Can someone explain what happens in the below situation
Looking at it from the planks frame of reference:
The cylinder Velocity= 20(-i)
Net friction force on cylinder f=2umg(i)
Therefore acceleration of centre of mass of cylinder a= 2ug(i)
Torque produced by friction: fxr=Ixalpha
(alpha =angular acc.)
Therefore alpha= (4ug)/r
But for rolling wihtout slipping: alpha should be a/r, which is not the case here
So considering that the cylinder will slip and using standard eq. of motion s=vt+1/at^2 and putting in the values i get a quadratic eq in time whose discriminant is negative.
What went wrong? what is the right approach?
A solid cylinder is kept on one edge of a plank of same mass and length 25 m placed on a smooth surface as shown i the figure. The coefficient of friction between the cylinder and the plank is 0.5. The plank is given a velocity of 20 m/s towards right. Find the time (in sec) after which plank and cylinder will separate.