below the starting point?

35. Example 3  A 2.00kg rock is released from rest from a height of 20.0m. Ignore air resistance & determine the kinetic, potential, & mechanical energy at each of the following heights: 20.0m, 12.0m, 0m (Round g to 10 m/s 2 for ease)

36. Example 4 Find the potential energy, kinetic energy, mechanical energy, velocity, and height of the skater at the various locations below. 36 Energy max

37. Power  Power : Rate of doing work. The work done per unit time.  Equation  P = W/t or P =(F d)/t  P is power ( Watts, ft lb/s, ft lb/min)  Horsepower : another unit for measuring power.  1 horsepower = 746 Watts (or 1 horsepower = 550 ftlb/s)  To find horsepower, divide P (in Joules) by 746.

38. Power Example #1  A weight lifter lifts a 75 kg weight from the ground to a height of 2.0 m. He performs this feat in 1.5 seconds. Find the weight lifter’s average power in A) Watts and B)Horsepower.

39. Power Example #2  A runner sprints 100 m up a hill in 25 seconds. Her average power during this run is 800 Watts. Find the force that the runner exerts during the run.

40. Power Example #3  A car accelerates from rest to 20.0 m/s is 5.6 seconds along a level stretch of road. Ignoring friction, determine the average power required to accelerate the car if A. The weight of the car is 9,000 N B. The weight of the car is 14,000 N.