- #1

smashueatu

- 18

- 4

- Homework Statement
- For the apparatus shown in the figure, find the equilibrium angle θ in terms of the two masses.

- Relevant Equations
- (1) ΔE = ΔU + ΔK = 0 (Conservation of energy)

(2) ΔE = 2My₁ + mgy₂ = 0

The solution is an application of the law of conservation of energy.

Start with equation (1). The masses are in equilibrium and are not accelerating. This implies that ΔK = 0, because the kinetic energy will not change without acceleration. Thus, we are left to find equation (2) in terms of θ.

Finally, we set up a geometry problem to find substitutions for the heights in equation (2).

This is where I fail. I can't find the heights in terms of the angle without introducing extra variables. I have tried constructing multiple triangles and applying some basic geometry and trigonometry, but to no success (pythagorean, law of sines, etc...).

Any hints or ideas would be greatly appreciated.