Rolling cylinder on surface with friction (initially slipping)

[vraeleragon]

Hi, I'm trying to solve this, but I keep getting both sides of the equation to be the same >.<
A solid cylinder is initially moving along a flat surface without rotating. Due to the action of friction, it eventually begins rolling without slipping. The coefficient of friction is 0.22, the radius of the cylinder is 0.5 m, its mass is 2.7 kg and its initial center of mass velocity is 1.5 m/s

Questions: a.) How long does it take to reach a rolling without slipping condition? b.) What is the total energy change of the system between the initial condition and the establishment of rolling without slipping? c.) Will it still roll without slip on an incline?

I tried using FΔt=mΔv and d=v$_{0}$t+1/2at$^{2}$so i got the distance for slipping d=(v$_{i}$$^{2}$-v$_{f}$$^{2}$)/(2μg)
And then I did 1/2mv$_{i}$$^{2}$ = fd + 1/2mv$_{f}$$^{2}$ + 1/2Iω$^{2}$ I kept getting the same answer no matter what formula or approach I use. I have no clue how to do this. Please help. Thank you :)

 

[tiny-tim]

hi vraeleragon!

I tried using FΔt=mΔv and

no, it starts at slipping without rolling, goes though slipping with rolling, and ends with rolling without slipping

use the work energy theorem …

work done = friction "dot" displacement ​

 

[ehild]

The force of friction decelerates translation of the CM and the torque of friction (with respect to the CM) accelerates rotation. Write up both equations and solve for the linear velocity v and angular velocity ω in terms of time. Find t when the condition of pure rolling applies (do you know it?).

ehild

 

[vraeleragon]

oh i forgot to say that i solved it. thank you.