- #1
Epiclightning
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Homework Statement
A hemispherical bowl of mass m and radius R is placed on a rough horizontal surface. Initially the centre C of the bowl is vertically above the point of contact with the ground(see figure).
Now the bowl is released from rest. Find the normal force acting on the hemisphere initially if the coefficient of static friction is 1/2 of that required to prevent initial slipping of the bowl.
Homework Equations
a =R(w), w= angular acceleration
Centre of mass of hollow hemisphere = R/2 distance from centre
Max = nN (n = coeff. Of friction)
Mg - N = May
MgR/2 = 5/3MR^2 (w) ...Torque about lowermost pt
w = 3g/10R
The Attempt at a Solution
I already figured out the minimum coefficient of friction for no slipping to be 6/17. This matches with the solution. But I am unable to find the normal force corresponding to half of this value(3/17).
I have 2 equations relating horizontal and vertical accelerations of the CM to N and Mg (above) but this is not enough as I need another to eliminate variables.