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## Homework Statement

A rod of length l and mass M is suspended from a pivot, as shown The rod is struck midway alongs its length by a wad of putty of mass m moving horizontally at speed v. The putty sticks to the rod. Find an expression for the minimum speed v, that will result in the rod’s making a complete circle rather than swinging like a pendulum.

## Homework Equations

## The Attempt at a Solution

Attempt at a solution:

Use Conservation of Energy

Kinetic Energy of Putty = Energy of Putty and Rod at the top of swing

multiply everything by 2

##mv_i^2=[(\frac{l}{2})^2m+\frac{1}{3}Ml^2]w_t^2+2(m+M)gl\\\\##

where w_t is the angular velocity at the top and v_i is the velocity of the putty originally

at the top of the swing the minimum velocity is related to the centripetal acceleration being equal to g

therefore,

##g=w_t^2l\\\\w_t^2=\frac{g}{l}\\\\##

substitute into conservation of energy stuff and solve for v_i

##v_i=\sqrt {[(\frac{l}{2})^2+\frac{Ml^2}{3m}]\frac{g}{l}+\frac{2(m+M)gl}{m} } ##

Answer in the back of the book…

##v_i=\sqrt {\frac{8(m+M)gl}{m^2}(\frac{1}{4}m+\frac{1}{3}M) }##