physics 218: mechanics instructor: dr. tatiana erukhimova lectures 30-32 hw: chapter 13 problems and...

Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova

Lectures 30-32

Hw: Chapter 13 problems and exercisesReading: 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:

)(2

constaisr

mF

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 , what must the distance from the mass M to the hole be if the mass m is to remain at rest?

0

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?

HR

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?

Have a great day!

Hw: Chapter 13 problems and exercisesReading: Chapter 14