The figure below shows three points in the operation of the ballistic pendulum. The projectile approaches the pendulum in part (a) of the figure. Part (b) of the figure shows the situation just after the projectile is captured in the pendulum. In part (c) of the figure, the pendulum arm has swung upward and come to rest at a height h above its initial position.Three points in the operation of a ballistic pendulum are shown in parts a, b, and c.A block of mass m2 is attached to the bottom of a rigid rod, which is suspended freely. The projectile (a sphere) has a mass of m1 and is approaching the block directly from the left with velocity vi.The sphere is superimposed on the block to show that the projectile has been captured in the pendulum. An arrow extends from the block and points to the right, and is labeled vf.The pendulum is angled to the right, with the sphere still superimposed on the block. The block is a vertical distance h above its starting height.(a)Prove that the ratio of the kinetic energy of the projectile–pendulum system immediately after the collision to the kinetic energy immediately before is m1/(m1 + m2). (Submit a file with a maximum size of 1 MB.)This answer has not been graded yet.(b)What is the ratio of the momentum of the system immediately after the collision to the momentum immediately before?(m1 + m2)/m1m12/(m12 + m22) m1/m21m1/(m1 + m2)(c)A student believes that such a large decrease in mechanical energy must be accompanied by at least a small decrease in momentum. How would you convince this student of the truth?

we will momentum conservation to solve this question P1 = P2

Answered: The figure below shows three points in…

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 67PQ

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The figure below shows three points in the operation of the ballistic pendulum. The projectile approaches the pendulum in part (a) of the figure. Part (b) of the figure shows the situation just after the projectile is captured in the pendulum. In part (c) of the figure, the pendulum arm has swung upward and come to rest at a height h above its initial position.

Three points in the operation of a ballistic pendulum are shown in parts a, b, and c.

A block of mass m₂ is attached to the bottom of a rigid rod, which is suspended freely. The projectile (a sphere) has a mass of m₁ and is approaching the block directly from the left with velocity v_i.
The sphere is superimposed on the block to show that the projectile has been captured in the pendulum. An arrow extends from the block and points to the right, and is labeled v_f.
The pendulum is angled to the right, with the sphere still superimposed on the block. The block is a vertical distance h above its starting height.

(a)

Prove that the ratio of the kinetic energy of the projectile–pendulum system immediately after the collision to the kinetic energy immediately before is

m₁/(m₁ + m₂)

. (Submit a file with a maximum size of 1 MB.)

This answer has not been graded yet.

(b)

What is the ratio of the momentum of the system immediately after the collision to the momentum immediately before?

(m₁ + m₂)/m₁

m₁²/(m₁² + m₂²)

m₁/m₂

m₁/(m₁ + m₂)

(c)

A student believes that such a large decrease in mechanical energy must be accompanied by at least a small decrease in momentum. How would you convince this student of the truth?

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