# Rotational Motion with Elastic P. Energy?

1. Dec 14, 2011

### phyzz

1. The problem statement, all variables and given/known data
Consider a small box of mass m sitting on a wedge with an angle θ and fixed to a spring
with a spring constant k and a length in a non-stretched state L. The wedge
rotates with an angular velocity ω around the vertical axis. Find the equilibrium
position of the box and discuss the conditions when such equilibrium is possible and when it is impossible. The box can move only in the direction along the wedge slope and cannot move in the perpendicular direction (e.g. it is on a rail)

2. The attempt at a solution
First of all I don't know what it's asking exactly so I started with Fmax? I.e. when the mass is going up the plane.

I started with Conservation of Energy:
1/2mv^2 = 1/2kx^2 + mgh (general equation using r = L and h = Lsinθ)

v^2/r = ω (circular motion)

vmax^2/r = kx^2/mr + 2gh/r (I divided everything by r so it fits into the Fmax equation using mrω^2 instead of mv^2/r)

In the end I get Fmax = kx^2 + 2mgLsinθ

Could someone help me out please? I'm really lost :(

2. Dec 14, 2011

### JHamm

The problem with your energy equation is that the system has rotational kinetic energy due to the spinning. For the box to be in equilibrium it will be moving in a circle which means there is a force $m\omega^2r$ on the box parallel to the horizontal pointing away from the slope. This force comes from the normal force from the slope and the spring.