Block On Conical Surface

[danago]

http://img357.imageshack.us/img357/6476/80028206ag6.gif [Broken]

This question had me a little confused. I started by drawing a free body diagram of the block:

http://img246.imageshack.us/img246/9121/59804825wo9.gif [Broken]

Where W is the weight, N is the normal force and F is the friction force.

Because the cone is spinning, does that mean there will also be a frictional force in the direction extending out/into the page?

Since the block will effectively be moving in a circular path, its net acceleration will be given by:

$$\overrightarrow {\bf{a}} = r\alpha \underline {\widehat{\bf{t}}} + \omega ^2 r\widehat{\underline {\bf{n}} }$$

The question states that the angular acceleration increases very slowly? Can i approximate this to be zero?

Thanks in advance for any help.
Dan.

 

[Gib Z]

Yes, the frictional force will apply along the surface on the cone. The question asks you the maximum angular velocity with which the cone can be spinning so that the block does not slip. The angular velocity is said to very slowly increase just so that we may assume it is continuous, and can take every angular velocity before the critical velocity at which the block slips. You can not approximate it with zero because then the angular velocity doesn't increase at all, which is critical to the question. Sadly, I know enough to tell you what's wrong, but not enough to tell you how to proceed =[ .

 

[kamerling]

The question states that the angular acceleration increases very slowly? Can i approximate this to be zero?

You'll have to, because they don't tell you what it is.