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Q.45

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 258

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Short Answer

A block of mass slides down a frictionless track, then around the inside of a circular loop-the-loop of radius . From what minimum height must the block start to make it around without falling off? Give your answer as a multiple of .

The block must start at a minimum height h to make it around the loop without falling off is .

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Step by Step Solution

Step 1 : Energy :  

A quantitative property that can be transmitted from an object so that it can do work.

Step 2 : Explanation : 

A mass block slides down a frictionless track then looping around the inside of a circular loop of radius R.

Mass potential energy at height h is .Object KE moving with velocity v is . The centripetal force acting on mass moving with speed v around a circle of radius R = .

At the loop's highest point, the minimum velocity required such that the mass does not without fall off is,

The loop's energy at the bottom is KE which is,

Since, the energy is conserved, this at height h from which the mass falls down.

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