# Homework Help: Potential Energy of System (Uniform Rod and String)

1. Mar 22, 2012

### FeDeX_LaTeX

1. The problem statement, all variables and given/known data
http://desmond.imageshack.us/Himg339/scaled.php?server=339&filename=53171696.jpg&res=medium [Broken]

2. Relevant equations
GPE = mgh, EPE = λx^2 / 2l

3. The attempt at a solution

I'm taking the horizontal line through A as the zero-level for potential energy. Clearly, the GPE of the rod is mgacosθ + constant. To find the elastic potential energy, I noted that:

$$EPE = \frac{0.5mgx^2}{4a}$$

I said that the extension x is given by the length of BC minus the natural length. To get BC, I used the cosine rule;

BC2 = 16a2 + 4a2 - 16a2cosθ

So BC = 2a√(5 - 4cosθ).

Then,

$$EPE = \frac{mg(2a \sqrt{5 - 4 \cos \theta} - 2a)^2}{8a}$$

Which, to me, simplifies to:

$$EPE = mga(3 - 2 \cos \theta - \sqrt{5 - 4 \cos \theta})$$

The total potential energy V can thus be expressed as:

$$V = -mga(\cos \theta - 3 + \sqrt{5 - 4 \cos \theta}) + \mathbb{constant}$$.

This is almost identical to what they've got, except without the 3. Where have I gone wrong?

Thanks.

Last edited by a moderator: May 5, 2017
2. Mar 22, 2012

### FeDeX_LaTeX

Sigh... just realised in the mark scheme they've counted the +3 as 'a constant' so negligible. Ugh. Sorry to whoever was reading this thread.