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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

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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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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