Download Quiz Suppose a particle of mass m is attracted to the origin with a

Physics 218: Mechanics
Instructor: Dr. Tatiana Erukhimova
Lectures 30-32
Hw: Chapter 13 problems and exercises
Reading: Chapter 14
Polar coordinates
A ball of mass m is swung around a circle at the
end of a string of length L. The string will break
if the tension in it exceeds a critical value, Tc.
What is the largest constant angular velocity the
ball can have without breaking the string?
Quiz
Suppose a particle of mass m is attracted to the origin
with a force proportional to the inverse square of the
distance to the origin, r:
 m
F  2
r
( is a const )
Calculate the work done by this force:
a) if the particle moves from A to B where A and B are
points on a circle, centered at the origin;
b) If the particle moves out along a radius vector from
B (rB from the origin) to C (rC from the origin).
A mass M is going around in a circle on a string
on a frictionless table and the string goes
through a hole where it is attached to a hanging
mass m. If the mass M is going around with
constant   0 , what must the distance from
the mass M to the hole be if the mass m is to
remain at rest?
M
m
Platform rotates with angular acceleration
(t)=t. A man starts a distance L from the
center and walks in along a straight line
painted on the platform towards the center. He
decreases his distance from the center as a
constant rate, vc. What force does the platform
exert on the man, as a function of his distance
from the center?
A plane is flying in an arc at the speed of v0.
At the top of arc the passengers experience a
sense of weightlessness. What is the radius of
the arc?
Conical pendulum
A race track designer wants to have the cars
able to maintain a speed vmax without skidding
on a circular track. If the track is flat with a
coefficient of friction  what does the radius
have to be?
A frictionless track contains a circular section of
radius R as shown. What is the minimum height
at which a block must be started in order for it
to go around the loop without falling off the
track?
H
R
Have a great day!
Hw: Chapter 13 problems and
exercises
Reading: Chapter 14