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Physics 218
Lecture 8: Dynamics
Alexei Safonov
Free Body Diagrams
Same tricks as in Chapters 1-3:
1. Draw a diagram: Draw each force on an
object separately! Force diagram!
2. Break each force into the X and Ycomponents, THEN sum!!!
– Show your TA that you know the difference
between a force, and a component of force
– GREAT way to pick up partial credit
Closer Look at Elevators
A box of mass m is hung with a string
from the ceiling of an elevator that is
accelerating upward. Which of the
following best describes the tension T
in the string:
A) T < mg
B) T = mg
C) T > mg
Lets walk over this step by step
a
Clicker Question
• You are traveling on an
elevator up the Sears
tower. As you near the top
floor and are slowing down,
your acceleration
• A) is upward
• B) is downward
• C) is zero
Clicker Question
• You are traveling on an
elevator up the Sears
tower, and you are standing
on a bathroom scale.
• As you near the top floor
and are slowing down, the
scale reads
• A) More than your usual
weight
• B) Less than your usual
weight
• C) Your usual weight
Rope Problems
If a rope is massless and doesn’t
stretch, this means:
• The acceleration of any part of a rope
is the same as any other part
• The magnitude of the acceleration of
the two things it attaches are equal
• The tension (Force) exerted by each
end is the same
Spring Scale
• What is the reading in the spring scale?
Friction
Two types of friction:
1. Kinetic: The friction force that
slows things down
2. Static: The force that makes it
hard to even get things moving
Refrigerator
• If you push a refrigerator when
there is no friction what happens?
• In the real world what happens?
Especially when it’s fully loaded
and on a sticky kitchen floor?
–When does static friction kick in?
–When does kinetic friction kick in?
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
Problem Solving
• Most problems are in the intersection of
Kinematics and Dynamics. Useful tips:
– If the motion is specified (e.g. “at rest”, “constant
speed”, “uniform circular”), that is important
information. Use it to get the net force (e.g. from the
acceleration value)
• You don’t yet know where it is from, but you know it got to be
there!
– Separately calculate forces acting on the object
– Connect the two pieces of information and solve for
the unknowns
Pulling a Box
• What is the
magnitude of the
static frictional force
acting on the box?
A.
B.
C.
D.
Mg
mMg
T
0
Pulling a Box
• What is the
magnitude of the
static frictional force
acting on the box?
A.
B.
C.
D.
Mg
mMg
T
0
Two Boxes and a Pulley
You hold two boxes, m1 and
m2, connected by a rope
running over a pulley at
rest. The coefficient of
kinetic friction between
the table and box I is m.
You then let go and the
mass m2 is so large that
the system accelerates
Q: What is the magnitude
of the acceleration of the
system?
Ignore the mass of the pulley
and rope and any friction
associated with the pulley
• In which case is the tension
in the string the biggest?
• Case 1
• Case 2
• Same
• In which case is the
tension in the string the
biggest?
• Case 1
• Case 2
• Same in both
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
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: how do you identify
the critical moment when something
happens that makes the car fall?
• 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?
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