1. © 2001-2005 Shannon W. Helzer. All Rights Reserved. Unit 8 Work and Energy

2. © 2001-2005 Shannon W. Helzer. All Rights Reserved.

4.  Work – the result of applying a CONSTANT FORCE on a body and moving it through a displacement d. Work 8-1

5. © 2001-2005 Shannon W. Helzer. All Rights Reserved. Kinetic Energy & Work-Energy Principle  Work-Energy Principle - the net work done on a body is equal to the change in its kinetic energy. 8-2 Kinetic Energy Work Energy Theorem Units of W & KE Pronounced as a Joule

6. © 2001-2005 Shannon W. Helzer. All Rights Reserved. Work Done by a Constant Force  Consider the bulldozer below. It has an initial velocity v 1 at time t 1 and velocity v 2 at time t 2.  How can we determine the net work done on the dozer by the constant force? 8-3  What kind of work do we have in the second case?

7. © 2001-2005 Shannon W. Helzer. All Rights Reserved. Negative Work  When a shuttle is launched, the force acts in the direction of the displacement and produces a positive work.  When the chute stops the shuttle, the force acts in the opposite direction of the displacement and produces a negative work. 8-4

8. © 2001-2005 Shannon W. Helzer. All Rights Reserved. A Closer Look at Work  Observe the animation below.  Pay close attention to the angle of the Tension relative to the direction of motion 8-5

9. © 2001-2005 Shannon W. Helzer. All Rights Reserved. A Closer Look at Work  What is the angle between the direction of motion and the Tension in the picture below?  Look at WS 35 #4. 8-6

10. © 2001-2005 Shannon W. Helzer. All Rights Reserved.  WS 35 4b. A Closer Look at Work 8-7

11. © 2001-2005 Shannon W. Helzer. All Rights Reserved.  WS 35 4c.  How does the work done in this figure compare with that done on 4b? A Closer Look at Work 8-8

12. © 2001-2005 Shannon W. Helzer. All Rights Reserved.  WS 35 4d.  How does the work done in this figure compare with that done on 4c? A Closer Look at Work 8-9

13. © 2001-2005 Shannon W. Helzer. All Rights Reserved.  WS 35 4e.  What is the angle between the direction of motion and the Tension in the picture below? A Closer Look at Work 8-10

14. © 2001-2005 Shannon W. Helzer. All Rights Reserved. Gravitational Potential Energy  The energy a body has due to its position from the “ground.”  The “ground” can be any surface that represents the origin: a table top, the planet’s surface, the floor of an airplane,….  The Lowest Point is ALWAYS equal to zero.  The equation for GPE is as follows: 8-11

15. © 2001-2005 Shannon W. Helzer. All Rights Reserved. Elastic Potential Energy  When a spring is compressed or stretched from its neutral position, elastic potential energy is stored within the spring.  k is a proportionality constant know as the spring constant or the force constant.  We use this constant in Hooke’s Law in order to determine the force required to stretch or compress a spring. 8-12  The work done to compress or stretch a spring is given by

16. © 2001-2005 Shannon W. Helzer. All Rights Reserved. Compressing  When a spring is compressed from its neutral position, elastic potential energy is stored within the spring.  According to Hooke’s law, the force needed to compress the spring is  The energy required to compress a spring is given by Note: x is the displacement. x is the value of the number on the number line 8-13

17. © 2001-2005 Shannon W. Helzer. All Rights Reserved. Stretching  When a spring is stretched from its neutral position, elastic potential energy is stored within the spring.  According to Hooke’s law, the force needed to stretch the spring is  The energy required to stretch a spring is given by 8-14

18. © 2001-2005 Shannon W. Helzer. All Rights Reserved. Law of Conservation of Energy  The total energy is neither created nor destroyed in any process.  Energy can be transferred from one form to another, and transferred from one body to another, but the total energy amount remains constant.  Alternatively, energy can neither be created nor destroyed only changed in form or transferred to another body. 8-15

19. © 2001-2005 Shannon W. Helzer. All Rights Reserved. Conservation of Energy  If there is no work being done on a system, then the total mechanical energy of the system (the sum of its KE & PE) remains constant.  The following equations apply to the conservation of energy. “Energy before equals energy after.” 8-16

20. © 2001-2005 Shannon W. Helzer. All Rights Reserved. Conservation of Energy  What are the kinetic and potential energies at the following points? Explain why. A B C 8-17

21. © 2001-2005 Shannon W. Helzer. All Rights Reserved. Conservation of Energy Example  A car’s engine (m car = 1500 kg) puts 10,000 J of energy into getting the car to the top of a hill.  Calculate the GPE & KE of the car at the three points below. h 3h/4 h/4 A B C 8-18

22. © 2001-2005 Shannon W. Helzer. All Rights Reserved. The MVE  A statement of the conservation of energy that includes most of the forms of mechanical energy. KE GPE EPE RKE Energy BeforeEnergy After 8-19

23. © 2001-2005 Shannon W. Helzer. All Rights Reserved. The MVE Energy before equals energy after. 8-20

