1. AP Physics Chapter 6
Force and Motion – II

2. AP Physics Turn in Chapter 5 Homework, Worksheet & Lab Report
Take Quiz 6
Lecture
Q&A

3. Review on Chapter 5 Newton’s Second Law: F = ma
Newton’s Third Law: Action and Reaction Forces
Forces
Weight
Normal Force
Tension
Apparent Weight

4. Four Fundamental (Basic) Forces in Nature
Gravitational Force
Electromagnetic Force
Strong (Nuclear) Force
Weak (Nuclear) Force

5. Gravitational Force
Gravity or Weight (Gravitational force Earth pulling on objects around it): W
Gravitational force always exist, but value of g can be different at different location.
On surface of earth, g = 9.81 m/s2.
Higher elevation, smaller g.
Higher latitude, larger g.

6. Electromagnetic Force
Almost all other forces we encounter in daily life are electromagnetic force in nature.
Electric force: F
Magnetic force: F
Tension (pull, string): T
Push: F
Normal (support): N (not to be confused with Newton, the unit of force)
Friction: ƒ (ƒs or ƒk)

7. Strong (Nuclear) Force
Holds protons and neutrons within the nucleus
Exist in very short distance only ( m)
Stable nucleus

8. Weak (Nuclear) Force
Also holds protons and neutrons within the nucleus
Also very short range ( m)
Not strong enough. Protons and neutrons can escape  nuclear reaction
Unstable nucleus

9. Relative Strength of Forces
Electromagnetic
Gravitational
Weak
Strong
Weakest
Strongest

10. Force at Distance Contact force: Field force / Distant force:
Force giver and receiver must be in contact
Tension, push, normal force, friction, …
Field force / Distant force:
Force giver and receiver do not have to be in contact
Gravity, electric force, magnetic force, …

11. Unification of Forces
Electromagnetic and weak forces have been unified into (understood as) one force: Electroweak force
It is believed that all four forces are different aspects of a single force.
Grand Unification Theories (GUTs) and Supersymmetric theories
Not yet successful

12. Friction
Friction: force opposing relative motion or tendency of relative motion between two rough surfaces in contact
Smooth surface  No friction
No normal force  No friction v

13. Two kinds of frictions Static friction: Kinetic (or sliding) friction:
s: coefficient of static friction
Static friction force is not constant, it has a maximum.
Kinetic (or sliding) friction:
k: coefficient of kinetic friction
Kinetic friction force is constant.
 is a constant depending on the properties of the two surfaces
 = 0 when one of the surfaces is smooth (frictionless.)
s > k for same surfaces.
 has no unit.

14. Example: What happens to the frictional force as you increase the force pushing on a table on the floor? N
Fapp f W
But what if the applied force increases just slightly? f
Table not moving yet. Static friction increases as applied force increases. fs = Fapp
sN •
Once table is moving, a smaller constant kinetic friction. fk < fs, max • • • •
Fapp
sN

15. Is friction always opposite to motion?
When you step on the pedal 4 v v v 1 7 v v 5 2 f1 3 f2 6

16. Example:
A trunk with a weight of 220N rests on the floor. The coefficient of static friction between the trunk and the floor is 0.41, while the coefficient of kinetic friction is 0.32.
a). What is the minimum magnitude for a horizontal force with which a person must push on the trunk to start in moving?
b) Once the trunk is moving, what magnitude of horizontal force must the person apply to keep it moving with constant velocity?
c) If the person continued to push with the force used to start the motion, what would be the acceleration of the trunk?

17. Solution y
N = W x f F W
Similarly,

18. Solution F f W
N = y x

19. Example: Pg135-57
The coefficient of kinetic friction in between the incline and the block is 0.20, and angle  is 60o. What is the acceleration of the block if
a) It is sliding down the slope and
b) It has been given an upward shove and is still sliding up the slope? 

20. Solution y x f N Wy Wx W 

21. Solution (2) W N f x y  Wx Wy

22. Practice:
An 11 kg block of steel is at rest on a horizontal table. The coefficient of static friction between block and table is 0.52.
What is the magnitude of the horizontal force that will just start the block moving?
What is the magnitude of a force acting upward 60o from the horizontal that will just start the block moving?
If the force acts down at 60o from the horizontal, how large can its magnitude be without causing the block to move?

23. Solution N f F W y Fx Fy F N  f x W

24. Solution (2) c) Similarly to Part b), we have
Another approach is to use the same equation as in b) but change the angel to –60o.

