1. Work Lecturer: Professor Stephen T. Thornton

2. Reading Quiz
A) yes
B) no
only in southern hemisphere
only in northern hemisphere
Is it possible to do work on an object that remains at rest?

3. Reading Quiz
Is it possible to do work on an object that remains at rest?
A) yes no
only in southern hemisphere
only in northern hemisphere
Work requires that a force acts over a distance. If an object does not move at all, there is no displacement, and therefore no work done.

4. Last Time Orbital maneuvers Ocean tides Geophysical applications
Free floating in space
Satellites and weightlessness
Principle of Equivalence
Black holes

5. Discuss the concept of work
Today
Discuss the concept of work

6. Let the force and displacement be in the same direction (for now).
W = Fd called Work
unit: N m, newton meter Work is so important that we give it its own unit: joule 1 J = 1 N m

7. How much work is a joule? Total annual U.S. energy use is ~1020 J.
Lifting an apple about 1 meter is a joule.
Total annual U.S. energy use is ~1020 J.
Lifting our text book 1 m.
F = (2.6 kg)(9.81 m/s2) = 26 N
W = (26 N)(1 m) = 26 J
Take book to class.

8. In the SI system, the units of work are joules:
As long as this person does not lift or lower the bag of groceries, he is doing no work on it. The force he exerts has no component in the direction of motion.
Figure 7-2. Caption: The person does no work on the bag of groceries since FP is perpendicular to the displacement d.

9. What happens when force is not in same direction as displacement?
We use component of force in direction of displacement.
What happens when force is not in same direction as displacement?

10. W = Fd cos. Work is a scalar
W = Fd cos. Work is a scalar. We can determine work two ways: Work is the 1) component of force in the direction of displacement times the magnitude of displacement. 2) component of displacement in the direction of the force times the magnitude of the force.

11. Work can be negative. See right.

12. Gravity does work on the apple as it falls. The apple accelerates
Gravity does work on the apple as it falls. The apple accelerates. Gravity does negative work on the apple if we throw it up.

13. Definition of the scalar, or dot, product:
Figure 7-6. Caption: The scalar product, or dot product, of two vectors A and B is A·B = AB cos θ. The scalar product can be interpreted as the magnitude of one vector (B in this case) times the projection of the other vector, A cos θ, onto B.
Therefore, we can write:

14. Usefulness of scalar products for general vectors:
Figure 7-6. Caption: The scalar product, or dot product, of two vectors A and B is A·B = AB cos θ. The scalar product can be interpreted as the magnitude of one vector (B in this case) times the projection of the other vector, A cos θ, onto B.

15. Notes about work Work is a scalar, not a vector.
Work can be positive, negative, or zero.
The angle  is always the angle between
and Be careful about this.
There is often more than one force acting
on an object. The total net work is the sum
of the work done by all the forces.

16. Conceptual Quiz: Negative work means A) the applied force is variable
Conceptual Quiz: Negative work means   A) the applied force is variable. B) the applied force is perpendicular to the displacement. C) component of the applied force is opposite to the displacement. D)  nothing, as there is no such thing as negative work.

17. Answer: C
Negative work simply means the product of is negative and that and are such that  > 900.

18. Conceptual Quiz: A block slides a certain distance down a straight incline. The work done by gravity is W. Next the block slides up a longer, curved incline of the same height. What is the work done by gravity for the second slope? A)  W B)  Zero C)  - W D)  Gravity cannot do work: some other force does the work. E)  The work cannot be determined unless the distance traveled is given.

19. Answer: C W
In the second case the displacement is somewhat opposite to the force of gravity, so the work is negative. Because the block goes back to the same height, the magnitude is the same.

20. Conceptual Quiz: A force F pushes a block along a horizontal surface against the force of friction f. If the block undergoes a displacement d at constant velocity, the work done by the net force on the block (hint on next slide)  A)  is zero. B)  is equal to the work done by friction. C)  increases the kinetic energy of the block. D)  decreases the kinetic energy of the block.

21. Conceptual Quiz: A force F pushes a block along a horizontal surface against the force of friction f. If the block undergoes a displacement d at constant velocity, the work done by the net force on the block is   A)  zero. B)  equal to the work done by friction. C)  increases the kinetic energy of the block. D)  decreases the kinetic energy of the block.

22. Answer: A
The key here is that the force F does positive work and the friction f does negative work. Because the velocity is constant, there is no net force and the forces F and f are equal and opposite. The total work done by the net force is zero.

23. Graphical Representation of the Work Done by a Constant Force

24. Work Done by a Non-constant Force

25. Work Done by a Varying Force
Particle acted on by a varying force. Clearly, is not constant!
Figure 7-8. Caption: A particle acted on by a variable force, F, moves along the path shown from point a to point b.

26. For a force that varies, the work can be approximated by dividing the distance up into small pieces, finding the work done during each, and adding them up.
Figure 7-9a. Caption: Work done by a force F is (a) approximately equal to the sum of the areas of the rectangles.

27. In the limit that the pieces become infinitesimally narrow, the work is the area under the curve:
Figure 7-9b. Caption: Work done by a force F is (b) exactly equal to the area under the curve of F cos θ vs. l.

28. The spring force varies with position
The spring force varies with position. It is a good example of the kind of force we are considering. k is the spring constant

29. Work Needed to Stretch a Spring a Distance x

30. The Work Done by a Spring Can Be Positive or Negative
Work done by spring is positive in this case.
Compressed spring is pushing out.

31. The Work Done by a Spring Can Be Positive or Negative
Work done by spring is negative in this case.
Block is moving against compressed spring compressing it more.

32. Work Done By Spring. If it requires 5
Work Done By Spring. If it requires 5.0 J of work to stretch a particular spring by 2.0 cm from its equilibrium length, how much more work will be required to stretch it an additional 4.0 cm?
Giancoli, 4th ed, Problem 7-38

33. Conceptual Quiz
A box is being pulled across a rough floor at a constant speed. What can you say about the work done by friction?
friction does no work
at all
B) friction does negative work
C) friction does positive work
Answer: 2

34. Conceptual Quiz
A box is being pulled across a rough floor at a constant speed. What can you say about the work done by friction?
friction does no work
at all
B) friction does negative work
C) friction does positive work
Friction acts in the opposite direction to the displacement, so the work is negative. Or using the definition of work (W = F d cos q ), because  = 180º, then W < 0. f N mg
Displacement
Pull

35. Conceptual Quiz
A ball tied to a string is being whirled around in a circle. What can you say about the work done by tension?
A) tension does no work at all
B) tension does negative work
C) tension does positive work
Answer: 1

36. Conceptual Quiz
A ball tied to a string is being whirled around in a circle. What can you say about the work done by tension?
A) tension does no work at all
B) tension does negative work
C) tension does positive work
No work is done because the force acts in a perpendicular direction to the displacement. Or using the definition of work (W = F d cos q ), because  = 180º, then W < 0. v T
Follow-up: Is there a force in the direction of the velocity?

37. Conceptual Quiz A) one force
B) two forces
C) three forces
D) four forces
E) no forces are doing work
A box is being pulled up a rough incline by a rope connected to a pulley. How many forces are doing work on the box?
Answer: 3

38. Conceptual Quiz A) one force
B) two forces
C) three forces
D) four forces
E) no forces are doing work
A box is being pulled up a rough incline by a rope connected to a pulley. How many forces are doing work on the box?
Any force not perpendicular to the motion will do work:
displacement N f T mg
N does no work
T does positive work
f does negative work
mg does negative work