1. Physics 218, Lecture X1 Physics 218 Lecture 10 Dr. David Toback

2. Physics 218, Lecture X2 Checklist for Today Things that were due last Tuesday: –Reading for Chapter 6 Things that were due Yesterday: –Chaps. 3 and 4 HW on WebCT –Progress on 5&6 problems Things due for Today –Reading for Chap 7 Things due for Wednesday’s Recitation: –Problems from Chap 5&6 –No Lab Things for Thursday: –Read Chapters 7, 8 & 9

3. Physics 218, Lecture X3 Overview: Chapters 7, 8 & 9 Combine Chapter 7, 8 & 9 into six lectures Today we’ll cover Work: The math Intuitive understanding Multiple ways to calculate work Next time: How much energy does it take to accomplish a task?

4. Physics 218, Lecture X4

5. 5 Why are we learning this stuff? This is Fundamental to Engineering How much work can a machine do? (today) How much energy does it take to accomplish a task? (next time)

6. Physics 218, Lecture X6 The plan… Need to start with some math…  Scalar product

7. Physics 218, Lecture X7 How do we Multiply Vectors? First way: Scalar Product or Dot Product –Why Scalar Product? Because the result is a scalar (just a number) –Why a Dot Product? Because we use the notation A. B A. B = |A||B|Cos 

8. Physics 218, Lecture X8 A. B = |A||B|Cos  First Question:

9. Physics 218, Lecture X9 Harder Example

10. Physics 218, Lecture X10 Back to Work The word “Work” means something specific in Physics (Kinda like Force) The amount of Work we do is the amount of Forcing we do over some distance Example: If we are accelerating a car for 1 mile, then there is a force and a distance  We do Work

11. Physics 218, Lecture X11 Calculating the work Work is done only if the force (or some component of it) is in the same (or opposite) direction as the displacement Work is the force done Parallel to the displacement

12. Physics 218, Lecture X12 Work for Constant Forces The Math: Work can be complicated. Start with a simple case Do it differently than the book For constant forces, the work is: …(more on this later) W=F. d

13. Physics 218, Lecture X13 1 Dimension Example You pull a box with a constant force of 30N for 50m where the force and the displacement are in the same direction How much work is done on the box?  W = F. d = 30N. 50m= 1500 N. M = 1500 Joules

14. Physics 218, Lecture X14 What if the Force and the Displacement aren’t in the same direction?

15. Physics 218, Lecture X15 Force Displacement 2 Dim: Force Parallel to Displacement Force Displacement Rotate F || = Fcos  W = F || d = F. d = Fdcos  where  is the angle between the net Force and the net displacement. You can think of this as the force component in the direction of the displacement.

16. Physics 218, Lecture X16 Work done and Work experienced Something subtle: The amount of work YOU do on a body may not be the same as the work done ON a body Only the NET force on the object is used in the total work calculation Add up all the work done on an object to find the total work done!

17. Physics 218, Lecture X17 Examples Holding a bag of groceries in place –Is it heavy? –Will you get tired holding it? –Are you doing “Work?” Moving a bag of groceries with constant speed across a room –Is it heavy? –Will you get tired doing it? –Are you doing “Work?” Lifting a bag of groceries a height h with constant speed –Work by you? –Work on the bag?

18. Physics 218, Lecture X18 Groceries: With the math Holding a bag of groceries –W=F. d = Fdcos  =(0)*(0)*cos  = 0 Moving a bag of groceries with constant speed across a room –Force exerted by you= mg, Net Force on bag = 0 –Work on bag= F. d = Fdcos  =0*dcos  =0 –Work exerted by you =Fdcos  =mgd*cos(90 0 )=0 Lifting a bag of groceries a height h with constant speed –Work on bag = Fd*cos  = (0)*h*(0 0 ) = 0 –Work by you =Fdcos  =(mg)hcos(0 0 )=mgh

19. Physics 218, Lecture X19 Work in Two Dimensions You pull a crate of mass M a distance X along a horizontal floor with a constant force. Your pull has magnitude F P, and acts at an angle of . The floor is rough and has coefficient of friction . Determine: The work done by each force The net work on the crate  X

20. Physics 218, Lecture X20 What if the Force is changing direction? What if the Force is changing magnitude?

21. Physics 218, Lecture X21 What if the force or direction isn’t constant? I exert a force over a distance for awhile, then exert a different force over a different distance (or direction) for awhile. Do this a number of times. How much work did I do? Need to add up all the little pieces of work!

22. Physics 218, Lecture X22 Fancy sum notation  Integral Find the work: Calculus To find the total work, we must sum up all the little pieces of work (i.e., F. d). If the force is continually changing, then we have to take smaller and smaller lengths to add. In the limit, this sum becomes an integral.

23. Physics 218, Lecture X23 Use an Integral for a Constant Force Assume a constant Force, F, doing work in the same direction, starting at x=0 and continuing for a distance d. What is the work? Region of integration W=Fd

24. Physics 218, Lecture X24 Non-Constant Force: Springs Springs are a good example of the types of problems we come back to over and over again! Hooke’s Law Force is NOT CONSTANT over a distance Some constant Displacement

25. Physics 218, Lecture X25 Work done to stretch a Spring How much work do you do to stretch a spring (spring constant k), at constant velocity, from x=0 to x=D? D

26. Physics 218, Lecture X26 Exam 1 Results Overall: Mean=71.5% People who took mini=76 People who didn’t = 54 1A, and 1B, 4C’s, 2D and 10 F’s Straight curve for now >90%  A >80%  B etc. If you got less than a 50% you REALLY need some help

27. Physics 218, Lecture X27 This Week Next Lecture: More on Work and Energy Finish the reading for Chapters 7, 8 & 9 Recitation on Chapters 5 & 6 Ch 5 & 6 due Monday on WebCT

28. Physics 218, Lecture X28

29. Physics 218, Lecture X29 Examples While you are lifting up a bottle with mass m, the bottle moves a distance d with constant velocity. As you lift it: –What is the force you exert? –What is the work done by you? –What is the work done by gravity? –What is the net work? You push a box with Force F on a rough floor with coefficient of friction  for a distance d, and the box moves with constant velocity. As it moves: –What is the work done by you? –What is the work done by friction? –What is the net work?

30. Physics 218, Lecture X30 Does the Earth do work on the Moon?

31. Physics 218, Lecture X31 Simple Case Start with our spherical cow: –Constant Forces in a single direction Work is the force done Parallel to the displacement Work is done only if the force (or some component of it) is in the same (or opposite) direction as the displacement

32. Physics 218, Lecture X32 Hiker A hiker carries a backpack of mass M with constant speed up a hill of angle  and height h. Determine: The work done by the hiker The work done by gravity The work on the backpack

33. Physics 218, Lecture X33 Simple Example with Unit Vectors A woman pulls a box of mass M with Force F P in the  direction for a distance d. Ignore friction Find the work using unit vectors