Homework Help: Tricky track problem (continued)

1. Oct 5, 2004

Ravnus9

Ok here is the track problem again except this time drawn out with some of my work.... this is using newtons second law..... i used microsoft word to draw the track and spring so its a little ruff but you get the idea... still could use some help no matter which way i do it i end up getting one more unknown than i have equations.... which is getting extremely old, please help, THANK YOU.
Nathan

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2. Oct 6, 2004

ehild

Nathan,

This problem is not easy at all, and I wonder how your teacher would solve it. Let us know what he said about the solution.

Energy is not conserved because of friction. The work of friction diminishes the mechanical energy. Friction is proportional to the normal force N, but the normal force depends on the speed of the collar, as the sum of the normal component of gravity and that of the spring force plus the normal force N from the track must be equal to the centripetal force, mv^2/R. The tangential acceleration of the collar is determined by the tangential components of gravity and spring force minus friction, which is proportional to N. You can plug in the expression for N from the previous equation and you get a second order nonlinear differential equation for the angle theta. This equation can be solved only numerically by a program. You find such program in Mathematica but there are others, or you can write yours, applying Newton's method, or the more sophisticated Runge-Kutta method.

ehild