Question

A bullet of mass m and speed v is fired at an at rest pendulum bob. The bullet goes through the bob, and exits with a speed of v/3. The pendulum bob is attached to a rigid pole of length L and negligible mass. What is the minimum value of v such that the pendulum bob will barely swing through a complete vertical circle?
I have no idea how to start this, have never been good at problem solving really.

Answer 1

Question #82155, Physics / Mechanics | Relativity

A bullet of mass $m$ and speed $v$ is fired at an at rest pendulum bob. The bullet goes through the bob, and exits with a speed of $v/3$. The pendulum bob is attached to a rigid pole of length $L$ and negligible mass. What is the minimum value of $v$ such that the pendulum bob will barely swing through a complete vertical circle?

Solution

Conservation of momentum gives

$$mv = MV + \frac{mv}{3}$$ $$V = \frac{2mv}{3M}$$

From the conservation of energy:

$$\frac{1}{2}MV^2 = Mg(2L)$$ $$\frac{1}{2}V^2 = g(2L)$$ $$V^2 = 4gL$$

Thus,

$$\left(\frac{2mv}{3M}\right)^2 = 4gL$$ $$v = \left(\frac{3M}{m}\right)\sqrt{gL}$$

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