A uniform rigid rod of length 2b and mass M lies flat and at rest on a frictionl

Question

A uniform rigid rod of length 2b and mass M lies flat and at rest on a frictionless surface. A hockey puck of mass m moving with speed v0 collides with it at it end. The collision is elastic.

a) In the special case where the puck is at rest after the collision,

find expressions for the center of mass speed of the rod and its

angular speed after the collision. Answer in terms of

m, M, v0, and/or b.

* VcM

* ? = ___________________________

b) Show that for the puck to be at rest after the collision, the rod must have mass

Bonus points: What point on the rod is at rest with respect to the surface immediately after the collision?

Explanation / Answer

let final rod velocity be V ...

initial total horizontal momentum=mVo

final horizontal momentum=MV

momentum conservation=MV=mVo........(1)

conserving angular momentum(AM) as there is no external torque so

initial AM= mVoL

final AM=ML^2/12 X w where w=V/L is the angular velocity

final AM=MVL/12

so mVoL=MVL/12........(2)

from 1 and 2 we get the required answers and relations among m,M

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