# Problem with Impure Rolling [closed]

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)
(here u=1/2)

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.

• Try to use math formatting for the equations. Enclose math expressions in dollar signs $...$ for inline math, and $$...$$ for paragraph math. See help/notation for more details. – ja72 May 10 '19 at 14:22
• Does the cylinder start from rest at the instant the plank is moving at 20 m/s? This is the implication, but it wasn't stated in the problem. – David White May 10 '19 at 15:51
• yes the cylinder starts from rest – Lelouche Lamperouge May 10 '19 at 15:54
• I'm refunding the bounty on this question because homework-like questions and check-my-work questions are generally considered off-topic here. We intend our questions to be potentially useful to a broader set of users than just the one asking, and prefer conceptual questions over those just asking for a specific computation. – ACuriousMind May 10 '19 at 16:16
• Hint: 1) Calculate the angular acceleration and find the time needed for the cylinder to match speed with the plank. 2) Find the distance the plank moves in this time. 3) Find the time needed to move the remaining distance to the end of the plank. Add the times from 1) and 2). If you use $g=10$ the numbers come out nicely. – ja72 May 10 '19 at 20:19