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Problem needs to solve: Show that the angle from the figure is given by 0 = cos¹1 (1 (Provide full solution of the problem). m²V0² 2gL(m+M)²

Problem needs to solve: Show that the angle from the figure is given by 0 = cos¹1 (1 (Provide full solution of the problem). m²V0² 2gL(m+M)²

Physics for Scientists and Engineers: Foundations and Connections
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter10: Systems Of Particles And Conservation Of Momentum
Section: Chapter Questions
Problem 4PQ: A mother pushes her son in a stroller at a constant speed of 1.52 m/s. The boy tosses a 56.7-g...
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Consider the ballistic pendulum setup: A bullet of mass m with speed vo hits a pendulum bob of mass M, suspended by a massless rope of length L. The bullet gets stuck inside, making the pendulum swing up to some height. The maximum height the pendulum can reach is solved below: L m M Solution: At the start, the bullet has a momentum muo. When they collide and the bullet gets inside, the speed of the combined masses can be obtained using conservation of linear momentum. muo (m+ M)v, where u is the speed of the combined masses. Therefore, we get Finally, we have h = V= m+ M At the instant the masses move, they initially have purely kinetic energy given by 1 m² 2 m+ M This kinetic energy becomes potential energy at the maximum height. We get 1 (m +1 ·(m + 1 m² 00² 2 (m+M)² g T= (m+ (m + M)v² m M)v². = VO- = 1 m² 2m+M 0 v². = (m + M)gh. Problem needs to solve: Show that the angle from the figure is given by 0 = cos-¹ (Provide full solution of the problem). m²V0² 2gL(m+M)2
Transcribed Image Text:Consider the ballistic pendulum setup: A bullet of mass m with speed vo hits a pendulum bob of mass M, suspended by a massless rope of length L. The bullet gets stuck inside, making the pendulum swing up to some height. The maximum height the pendulum can reach is solved below: L m M Solution: At the start, the bullet has a momentum muo. When they collide and the bullet gets inside, the speed of the combined masses can be obtained using conservation of linear momentum. muo (m+ M)v, where u is the speed of the combined masses. Therefore, we get Finally, we have h = V= m+ M At the instant the masses move, they initially have purely kinetic energy given by 1 m² 2 m+ M This kinetic energy becomes potential energy at the maximum height. We get 1 (m +1 ·(m + 1 m² 00² 2 (m+M)² g T= (m+ (m + M)v² m M)v². = VO- = 1 m² 2m+M 0 v². = (m + M)gh. Problem needs to solve: Show that the angle from the figure is given by 0 = cos-¹ (Provide full solution of the problem). m²V0² 2gL(m+M)2
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