A ball of mass m is attached to a string of length L. The ball is...

 

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A ball of mass m is attached to a string of length L. The ball is then swung in a circle of radius R such that the string traces out the surface of a cone. A. Sketch the physical situation. Write a table of knowns and unknowns. Label your sketch with known and unknown information. Establish an appropriate coordinate system. Identify any physical assumptions you will make to solve the problem. B. Draw a free body diagram for the ball and write the force balance equations using Newton's 2nd Law. C. Determine a symbolic expression for the force of tension Fr in the string and the angular velocity w of the ball. These should be expressed in terms of the given quantities L, m, R and the acceleration due to gravity, g. D. Perform either a unit analysis or dimensional analysis of your expressions for tension and angular velocity. E. Explain in words how you would expect the tension Fr in the string and the angular velocity @ to change if it was swung in the same fashion but on an exoplanet where the acceleration due to gravity is 1/4 the value here on Earth. Then perform a short symbolic calculation to back up your explanation. A ball of mass m is attached to a string of length L. The ball is then swung in a circle of radius R such that the string traces out the surface of a cone. A. Sketch the physical situation. Write a table of knowns and unknowns. Label your sketch with known and unknown information. Establish an appropriate coordinate system. Identify any physical assumptions you will make to solve the problem. B. Draw a free body diagram for the ball and write the force balance equations using Newton's 2nd Law. C. Determine a symbolic expression for the force of tension Fr in the string and the angular velocity w of the ball. These should be expressed in terms of the given quantities L, m, R and the acceleration due to gravity, g. D. Perform either a unit analysis or dimensional analysis of your expressions for tension and angular velocity. E. Explain in words how you would expect the tension Fr in the string and the angular velocity @ to change if it was swung in the same fashion but on an exoplanet where the acceleration due to gravity is 1/4 the value here on Earth. Then perform a short symbolic calculation to back up your explanation.

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Since the question describes a physical scenario without providing a visual representation Ill first describe the sketch and freebody diagram then proceed to provide the symbolic expressions and analy... View the full answer