## Essential University Physics: Volume 1 (3rd Edition)

Published by Pearson

# Chapter 12 - Exercises and Problems - Page 215: 22

#### Answer

a) 47 meters b) Unstable

#### Work Step by Step

a) We know that at this point, the value of the force, which equals $\frac{dU}{dx}$, must be 0. Thus, we find: $U=mg(.94x-.01x^2) \\ \frac{dU}{dx}=mg(.94-.02x) \\ 0 = mg(.94-.02x)\\x =\fbox{47 meters}$ b) We take the second derivative to find: $\frac{d^2U}{dx^2}=-.02$ Since this is less than 0, the equilibrium is unstable.

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