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Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova Lectures 30-32 Hw: Chapter 13 problems and exercises Reading: Chapter 14
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Polar coordinates
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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, T c. What is the largest constant angular velocity the ball can have without breaking the string?
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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: 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 (r B from the origin) to C (r C from the origin).
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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? M m
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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, v c. What force does the platform exert on the man, as a function of his distance from the center?
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A plane is flying in an arc at the speed of v 0. At the top of arc the passengers experience a sense of weightlessness. What is the radius of the arc?
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Conical pendulum
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A race track designer wants to have the cars able to maintain a speed v max without skidding on a circular track. If the track is flat with a coefficient of friction what does the radius have to be?
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H R 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?
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Have a great day! Hw: Chapter 13 problems and exercises Reading: Chapter 14
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