24. © 2001-2005 Shannon W. Helzer. All Rights Reserved. Recognizing the Elements of the MVE  In order to be successful in applying the MVE (conservation of energy), we must first be able to recognize the individual elements (energy types) found in the equation.  In the next several slides, you will see different transitions from one energy type to another.  Attempt to understand why each selected term in the MVE is important relative to the physical scenario observed.  Let’s review again the MVE and its individual elements. 8-21

25. © 2001-2005 Shannon W. Helzer. All Rights Reserved. Understanding the MVE – Free Fall  For our first energy transition, we will exam the energies associated with dropping a ball from a deck. Key Factor What is the ball’s final height? What is the ball’s GPE? The height is always equal to zero, and the GPE is always equal to zero at the Lowest Point. 8-22

26. © 2001-2005 Shannon W. Helzer. All Rights Reserved. Understanding the MVE - Launch  The next transition is similar to the previous except for the fact that the projectile will be launched up from the ground. Key Factor What did the explosion do to the ball? Do you remember the Work-Kinetic Energy Principle? The net work done on a body is equal to the change in its kinetic energy. 8-23

27. © 2001-2005 Shannon W. Helzer. All Rights Reserved.  Basketball demonstrates many wonderful energy transitions.  Here we will analyze the scenario starting just as the ball leaves the player’s hand.  However, just as with the mortar problem, the player exerted work on the ball causing it to fly. Understanding the MVE – Hoops, Anyone? Key Factor RKE changes very little during the flight of a projectile. However, you must still be able to recognize it when it exists because it does have a significant impact on many problems. 8-24

28. © 2001-2005 Shannon W. Helzer. All Rights Reserved. Understanding the MVE - Archery  Archery Problems are excellent examples of energy transitions.  What energy type is associated with the pulling back of the bow?  The releasing of the bow exerts work on the arrow in the same way that the basketball player’s muscles exerted work on the basketball and in the same way as the exploding powder exerted work on the mortar. Key Factor What was the GPE of the arrow just as it struck the target? Why? 8-25

29. © 2001-2005 Shannon W. Helzer. All Rights Reserved. Understanding the MVE – More Archery  Let’s get a bulls eye hit this time! Key Factor What was the GPE of the arrow at the beginning and the end of the arrow’s flight? We could treat it as zero since both points have the same GPE and are also the lowest points in the problem. 8-26

30. © 2001-2005 Shannon W. Helzer. All Rights Reserved. Understanding the MVE – In the Factory  In this problem we will look at the work done by a conveyor belt.  This work is done over several seconds; however, for the sake of analysis, we will assume that the work was done instantaneously on the crate.  We will also more closely examine the impact that friction has in MVE problems. Key Factor What role did friction play in this problem? Friction resulted in the apparent loss of energy to the system. However, the energy is still accounted for as work other (W O ). 8-27

31. © 2001-2005 Shannon W. Helzer. All Rights Reserved. Understanding the MVE – On the Gym Floor  In this problem we will look at the work done by a weight lifter lifting weights.  Again, this work is done over several seconds; however, for the sake of analysis, we will assume that the work was done instantaneously on the weight. Key Factor How much work is the weight lifter doing while holding the weights in the air. None! No motion, no work! Recall: W = f x d 8-28

32. © 2001-2005 Shannon W. Helzer. All Rights Reserved. Understanding the MVE – On the Road  Imagine a motorcycle is driving quickly into view from the left.  What type of energy does it have? Key Factor When the rider squeezed his brakes, what element of the MVE did he introduce? Work Other (W O ) – friction opposed the bike’s motion bringing it to a stop. Could you ignore the RKE in this problem? NO! It was overcome by the work too. 8-29

33. © 2001-2005 Shannon W. Helzer. All Rights Reserved. Energy Transition – WS 38 # 1  Although not required, a FBD may assist you in correctly answering energy questions especially when looking at work. 8-30

34. © 2001-2005 Shannon W. Helzer. All Rights Reserved. Energy Transition – WS 38 #2  Again, read and understand the entire problem before you attempt to solve any of the problem. 8-31

35. © 2001-2005 Shannon W. Helzer. All Rights Reserved. How far does it fall?  If the block slides a distance d down the plane, then how far does it fall at the same time? 8-32

36. © 2001-2005 Shannon W. Helzer. All Rights Reserved. Wrap it Up! WS 39 #1  Try to understand what is happening in the entire problem before you try to solve any of the problem.  Here is a good example. 8-33

37. © 2001-2005 Shannon W. Helzer. All Rights Reserved. Wrap it up! WS 39 #1  You have to love geometry! 8-34

38. © 2001-2005 Shannon W. Helzer. All Rights Reserved. Wrap it up! WS 39 #2  Again, read and understand the entire problem before you attempt to solve any of the problem. 8-35

39. © 2001-2005 Shannon W. Helzer. All Rights Reserved. This presentation was brought to you by Where we are committed to Excellence In Mathematics And Science Educational Services.