A small 0.360-kg object moves on a frictionless horizontal table in a circular path of radius 3.00 m. The angular speed is 4.97 rad/s. The object is attached to a string of negligible mass that passes through a small hole in the table at the center of the circle. Someone under the table begins to pull the string downward to make the circle smaller. If the string will tolerate a tension of no more than 160 N, what is the radius of the smallest possible circle on which the object can move?

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A small 0.360-kg object moves on a frictionless horizontal table in a circular path of radius 3.00 m. The angular speed is 4.97 rad/s. The object is attached to a string of negligible mass that passes through a small hole in the table at the center of the circle. Someone under the table begins to pull the string downward to make the circle smaller. If the string will tolerate a tension of no more than 160 N, what is the radius of the smallest possible circle on which the object can move?
Transcribed Image Text:A small 0.360-kg object moves on a frictionless horizontal table in a circular path of radius 3.00 m. The angular speed is 4.97 rad/s. The object is attached to a string of negligible mass that passes through a small hole in the table at the center of the circle. Someone under the table begins to pull the string downward to make the circle smaller. If the string will tolerate a tension of no more than 160 N, what is the radius of the smallest possible circle on which the object can move?
Expert Solution
Step 1: Given information


Mass of object is  m= 0.360 kg

Initial radius of circular path is ri= 3.00 m

Initial angular speed is w= 4.97 rad / s

Maximum tension in string is T = 160 N

Note:

Explanation:

The radius of the smallest possible circle on which the object can move 

r subscript f equals open parentheses fraction numerator m open parentheses omega subscript i close parentheses squared r subscript i to the power of 4 over denominator T end fraction close parentheses to the power of 1 third end exponent

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