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RoyalFlush100

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## Homework Statement

A 3-kg block is at rest relative to a parabolic dish which rotates at a constant rate about a vertical axis. Knowing that the coefficient of static friction is 0.66 and that

*r*= 2 m, determine the maximum allowable velocity

*v*of the block.

Picture attached below

## Homework Equations

F = ma

## The Attempt at a Solution

I began by drawing a FBD on the mass:

W: Weight, pointing vertically downwards

N: Normal, pointing perpendicular to the surface

f: Friction, pointing 90 degrees clockwise from N.

From there I calculated the angle from the origin:

y = (2^2)/4 = 1

Θ = tan^-1(1/2), with the adjacent arm being 2, vertical arm being 1, and the hypotenuse being sqrt5

Then I determined that the net force should be horizontally pointed inwards, with the formula: F = mv^2/r

So Fy is 0, meaning:

(3)(9.81) = 0.66N[1/sqrt(5)] + N[2/sqrt(5)]

--> N = (29.43sqrt[5])/(2.66)

Now for Fx:

[3v^2]/2 = N[1/sqrt(5)] - 0.66N[2/sqrt(5)]

The problem is this resolves to be:

[3v^2]/2 = -3.54...

which has no solution.

So, what am I supposed to do from here?

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