Explanation Given: The mechanical energy of roller coaster is m g . Formula used: Write the expression for radial acceleration. a B = v B 2 R Here, a B is radial acceleration at bottom point, v B is radial velocity at bottom point and R is radius of loop. Write the expression for resultant force at bottom point. F n − m g = m a B Substitute v B 2 / R for a B and rearrange the above expression in terms of F n . F n = m g + m v B 2 R ........(1) Here, m is mass of ball, g is gravitational acceleration and F n is net force. Write the expression for radial acceleration. a T = v T 2 R Here, a T is radial acceleration at top point and v T is radial velocity at top point. Write the expression for resultant force at top point. m g = m a T Substitute v T 2 / R for a T in above expression and rearrange in terms of v T . v T 2 = g R Mechanical energy of ball is conserved at all points. Work done by external force is equal to the sum of change in gravitational potential energy and kinetic energy. Write the expression of work done by external force. W external = Δ U + Δ K ........(2) Here, Δ U is the change in potential energy, Δ K is the change in kinetic energy and W external is the work done by external force

Physics for Scientists and Engineers, Vol. 1

6th Edition

ISBN: 9781429201322

Author: Paul A. Tipler, Gene Mosca

Publisher: Macmillan Higher Education

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Chapter 7, Problem 49P

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The normal force at the bottom of the loop.

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Chapter 7, Problem 48P

Chapter 7, Problem 50P

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The normal force at the bottom of the loop.

Solution Summary: The author explains the formula used to write the expression for radial acceleration.

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The normal force at the bottom of the loop.

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