A uniform rod of mass M and length L hangs vertically and is free to rotate abou

Question

A uniform rod of mass M and length L hangs vertically and is free to rotate about

one end. A blob of putty with mass m=M/6 is moving horizontally with initial speed

v0. The putty strikes the end of the rod and sticks to it.

(a) Determine the initial angular velocity of the rod immediately after the putty hits.

(b) What fraction of the initial kinetic energy is lost on this inelastic collision?

(c) What is the minimum initial velocity v0 such that the rod will rotate 180 degrees,

so that it is vertically upward?

A uniform rod of mass M and length L hangs vertically and is free to rotate about one end. A blob of putty with mass m=M/6 is moving horizontally with initial speed v0. The putty strikes the end of the rod and sticks to it. Determine the initial angular velocity of the rod immediately after the putty hits. What fraction of the initial kinetic energy is lost on this inelastic collision? What is the minimum initial velocity v0 such that the rod will rotate 180 degrees, so that it is vertically upward?

Explanation / Answer

a.)applying conservation of angular momentum we have

M/6*v0*r=(M+M/6)*v*r

v=v0/7

so angular velocity just after the collision

w=v0*L/7

b.)kinetic energy lost

1/2*M/6*v0^2-(1/2*7*M/6*(v0/7)^2)

=M*v0^2/14

c.)this Kinetic energy(as calculated in the second case) is equal to the Potential energy of the System so change in potential energy of the system

M/6*g*2L+M*g*L=1/2*7*M/6*(v0/7)^2

v0=sqrt(112*mgL) ans

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