1. Frictional Forces

2. Friction:
Friction: from book, ever present resistance to motion whenever two materials are in contact with each other.
Friction: Two surfaces rubbing together and their stickiness
Causes Frictional Forces

3. Friction: Two surfaces rubbing together and their stickiness
Friction: Two surfaces rubbing together and their stickiness. Always direction opposite of motion.
frictional force: A force that slows motion, or prevents motion from starting.
Friction: frictional forces arise at the contact points between the molecules of the different bodies. Contact force that is resistance to Motion.
ALWAYS OPPOSES MOTION, i.e, in opposite direction of motion. Friction increases as contact pressure increases, i.e., more weight means more friction. Usually dissipated as heat or usually generates heat.
SURFACE AREA DOES NOT CHANGE FRICTION.
* Friction Force is Usually lowercase “f ” usually in italics.

4. Frictional Forces Static friction – REST occurs during Motion.
frictional force: A force that slows motion, or prevents motion from starting.
Kinetic friction – MOTION
slows objects down.
occurs during Motion.
Static friction – REST
prevents motion from starting.
occurs before motion, when still,
not moving, or at REST.
Which is bigger?????

5. New Symbol μ – greek letter “Mu” Coefficient of friction.
μs – coefficient of static friction
μk – coefficient of kinetic friction
Coefficient of friction: Decimal between 0.0 and 1.0, unitless. Decimal percent of force in the normal direction. (Mu is percent of weight that turns into friction force.)
Coefficient of friction: μ where f = μ FN
Usually just given in the problem, depends on materials used and their surface conditions.

6. Static and Kinetic Frictional Forces
Kinetic Frictional Force: friction force that occurs while sliding.
The magnitude fk of the kinetic frictional force is given by:
fk = k FN
where  k is the coefficient of Kinetic friction, and FN is the magnitude of the normal force.
Normal Force: Force that is 90 degrees to the surfaces. (Normal is 90) degrees.
Kinetic frictional forces occur when the object is moving;
it acts to slow down the motion!
Frictional forces are independent
of the area of contact between
the surfaces! (talk about sides of block then race tires)

7. Static and Kinetic Frictional Force
Example
A sled is traveling 4.00m/s along a horizontal stretch of snow.
The coefficient of kinetic friction is k = How far
does the sled go before stopping?

8. Static and Kinetic Frictional Force
Formula
1) FN= mg = weight
2) ΣF= fk , fk = k FN
3) ΣF= max = k FN
4) max = k mg
5) (/m=>) ax= k g
6) ax = .05 (9.80m/s2)
7)vf2=vo2+2axx. Find x
Known Variables
k = vo = 4.00 m/s
vf = 0.00 m/s
Unknown Variables
ax =
x =

9. Static and Kinetic Frictional Force
Formula
1) FN= mg = weight
2) ΣF= fk , fk = k FN
3) ΣF= max = k FN
4) max = k mg
5) (/m=>) ax= k g
6) ax = .05 (9.81m/s2)
7)vf2=vo2+2axx. Find x
Known Variables
k = vo = 4.00 m/s
vf = 0.00 m/s
Unknown Variables
ax = 0.49 m/s2
x =16.3m

10. Static and Kinetic Frictional Force
Formula
1) FN= mg = weight
2) ΣF= fk , fk = k FN
3) ΣF= max = k FN
4) max = k mg
5) (/m=>) ax= k g
6) ax = .05 (9.80m/s2)
7)vf2=vo2+2axx. Find x
Did we need to know the mass of the sleder? No.
Why? It cancels out in the ax equation.
Real Life Ap: This applies to car tires in accidents. By measuring the length of skid marks, they can calculate the speed a car was going before an accident. k of a tire is the same for all cars since it does not depend on car mass or surface area of the tires.

11. Static and Kinetic Frictional Forces Static Frictional Force:
Reaction force to anything trying to
start motion.
Equal and opposite to applied force.
DOES NOT EXCEED THE APPLIED FORCE,
but is equal to it.

12. Static and Kinetic Frictional Forces
Static Frictional Force Breaks at a certain value:
fs = s FN
fs = force of static friction
s = coefficient of static friction
FN = Normal force

13. Static and Kinetic Frictional Forces
Static Frictional Force Breaks at a certain value:
fs = s FN
fs = force of static friction
s = coefficient of static friction
FN = Normal force
s is a given value. It depends on the object and the surface.

14. Static and Kinetic Frictional Forces Static Frictional Force:
fs = force of static friction
s = coefficient of static friction
FN = Normal force (usually weight)
Normal force is usually just the weight of the object.
FN = Mass* 9.80 m/s2
IMPORTANT!!!!!
If the surface is not horizontal use trig.
Multiply by cos of the angle of incline.

15. Notes on friction Almost always: μs > μk
It is easier to keep an object moving than it is to start from rest. Think about pushing a car.
Both are almost always less than 1. If it was greater than one, it would be easier to pick the object up and carry it than it would be to push it across the flat surface (something like velcro)

16. Problem
Box: How much force is needed to “budge” this box? If we keep pushing that hard, what will the acceleration be?

17. Problem
Box: fs = s FN = .4 (10kg) ( 9.80m/s2) fs = 39 N (Breaking Force)

18. Problem
Box: fk = k FN = .2 (10kg) ( 9.80m/s2) fk = 19.5 N (Kinetic Force) Net Force = Pushing Force – Kinetic Friction Force Net Force = 39N – 19.5N = 19.5N a = F / m = 19.5N / 10kg = 1.95 m/s2 = 2 m/s2

19. The Tension Force

20. The Tension Force
Tension is the force balanced by a rope, cable or wire.
A “simple pulley” changes direction without affecting tension.
Tension is the same at every point in a single rope.

21. Equilibrium Applications of Newton’s Laws of Motion
An object is in equilibrium when it has zero acceleration
“equilibrium” refers to a lack of change, but in the sense
that the velocity of an object isn’t changing, i.e, there is no
acceleration.
Equilibrium: Constant Speed and Direction.
Fx = 0 and Fy = 0, ax = 0 m/s2 and ay = 0 m/s2
ax = 0 m/s2 and ay = 0 m/s2
 Fx = 0 and Fy = 0

22. Reasoning Strategy If F = 0, then Fx = 0 and Fy = 0.
Draw a free-body diagram the object. Be sure to include only the forces that act on the object; do not include forces that the object exerts on its environment.

23. Example
A jet plane is flying with a constant speed along a straight line at an angle of 30.0o above the horizontal. The plane has a weight W whose magnitude is W=86,500 N and its engine provide a forward thrust T of magnitude T=103,000 N. In addition, the lift force L (directed perpendicular to the wings) and the force R of air resistance (directed opposite to the motion)
act on the plane. Find L and R.

24. Shortcut:
Since 3 of our forces are
Perpendicular, lets change
The axes...

25. R=59,750N and L = 74,911 N