Alexei Safonov Lecture 9 Dynamics Kinetic Friction For kinetic friction it turns out that the larger the Normal Force the larger the friction We can write F Friction m Kinetic ID: 564483
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Slide1
Physics 218
Alexei Safonov
Lecture
9:
DynamicsSlide2
Kinetic Friction
For kinetic friction, it turns out that the larger the
Normal Force
the larger the friction. We can write
F
Friction
=
m
Kinetic
F
Normal
Here
m
is a constant
Warning:
THIS IS
NOT
A VECTOR EQUATION!Slide3
Static Friction
This is more complicated
For static friction, the friction force can vary
F
Friction
m
Static
F
Normal
Example of the refrigerator:
If I don’t push, what is the static friction force?
What if I push a little?Slide4
Friction
Only appears if there is a force trying to move an objectIf force is applied, but object is not yet moving: Static Friction.Friction is EQUAL to the force
Friction can’t grow beyond
m
N, so when external force gets big enough, motion starts – Kinetic Friction.
Always equal to
m
NSlide5
Is it better to push or pull a sled?
You can pull or push a sled with the same force magnitude,
F
P
, but different angles
Q
, as shown in the figures.
Assuming the sled doesn’t leave the ground and has a constant coefficient of friction,
m
, which is better?
F
PSlide6
You push a crate from the back of an elevator to the front (with friction). Which requires the least force?
Elevator is moving up with constant speed.
Elevator is moving down with constant speed.
Elevator is accelerating upwards.
Elevator is accelerating downwards.
All require the same force.Slide7
Acceleration & Friction
Which of the following diagrams best describes the static frictional force acting on the box?Slide8
Acceleration & Friction
Which of the following diagrams best describes the static frictional force acting on the box?Slide9
Box on an inclined plane 2
A box has non-negligible friction with the surface and the coefficient of friction is m
. The inclined plane is adjustable and we change
q
from 0 to 90 degrees. Mass is known and is equal to
m
. Calculate and draw a graph of:
q
How does the friction
force
depend on
q
Acceleration
?Slide10
Pulleys and Strings
If m2 and m3 are given, what should be the value of m
2
to ensure that pulley B remains at its position?
Assume both pulleys to be massless Slide11
Rock on a String
A girl twirls a rock on the end of a string in a horizontal circle above her head. The diagram illustrates how this looks from above.If
the string breaks at the instant shown, which arrow best represents the path the rock will follow?
A
B
C
DSlide12
Rock on a String
A girl twirls a rock on the end of a string in a horizontal circle above her head. The diagram illustrates how this looks from above.If
the string breaks at the instant shown, which arrow best represents the path the rock will follow?
A
B
C
DSlide13
*
They can have also have tangential acceleration if their speed is not constant
Circular Motion,
c
entripetal
acceleration and force
1) Objects moving in a circle always have a component of acceleration, called centripetal, which is toward the center of the circle.
*
2) Centripetal acceleration must be caused by a force:
Friction, gravity – whatever force keeps it moving in a circle.
This force is often called the “centripetal force”
3) There is no “new” kind of force here.
4) There is no such thing as centrifugal force
.Slide14
Banking Angle
You are a driver on the NASCAR circuit. Your car has
m
and is traveling with a speed
V
around a curve with Radius
R
What angle,
Q
, should the road be banked so that no friction is required?Slide15
Problems with Circular Motion
Most of these problems are solved by:Considering kinematics (centripetal acceleration) which yields the resultant forceIt’s not a real force really, you are basically “guessing” the answer for how the real forces must have added up to allow the kind of motion that happens here
Be careful with the direction of acceleration!
Step back and look at real forces
You already know how they must have added up, now your task is to see how that can happen
Bring the two pieces of the puzzle together and find what they are asking aboutSlide16
Other tricks
What is minimum velocity for the car not to fall down?Radius, mass are givenKey question: what tells you that the car may not make it through the top point?
Normal force!
How about a problem with a ball on a string that you rotate in vertical plane with constant speed and you want it to swing without sagging at the top?
What force should you look at instead?
What if it is a bucket with a rock in it and you don’t want it to fall on you?
What force?Slide17
Conical Pendulum
A small ball of mass
m
is suspended by a cord of length
L
and revolves in a circle with a radius given by
r = Lsin
Q
.
What is the velocity of the ball?
Tension F
T
?
Calculate the period of the ball.Slide18
An Incline, a Pulley and two Boxes
In the diagram given,
m
1
and
m
2
remain at rest and the angle
Q
is known. The coefficient of static friction is
m
and
m
1
is known.
What is the mass
m
2
?
Is it a single value or a range?
Q
m
2
m
1
Ignore the mass of the pulley and cord and any friction associated with the pulley