Pendulum problem in KE chapter

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To determine the minimum speed v for the bullet that allows the pendulum bob to complete a vertical circle, two conservation laws must be applied: conservation of momentum and conservation of energy. The bullet, with mass m, passes through the pendulum bob of mass M and exits with half its initial speed. The momentum before and after the bullet's passage must be equal, while the energy considerations will ensure the pendulum bob has enough kinetic energy at the top of the swing to maintain motion. Solving these equations will yield the required minimum value of v. Understanding these principles is essential for solving the pendulum problem effectively.
esinn08
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Hi Everyone,

My question is as follows:

A bullet of mass m and speed v passes completely through a pendulum bob of mass M. The bullet emerges with a speed v/2. The pendulum bob is suspended by a stiff rod of length and negligible mass. What is the minimum value of v such that the pendulum bob will barely swing through a complete vertical circle? (Use M for M, m for m, l for , and g for gravity, as necessary.)

Any suggestions would be greatly appreciated! :smile: Thanks so much!

esinn08
 
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Why don't you give it a shot? Here's a hint: You'll need to use two conservation laws.
 
Doc Al said:
Why don't you give it a shot? Here's a hint: You'll need to use two conservation laws.

1) conservation of momentum
2) conservation of energy

Am I right?
 
You are correct.
 
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