Explanation Concept: We can use the principle of conservation of momentum, initial and final Kinetic Energy of collision to find the final speed of spring gun and fraction of initial K.E. stored in the spring. 1) Formula: i) P i = P f ii) P = m v iii) K = 1 2 m v 2 2) Given: i) Mass of the ball, m b = 60 g = 0.06 k g ii) Initial speed of ball, v i b = 22 m / s iii) Mass of the spring gun, m s = 240 g = 0.24 k g iv) Initial speed of spring gun, v i s = 0 m / s 3) Calculations: a) To find final speed of spring gun applying the principle of conservation of momentum Total momentum P i → before collision = Total momentum after collision P f → For the given situation Total initial momentum = Initial momentum of ball + Initial momentum of spring gun. P i → = P i b → + P i s → As initially spring gun is at rest, P i s → = 0 ∴ P i → = P i b → = m b v i b … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … ( 1 ) Total final momentum = final momentum of ball + final momentum of spring gun As after collision, the ball sticks in the barrel, final speed of both ball and the spring gun will be the same. P f → = m b v f b + m s v f s v f b = v f s = v f P f → = ( m b + m s ) v f … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … ( 2 ) Equating equation (1) and (2) m b v i b = ( m b + m s ) v f v f = m b v i b ( m b + m s ) v f = 0

11th Edition

ISBN: 9781119459170

Author: Halliday

Publisher: WILEY

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Chapter 9, Problem 57P

To determine

To find

a) Final speed of spring gun vf

b) Fraction of initial K.E. of the ball stored in the spring.

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Chapter 9, Problem 56P

Chapter 9, Problem 58P

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To find a) Final speed of spring gun v f b) Fraction of initial K.E. of the ball stored in the spring.

Solution Summary: The author explains the principle of conservation of momentum, initial and final Kinetic Energy of collision to find the final speed of spring gun and tion of initial K.E.

Concept explainers

To find

a) Final speed of spring gun vf

b) Fraction of initial K.E. of the ball stored in the spring.

Want to see the full answer?

Chapter 9 Solutions

To find a) Final speed of spring gun v f b) Fraction of initial K.E. of the ball stored in the spring.

Solution Summary: The author explains the principle of conservation of momentum, initial and final Kinetic Energy of collision to find the final speed of spring gun and tion of initial K.E.

Concept explainers

To find a) Final speed of spring gun vf b) Fraction of initial K.E. of the ball stored in the spring.

Want to see the full answer?

Chapter 9 Solutions

To find

a) Final speed of spring gun vf

b) Fraction of initial K.E. of the ball stored in the spring.