Explanation Given information: The weight of plank = 15 k g The weight of gymnast A = 55 k g The weight of gymnast B - = 70 k g Height at which gymnast A jumps = 2.5 m Concept used: Impulse momentum principle Moment of inertia = I = 1 / 12 m p L 2 Calculation: According to impulse momentum principle. Moment of inertia = I = 1 / 12 m p L 2 = 1 / 12 m p ( 2 L ) 2 = 1 / 3 m p L 2 The velocity of the person who jumps at E = v 1 = 2 g h According to kinematics, v c = L w a n d v D L w Taking moment at D, m E v 1 L + 0 = m E v E L + m c v c L + I w = m E l 2 w + m c L 2 w + 1 / 3 m p L 2 w m E v 1 = L 2 w ( m E + m c + 1 / 3 m p ) w = m E v 1 L / ( m E + m c + 1 / 3 m p ) L 2 w = m E v 1 / ( m E + m c + 1 / 3 m p ) L v c = L

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 17.3, Problem 17.122P

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Calculate the increase in height of gymnast B when gymnast A jumps from 2.5 m a height onto plank? Gymnast A weighs 55 kg and gymnast B weighs 70 kg. plank CDE has 15 kg weight rests on a small pivot.

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Chapter 17.3, Problem 17.121P

Chapter 17.3, Problem 17.123P

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Calculate the increase in height of gymnast B when gymnast A jumps from 2.5 m a height onto plank? Gymnast A weighs 55 k g and gymnast B weighs 70 k g . plank CDE has 15 k g weight rests on a small pivot.

Solution Summary: The author calculates the increase in height of gymnast B by using the Impulse Moment of Inertia principle.

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Calculate the increase in height of gymnast B when gymnast A jumps from 2.5 m a height onto plank? Gymnast A weighs 55 kg and gymnast B weighs 70 kg. plank CDE has 15 kg weight rests on a small pivot.

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