Explanation Given: Radius of arc A B is 27 m . Radius of arc C D is 72 m . Mass of car and occupants is 250 kg . Velocity at point A is 0 m/s . Angle of Arc from A to B is 40 ° . Concept used: Write the expression for the displacement of car from A to B . h = R ( 1 − cos θ ) ...... (1) Here, h is the displacement of car from A to B , R is the radius of A B and θ is the angular displacement of car from A to B . Write the expression for kinetic energy at point A . T A = 1 2 m v A 2 Here, T A is the kinetic energy at point A , m is the mass of car and occupants and v A is the velocity of car at point A . Write the expression for kinetic energy at point B . T B = 1 2 m v B 2 Here, T B is the kinetic energy at point B and v B is the velocity of car at point B . Write the expression for the potential energy at point A . V A = m g h A Here, V A is the potential energy at point A , g is the acceleration due to gravity and h A is the elevation of point A from ground. Write the expression for the potential energy at point B . V B = m g h B Here, V B is the potential energy at point B and h B is the elevation of point B from ground. Write the expression for conservation of energy for point A to point B . T A + V A = T B + V B Substitute 1 2 m v A 2 for T A , 1 2 m v B 2 for T B , m g h A for V A and m g h B for V B in above equation. 1 2 m v A 2 + m g h A = 1 2 m v B 2 + m g h B Simplify the above expression. 1 2 m ( v B 2 − v A 2 ) = m g ( h A − h B ) Substitute 0 for v A and h for ( h A − h B ) in above expression

Vector Mechanics for Engineers: Dynamics

11th Edition

ISBN: 9780077687342

Author: Ferdinand P. Beer, E. Russell Johnston Jr., Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 13.2, Problem 13.70P

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The normal reaction at point B.

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A section of track for a roller coaster consists of two circular arcs ABC and CD joined by a straight portion BC. The radius of AB is 27 m and the radius of CD is 72 m. The car and its occupants, of total mass 250 kg, reach point A with practically no velocity and then drop freely along the track. Determine the normal force exerted by the track on the car as the car reaches point B . Ignore air resistance and rolling resistance.

A section of track for a roller coaster consists of two circular arcs AB and CD joined by a straight portion BC. The radius of AB is 27 m and the radius of CD is 72 m. The car and its occupants, of total mass 263 kg, reach point A with practically no velocity and then drop freely along the track. Determine the maximum and minimum values of the normal force exerted by the track on the car as the car travels from A to D. Ignore air resistance and rolling resistance. 27 m 18 m r=72m The minimum normal force exerted by the track is The maximum normal force exerted by the track is [ 6955 N. 6955 N

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Vector Mechanics for Engineers: Dynamics

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