25. Practice: Pg133-21
Block B in the diagram weighs 711 N. The coefficient of static friction between block and horizontal surface is Find the maximum weight of block A for which the system will be stationary?
30o B A

26. Solution: Pg133-21 y y N TA f T x B T  WB x P  WA

27. Drag Force
Drag Force:
C: drag constant (not a true constant)
: density of fluid (air or liquid)
A: cross-sectional area of object moving in fluid
v: speed of object relative to fluid
Source: fluid in relative motion pushing on object
Direction: opposing relative motion of object relative to fluid, same direction as relative motion of fluid

28. Terminal velocity D W Initially, v: small  D: small W _____ D >+
Fnet:
downward
 a:
downward W
 v:
Increases
 D:
increases
Eventually, D ___ W: =
 Fnet =
:  v:
 a =
constant

29. Practice: Pg Calculate the ratio of the drag force on a jet flying with a speed of 1000 km/h at an altitude of 10 km to the drag force on a prop-driven transport flying at half the speed and half the altitude. The density of air is 0.38 kg/m3 at 10 km and 0.67 kg/m3 at 5.0 km. Assume that the airplanes have the same effective cross-sectional area and the same drag coefficient C.

30. Review: Uniform Circular Motion and Centripetal Acceleration
v: speed of particle
r: radius of circle or circular arc
, where v
Direction of acceleration is always toward the center of circle (or circular arc)
 Centripetal a a v a v
for uniform circular motion at any time.

31. Centripetal Force
Centripetal force is in general not a single physical force; rather, it is in general the net force.
Do not draw centripetal force on force diagram (Free Body Diagram)

32. Examples of centripetal forces
Rear View N N  W f W
Examples of centripetal forces
Rounding a curve in a car
Flat curve:
Static friction provides the centripetal force (when no skidding)
Max velocity w/o skidding
Banked curve:
a component of Normal force (net force)
No friction
Orbiting the Earth (Sun or other object)
Gravity

33. Example: Pg138-87 A car weighing 10. 7 kN and traveling at 13
Example: Pg A car weighing 10.7 kN and traveling at 13.4 m/s attempts to round an unbanked curve with a radius of 61.0 m. a) What force of friction is required to keep the car on its circular path? b) If the coefficient of static friction between the tires and road is 0.35, is the attempt at taking the curve successful? y N f x W
Yes, successful.

34. Practice: Pg A banked circular highway curve is designed for traffic moving at 60 km/h. The radius of the curve is 200 m. Traffic is moving along the highway at 40 km/h on a rainy day. What is the minimum coefficient of friction between tires and road that will allow cars to negotiate the turn without sliding off the road? y N Nx Ny f fx fy  x W

35. Practice: Pg (Modified wording) A student of weight 667 N rides a steadily rotating Ferris wheel (the student sits upright). At the highest point, the apparent weight of the student is 556 N. (a) Does the student feel “light’ or “heavy” there? (b) What is the apparent weight at the lowest point? If the wheel’s speed is doubled, what is the apparent weight at the (c) highest point and (d) lowest point?
Ntop W N
a) Wapp < W
 Feel “light” W
Nbottom
Top: W
Bottom:

36. Practice: Pg (Modified wording) A student of weight 667 N rides a steadily rotating Ferris wheel (the student sits upright). At the highest point, the apparent weight of the student is 556 N. (a) Does the student feel “light’ or “heavy” there? (b) What is the apparent weight at the lowest point? If the wheel’s speed is doubled, what is the apparent weight at the (c) highest point and (d) lowest point?
Nbottom’ W
Ntop’

37. Practice: Pg A certain string can withstand a maximum tension of 40 N without breaking. A child ties a 0.37 kg stone to one end and, holding the other end, whirls the stone in a vertical circle of radius 0.91 m, slowly increasing the speed until the string breaks. a) Where is the stone on its path when the string break? b) What is the speed of the stone as the string breaks?
a) In order to keep the same speed, and therefore the same centripetal force, the tension required is largest when the rock is at the bottom. • a W T T T

38. Practice: Pg Two blocks (m = 16 kg and M = 88 kg) are not attached to each other. The coefficient of static friction between the blocks is s = 0.38, but the surface beneath the larger block is frictionless. What is the minimum magnitude of the horizontal force F required to keep the smaller block from slipping down the larger block? m: F m M x y f F N N2 M: W N f W2

39. Practice: A little girl of mass m1 = 10 kg sits on a slab of mass m2 = 20 kg on a frozen lake. Between girl and slab, the coefficient of static friction is 0.60, and the coefficient of static friction between the sled and lake is The sled is pulled forward by a horizontal force F. What is the maximum magnitude of F such that the girl stays on the sled?
m1: F N1 f1 W1
m2: N2 f1 F f2 W2 N1

40. Practice (Continued) F W1 W2 N1 N2 f1 f2