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susus · Dec 9, 2010, 07:05 AM

I have a Mass inside a tube
how can I Calculate the linear speed of the mass at that equilibrium location ?
here is it's picture
http://i49.tinypic.com/2cr845u.jpg
I tried to use , v = 2pi*f*r.. but I do not think it's right..

ebaines · Dec 9, 2010, 11:28 AM

I can't reallty tell from the picture, but I assume that the mass is trying to slide down the wall while the rotation of the tube causes it to move up the wall, right? You need to break both the force acting on the mass due to gravity and the force due to the centripedal acceleration into compnents - one component that is perpendicular to the tube wall (the normal force) and the other component that is parallel to the tube wall. The mass is in equilibrium when the forces parallel to the wall balance out - that's what determines the angle $\theta$ . The weight of the object is $F_w = mg$ , and the component of the weight that acts parallal to the wall is $F_w\sin\theta$ . The force due to centripedal acceleration is $F_c = m\omega^2 r$ , where $r = R\sin \theta$ , and the component of that force acting parallel to the wall is $F_c \cos \theta$ . So set these equal and see what you get for $\theta$ . Then the speed of that mass as the tube rotates is $v = r \omega$ , where again $r = R \sin \theta$ .