Consider the ballistic pendulum setup: A bullet of mass m with speed vo hits a pendulumbob 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:LmMSolution: 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 getFinally, we have h =V=m+ MAt the instant the masses move, they initially have purely kinetic energy given by1 m²2 m+ MThis kinetic energy becomes potential energy at the maximum height. We get1(m +1·(m +1 m² 00²2 (m+M)² gT= (m+(m + M)v²mM)v².=VO-=1 m²2m+M 0v².= (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).m²V0²2gL(m+M)2

Answered: Image /qna-images/answer/7705419f-5a0c-4739-9ef5-6c90db3920c0.jpg

Answered: Problem needs to solve: Show that the…

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

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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Proper Length

The theory of special relativity explains the connection between space and time to objects that move in a straight line at a constant speed. The objects move at the speed of light. When an object approaches light speed, its mass is endless and cannot move faster than light. The most crucial postulate of Einstein's special relativity is that the laws of nature do not change in each frame of reference.

Question

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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