Direction of vector 1 and magnitude 2v Direction of vector 2 and magnitude v Dir

Question

Direction of vector 1 and magnitude 2v Direction of vector 2 and magnitude v Direction of vector 3 and magnitude v Direction of vector 2 and magnitude v Direction of vector 1 and magnitude 1/2 v As shown in the figure, a bullet of mass m and speed v passes completely through a pendulum bob of mass M. The bullet emerges with a speed of v/2. the pendulum bob is suspended by a stiff rod of length L and negligible mass. If L = 1.0 m and M / m = 5.0, what is the minimum value of v such that the pendulum bob will barely swing through a complete vertical circle? Hint: Use conservation of linear momentum and conservation of mechanical energy. An object at rest suddenly explodes into three parts of equal mass Two of the parts move away at right angles to each other and with equal speeds v. What is the initial velocity of the third part? Direction of vector 1 and magnitude 2v Direction of vector 2 and magnitude v Direction of vector 3 and magnitude v Direction of vector 2 and magnitude v Direction of vector 1 and magnitude 1/2 v

Explanation / Answer

only 1 question per post so I am answering question #2 conservation of momentum m v + M 0 = m v/2 + M V v = v/2 + 5 V 5 V = v/2 V = v/10 now use conservation of energy have to just barely get to the top of the circle so Ei = Ef 1/2 M V^2 = M g h 1/2 (v/10)^2 = g * 2L v^2/200 =9.81*2*1 v=62.64 m/s

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