Question

A block of mass mb and a disk of mass md and radius r are placed on a symmetric triangular slope connected with a massless string over a massless pulley. The string is connected to a center axle of the disk so that the disk is free to rotate. The moment of inertia of the disk about its axle is I=1/2*md*r^2. The coefficient of static friction between the slope and the block/disk is 0.05 and the coefficient of kinetic friction between the slope and the block/disk is 0.1. The angle theta is 30 degrees.

Find the maximum ratio mb/md such that the disk still rolls without slipping up the hill.

Answer 1

Have you written any equations yet?

Answer 2

No, I have no idea where to start. Rotational motion confuses me so much haha

Answer 3

Well, start with the equations relative to the block, then.

Answer 4

I would like to see this with the langranian, what have you tried?

Answer 5

Okay so a FBD for the block would include tension pointed up the ramp, friction pointed down the ramp, Fg straight down, and Fn perpendicular to the block.

Answer 6

iambatman, what is langranian?

Answer 7

Careful, since the problem requires the block to move down the ramp, friction must act up the ramp.
Now can you write down Newton's second law with these forces you've just mentioned?

Answer 8

Lagrangian is a sort of extended work-energy method, but you have probably not studied it yet.

Answer 9

Oh okay. Yeah, I have not studied that yet haha.
But for this problem:
\[\sum Fx = Ff + Ft = m*a\] \[\sum Fy = Fn - Fg = 0\] Yes?

Answer 10

That's taking the x-axis to be parallel to the incline and y-axis to be perpendicular to that along the Normal force. Which actually would then make Fg into Fgsin(theta) I think.