Concept Problem: Oscillation and friction

[cjavier]

So I feel as though I have the correct solution, but am not positive. My problem is as follows: A block of mass M is at rest with respect to a surface which oscillates horizontally with sinusoidal motion described by the equation x(t)=Asin(ωt). Find an expression for the minimum value of the coefficient of static friction between the block and surface so that the block does not slip as the surface oscillates. ALSO: If the block were to slip, where in the oscillation would this happen?

I stated that if the block were to slip, it would be when x''(t) is at a maximum. The expression for x''(t) is -ω²Asin(ωt) and so when ωt=^∏/₂, the acceleration is at it's max, because the sine is at 1.

And I set the kinetic force equal to this expression for acceleration times the mass of the block. Like so: Mgμ_k = -ω²A.

I finished with μ_k = ^-ω2A / _g
Let me know if you feel as though I am correct. Thanks!

 

[TSny]

Overall, that looks very good. But are you dealing with kinetic friction or static friction?

(In your force equation, I think you left out the mass on the right side. But, I believe that's just a typing error.)

 

[cjavier]

Overall, that looks very good. But are you dealing with kinetic friction or static friction?

(In your force equation, I think you left out the mass on the right side. But, I believe that's just a typing error.)

Static friction, and yes I did, thank you

 

[TSny]

The coefficient of friction should be a positive number. So, you should consider how you ended up with a negative value.