- #1

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## Homework Statement

## Homework Equations

F = -dU/dx

## The Attempt at a Solution

[itex]U = \frac{1}{2}kx^2 + mgxsin\theta \\\\

F = -(kx + mgsin\theta) \\\\

F = -kx - mgsin\theta \\\\[/itex]

We want to set the force = 0 because that's when the block is in equilibrium with no forces acting on it.

[itex]0 = -kx - mgsin\theta \\\\

x = -\frac{mgsin\theta}{k} \\\\

x = -\frac{\frac{14.0}{g}gsin\theta}{k} \\\\

x = -\frac{14.0sin(40 deg)}{120} \\\\

x = -0.075[/itex]

So since 0.075 m is the equilibrium position, it is the distance from the top of the incline to the equilibrium position, but the solution says that 0.075 m is the displacement from the position 0.450 m to equilibrium. I didn't even include 0.450 m in the equation, how can I assume that x is the distance from 0.450 to 0.075? Why is it not some arbitrary position to 0.075?