A rod of length L and mass M is fixed at one of its end and is free to rotate about that point.A pendulum of mass m(the bob) and length L also hangs from that position.Now the bob of pendulum is allowed to fall from height L (refer the pic) such that it strikes the lower most point of the rod.If the co-efficient of restitution is e.Find the maximum angle(α) upto which the rod will rotate on first collision.
262velocity of bob just before striking rod ,v = √2gL
after impact let vel. of rod(lowermost point) =v1
and vel. of bob =v2 (both in left direction)
now e =vel. of separationvel. of approach = v1-v2v .... (i)
from conservation of momentum ,
mv = Mv1 + mv2 ...(ii)
from i) and ii) v1 can be found
now vel. of center of mass of rod = v1/2
now lastly using conservation of energy for rod ,
increase in PE = Decrease in KE
MgL(1-cosθ)2 = 12M.(v12) 2
thus angle can be found.
79IF possible find θ after n collisions.
Aditya Bhutra too tiresome to write here. try it yourself. you know the procedure.