1. Honors Physics Today's Agenda
Friction
What is it?
How do we characterize it?
Model of friction.
Static & Kinetic coefficients of friction.
Some problems involving friction 1

2. New Topic: Friction See text: 6-4 What does it do? It opposes motion!
How do we characterize this in terms we have learned?
Friction results in a force in a direction opposite to the direction of motion! j N
FAPPLIED i ma
fFRICTION mg 2

3. See text: 6-4
Friction...
Friction is caused by the “microscopic” interactions between the two surfaces:
Figure 4-22(p. 143) in Text 3

4. Friction... See text: 6-4 Force of friction acts to oppose motion:
Parallel to surface.
Perpendicular to Normal force. j N F i ma fF mg
See figure 5-11 4

5. Model for Sliding Friction
See text: 6-4
Model for Sliding Friction
The direction of the frictional force vector is perpendicular to the normal force vector N.
The magnitude of the frictional force vector |fF| is proportional to the magnitude of the normal force |N |.
|fF| = mK | N | ( = mK | mg | in the previous example)
The “heavier” something is, the greater the friction will be...makes sense!
The constant mK is called the “kinetic coefficient of friction”. 5

6. Model... See text: 6-4 Dynamics: i : F -mKN = m a j : N = mg
so F - mKmg = m a j N F i ma
mK mg mg 6

7. Static Friction... See text: 6-4
We can also measure mS in a “flat” geometry:
Just like in the sliding case except a = 0.
i : F - fF = 0
j : N = mg
While the block is static: fF = F j N F i fF mg 13

8. Static Friction... See text: 5-2
mS is discovered by increasing F until the block starts to slide:
i : FMAX - mSN = 0
j : N = mg
mS = FMAX / mg j
demostrate with pulley & blocks N
FMAX i
mSmg mg 14

9. Additional comments on Friction:
See text: 6-4
Additional comments on Friction:
Since fF = mN , the force of friction does not depend on the area of the surfaces in contact.
By definition, it must be true that mS > mK for any system (think about it...).
demonstrate that as you increase the angle of the ramp, once the block starts to slice it is not moving very slowly 15

10. Aside: See text: 6-4 Graph of Frictional force vs Applied force:
fF = mSN
fF = mKN fF
suitcase with rope & scale
fF = FA FA 16

11. Problem: Box on Truck See text: 6-4
A box with mass m sits in the back of a truck. The static coefficient of friction between box and truck is mS
What is the maximum acceleration a that the truck can have without the box slipping?
mS N m a 17

12. Problem: Box on Truck See text: 6-4 Draw Free Body Diagram for box:
Consider case where fF is max... (i.e. if the acceleration were any larger, the box would slip). N j i
fF = mSN mg 18

13. Problem: Box on Truck See text: 6-4
Use FTOT = ma for both i and j components
i mSN = maMAX
j N = mg
aMAX = mS g N j
aMAX i
fF = mSN mg 19

14. Problem: Putting on the brakes
See text: 6-4
Problem: Putting on the brakes
Anti-lock brakes work by regulating making sure the wheels roll without slipping. This maximizes the frictional force slowing the car since mS > mK .
The driver of a car moving with speed vo slams on the brakes. The static coefficient of friction between wheels and the road is mS . What is the stopping distance D? ab vo
v = 0 D
See example Stopping a car 20

15. Problem: Putting on the brakes
See text: 6-4
Problem: Putting on the brakes
As in the last example, find ab = mSg.
Using the kinematic equations: x = x0 + v0 t + 1/2 at v = v0 + at
In our problem: D = v0 t - 1/2 abt = v0 - abt vo ab
v = 0 D
See example: Stopping a car 21

16. Problem: Putting on the brakes
See text: 6-4
Problem: Putting on the brakes
In our problem: D = v0 t - 1/2 abt = v0 - abt
Solving for D:
Putting in ab = mSg ab vo
v = 0 D
See example : Stopping a car 22

17. Recap of today’s lecture
Friction
What is it?
How do we characterize it?
Model of friction.
Static & Kinetic coefficients of friction. (CRC)
Some problems involving friction.
Box on truck.
Braking distance.
Finish Textbook problems 23