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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Chapter 13.2, Problem 13.69P

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Vector Mechanics for Engineers: Dynamics

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The normal reaction at point B .

Solution Summary: The author explains the normal reaction at point B and the expression for kinetic energy.

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The normal reaction at point B.

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