1. More Forces Lecturer: Professor Stephen T. Thornton

2. Reading Quiz: You try to move a heavy couch around your living room
Reading Quiz: You try to move a heavy couch around your living room. When does the maximum friction occur?
When you push so hard that it almost moves, but it does not move, because it is so heavy.
When you move it slowly on the floor.
When two people move it at a faster speed on the floor.
Right when it almost stops moving.

3. Answer: A
Static friction is generally larger than kinetic friction.

4. Last Time Forces Free body diagrams Weight and mass Normal force
Tension
Lots of conceptual quizzes
Work Problems

5. Today
Review
Friction

8. Accelerated Mass. A particle of mass m, initially at rest at is accelerated by a force that increases in time as Determine its velocity and position x as a function of time.
Giancoli, 4th ed, Problem 4-60

9. Conceptual Quiz: A person hoists a bucket from a well using a rope
Conceptual Quiz: A person hoists a bucket from a well using a rope. Let the bucket be at rest. She then ties the other end of the rope to the handle. In which case is the tension in the rope the greatest? A B A. Case A B. Case B C. They are the same

10. Answer: A

11. Common Forces Revisited
Tension
Tension always pulls, never pushes.
For light (negligible-mass) ropes, the magnitude of the tension is the same everywhere along the rope.

12. The Normal Force
Normal force is always perpendicular to surface. It is self adjusting unless structure is too weak.

13. Applying Newton’s Laws with Constant Forces
If force is constant, acceleration is constant:
These equations apply to each component: x, y, z.

14. Conceptual Quiz
A block of mass m rests on the floor of an elevator that is moving upward at constant speed. What is the relationship between the force due to gravity and the normal force on the block?
A) N > mg
B) N = mg
C) N < mg (but not zero)
D) N = 0
E) depends on the size of the elevator m v
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15. Conceptual Quiz
A block of mass m rests on the floor of an elevator that is moving upward at constant speed. What is the relationship between the force due to gravity and the normal force on the block?
A) N > mg
B) N = mg
C) N < mg (but not zero)
D) N = 0
E) depends on the size of the elevator m v
The block is moving at constant speed, so it must have no net force on it. The forces on it are N (up) and mg (down), so N = mg, just like the block at rest on a table.

16. Friction is always present when two solid surfaces slide along each other.
The microscopic details are not yet fully understood.
Figure 5-1. Caption: An object moving to the right on a table or floor. The two surfaces in contact are rough, at least on a microscopic scale.

17. Facts about friction
Leonardo da Vinci performed experiments on friction (~1500). He found it was the normal force that was important, not the surface area.
Show block on table.
Friction is bad. $1B of research/year.
Friction is good. Many examples; we walk, drive cars, etc.
Italian ( ) painter, sculptor, architect, musician, scientist, mathematician, engineer, inventor, geologist, cartographer, botanist, and writer.

18. Kinetic Friction and the Normal Force
Constant velocity.
Do demo

19. Experimental results
It requires a certain force to overcome friction. Energy is used up. Experiments (done in 1429) show
The subscript k indicates kinetic (or sliding) friction. We use the terms kinetic and sliding interchangeably.

20. Experimental Results You will do these experiments in lab.
Sliding friction is also called kinetic friction.
Approximation of the frictional force fk :
Here, FN (or N) is the normal force, and μk is the coefficient of kinetic friction, which is different for each pair of surfaces.

21. More experimental results
Friction is proportional to the magnitude of the normal force.
Friction is independent of the relative speed of the surfaces.
Friction is (to first order) independent of the area of contact between surfaces.
We are examining kinetic friction.

22. Static friction
In kinetic or sliding friction the two objects are moving with respect to each other.
In static friction the object is at rest, but we want it to move. We have to overcome friction to have it move. We find there is a certain amount of force needed to do this.

23. Example of static friction
Do demo

24. Experimental result for static friction
There is an upper limit of static friction that we have to overcome in order to move an object.
Static friction can have any value up to this maximum amount.
These are concepts!

25. Facts about static friction
Static friction can have any value from zero to its maximum amount.
Value:
Static friction is independent of area of contact between surfaces.
Static friction is parallel to surface of contact, and in the direction that opposes the relative motion.

26. When we walk, is it static friction or kinetic friction when our feet are in contact with the ground?
Answer: static
Same with car tires.

27. Do coefficient of friction measurement.

28. Note that, in general, μs > μk.

29. Conceptual Quiz An object is held in place by friction on an inclined surface. The angle of inclination is slowly increased until the object starts to move. If the surface is kept at this angle when it first moves, the object   A) speeds up. B) moves at uniform speed. C) slows down. D) soon stops.

30. Answer: A
We just did this experiment. Remember that the coefficient of static friction is greater than that of kinetic friction. So when static friction is overcome and the object starts sliding, the kinetic frictional force becomes smaller, and the net force (due to gravity) is down the plane.

31. Conceptual Quiz: A block of mass m is pulled in the direction shown in the figure across a rough surface at constant velocity. The magnitude of the frictional force is A. mk m g B. mk T cosq C. mk (T - mg) D. mk T sinq E. T cosq

32. Answer: E
Because the velocity is constant, there is no horizontal net force. Therefore the horizontal component of the tension (Tcos) must have the same magnitude as the frictional force, which is the only other horizontal force. This also has the magnitude

33. Forces when pushing box from dead start:
Do this Lou’s box.

34. Pushing Box on Vertical Wall
Pushing Box on Vertical Wall. A small box is held in place against a rough vertical wall by someone pushing on it with a force directed upward at 28° above the horizontal. The coefficients of static and kinetic friction between the box and wall are 0.40 and 0.30, respectively. The box slides down unless the applied force has magnitude 23 N. What is the mass of the box?
Giancoli, 4th ed, Problem 5-16