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Physics 218
Lecture 9: Dynamics
Alexei Safonov
Kinetic Friction
• For kinetic friction, it turns out that the
larger the Normal Force the larger the
friction. We can write
FFriction = mKineticFNormal
Here m is a constant
• Warning:
– THIS IS NOT A VECTOR EQUATION!
Static Friction
• This is more complicated
• For static friction, the friction force can vary
FFriction  mStaticFNormal
Example of the refrigerator:
– If I don’t push, what is the static friction
force?
– What if I push a little?
Friction
• Only appears if there is a force trying to
move an object
• If force is applied, but object is not yet
moving: Static Friction.
– Friction is EQUAL to the force
• Friction can’t grow beyond mN, so when
external force gets big enough, motion
starts – Kinetic Friction.
– Always equal to mN
Is it better to push or pull a sled?
You can pull or push a sled with the same force
magnitude, FP, 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?
FP
You push a crate from the back of an
elevator to the front (with friction).
Which requires the least force?
A. Elevator is moving up with constant
speed.
B. Elevator is moving down with constant
speed.
C. Elevator is accelerating upwards.
D. Elevator is accelerating downwards.
E. All require the same force.
Acceleration & Friction
• Which of the following
diagrams best describes the
static frictional force acting
on the box?
Acceleration & Friction
• Which of the following
diagrams best describes
the static frictional force
acting on the box?
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:
– How does the friction
force depend on q
– Acceleration ?
q
Pulleys and Strings
• If m2 and m3 are given,
what should be the
value of m2 to ensure
that pulley B remains
at its position?
– Assume both pulleys to
be massless
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
• D
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
• D
Circular Motion, centripetal
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.
* They can have also have tangential acceleration if their speed is not constant
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?
Problems with Circular Motion
• Most of these problems are solved by:
– Considering kinematics (centripetal
acceleration) which yields the resultant force
• It’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 about
Other tricks
• What is minimum velocity for the car
not to fall down?
– Radius, mass are given
– Key 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?
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 = LsinQ.
1. What is the velocity
of the ball?
2. Tension FT?
3. Calculate the period
of the ball.
An Incline, a Pulley and two
Boxes
In the diagram
given, m1 and m2
remain at rest and
the angle Q is
known. The
coefficient of static
friction is m and m1
is known.
What is the mass
m2?
Is it a single value
or a range?
Ignore the mass of the pulley
and cord and any friction
associated with the pulley
m2
Q