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Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 8
Course website: http://faculty.uml.edu/Andriy_Danylov/Teaching/PhysicsI
Lecture Capture:
http://echo360.uml.edu/danylov2013/physics1fall.html
Lecture 8
Chapter 5
Friction force
09.30.2013 Physics I
Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 8
Exam I.
Wed Oct. 2; 9 - 9.50 am; Olney 150
Have your student ID Remember your recitation section Calculators are allowed A sheet with formulae will be provided
Review Session Mon 6-8:30 pm, Ball 210
Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 8
Chapter 5. Sections 5.1 Friction More Newton’s Laws
Outline
Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 8
A new contact force…friction
Friction is always present when two solid surfaces slide along each other.
The microscopic details are not yet fully understood.
Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 8
Friction
m
mg
m
FN FA
mg
FN
mg
m
FN
FA
Ffr Ffr no motion
static no motion
static
Static. Limit. Motion is about to start
0=− frA FF
Afr FF =
0 ANSfr FFF == µ
frF
AF
NS Fµ
45
m
FN
FA
Ffr Sliding.
Friction (kinetic) is constant
NKfr FF µ=
Afr FF =
Kinetic friction
NKfr FF µ=Static friction
frictionstaticoftcoefficienS −µ
frictionkineticoftcoefficienK −µ
NS Fµ<
NSfr FF µ≤ If a horizontal force is applied on an object ,
the object does not move. It means a second force, Static Friction, must be
opposing the applied force.
Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 8
Static friction
Static friction applies when two surfaces are at rest with respect to each other (such as a book sitting on a table).
The static frictional force is as big as it needs to be to prevent slipping, up to a maximum value.
Usually it is easier to keep an object sliding than it is to get it started.
NSfr FF µ≤
Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 8
Kinetic friction
Sliding friction is called kinetic friction.
Approximation of the frictional force:
FN is the normal force
μk is the coefficient of kinetic friction, which is different for each pair of surfaces.
NKfr FF µ=
Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 8
Friction
Friction is the contact force parallel to the surfaces Force opposite to a direction of motion. Magnitude of friction depends on:
– Properties (roughness) of the two surfaces – Normal Force between the two surfaces
Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 8
Coefficients of Friction
Note that, in general, μs > μk.
Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 8
Static and Kinetic Friction
Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 8
Example A 10-kg box moves on a horizontal surface. The system has coefficients of friction μK=0.5. [Use g=10 m/s2] A horizontal force of 60N is applied. What is the acceleration?
x
y
Fg=mg
m Ffr
FN
=μKFN mgFN =
NKfr FF µ= mgKµ=
maFFF frAx =−+=∑
FA
mamgF KA =− µm
mgFa KA µ−= 2
2 110
10105.060s
msm
kgkgN
=⋅⋅−
=
The static friction force has a maximum of µsN = 50 N. The tension in the rope is only 30 N. So the pulling force is not big enough to overcome friction.
ConcepTest 1. Will It move? 1) moves to the left
2) moves to the right
3) moves up
4) moves down
5) the box does not move
A box of weight 100 N is at rest on a floor where µs = 0.5. A rope is attached to the box and pulled horizontally with tension T = 30 N. Which way does the box move?
T=30N m
Follow-up: What happens if the tension is 55 N?
NSfr FF µ= forceNmgS max501005.0 =⋅== µ
Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 8
mg
Fn
θ θ
How to measure μS?
Given: m, μs, with friction
Find: θ
A block lies on an inclined plane with μk. The angle of the incline is slowly increased. At what angle does the block start to move?
Ffr
NSfr FF µ= θµ cosmgS=
0
About to start moving
By measuring angle, when an object gets lose, we can find static friction coefficient
Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 8
Demonstrations
Two Interleaved Books
Simply lay the pages of two phone books on top of each other one by one before attempting
to pull them apart.
mg
Fn
θ θ
Ffr
(I)
(II)
(III)
Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 8
What is going to happen with a car parked on a street with a slope of more than 45 degrees if µs=1?
sµθ =tanSince , then at 45 deg the car will be about to get loos and start sliding down.
1=sµ
Example: A car parked on a hill
Die Hard
Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 8
Conceptual Example: A box against a wall
You can hold a box against a rough wall and prevent it from slipping down by pressing hard horizontally. How does the application of a horizontal force keep an object from moving vertically?
You have to press the box hard so that the force of static friction, which depends on the normal force, would be equal to box’s weight.
Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 8
Example 5-7: A ramp, a pulley, and two boxes.
Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 8
Example 5-7: A ramp, a pulley, and two boxes
ConcepTest 2. Going Sledding
1
2
In case 1, the force F is pushing down (in addition to mg), so the normal force is larger. In case 2, the force F is pulling up, against gravity, so the normal force is lessened. Recall that the frictional force is proportional to the normal force.
1) pushing her from behind
2) pulling her from the front
3) both are equivalent
4) it is impossible to move the sled
5) tell her to get out and walk
Your little sister wants you to give her a ride on her sled. On level ground, what is the easiest way to accomplish this?
Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 8
Example 5-7: A ramp, a pulley, and two boxes
If m1 moves up the incline plane. Friction force will change its direction
Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 8
Similar: Example 5-5: Two boxes and a pulley. Two boxes are connected by a cord running over a pulley. The coefficient of kinetic friction between box A and the table is 0.20. We wish to find the acceleration, a, of the system. As box B moves down, box A moves to the right.
Fg=mA g
Ffr
FN
FT
Fg=mB g
FT
Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 8
Similar: Example 5-6: The skier.
This skier is descending a slope, at constant speed. What can you say about the coefficient of kinetic friction?
Department of Physics and Applied Physics 95.141, Fall 2013, Lecture 8
Thank you See you on Wednesday
Exam I
Please!!! Remember your recitation section number!!!