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dtavob

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## Homework Statement

An object is restricted to movement in 1-D. Its position is specified along the x-axis. The potential energy of the object as a function of its position is given by

**U(x)= a(x4 − 2b2x2)**, where a and b represent positive numbers. Determine the location(s) of any equilibrium point(s), and classify the equilibrium at each point as stable, unstable, or neutral. (Enter your answers from smallest to largest. Enter NONE in any unused answer blanks. Use any variable or symbol stated above as necessary.)

## Homework Equations

F = - dU/dx

## The Attempt at a Solution

What I did was find the second derivative of the given function, which is = -12axˆ2 + 4ab^2), then I tried using a=2 and b=3 and then use x=-1,0,1 to see if it's stable, unstable or neutral. But, the way the web-homework wants me to input the answers is where I'm lost.

I was able to get the correct answers for the classification of the 3 equilibrium points, but I don't know how to input the other part.

x =_________ ---stable

x =_________ ---unstable

x =_________ --- stable

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## Homework Statement

A uniform rigid pole of length L and mass M is to be supported from a vertical wall in a horizontal position, as shown in the figure. The pole is not attached directly to the wall, so the coefficient of static friction, μs, between the wall and the pole provides the only vertical force on one end of the pole. The other end of the pole is supported by a light rope that is attached to the wall at a point a distance D directly above the point where the pole contacts the wall. Determine the minimum value of μs, as a function of L and D, that will keep the pole horizontal and not allow its end to slide down the wall. (Use any variable or symbol stated above as necessary.)

## Homework Equations

FnetX = 0

FnetY = 0

TorqueNet = 0

Friction = μsFn

## The Attempt at a Solution

What I did is:

FnetX= 0

Fn-Tcos(x) = 0

FnetY = 0

μsFn+Tsin(x)-mg = 0

TorqueNet = 0

TorqueRod - TorqueTension = 0

L/2mgsin90 - LTsin(x) = 0

If what I did is right then the answer would be: μs = [mg-Tsin(x)]/Tcos(x)

but the problem is asking me to use L and D in my final answer, that's where I'm lost...

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Thanks in advanced and I'm sorry for such a long post =/.

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