Tricky track problem (continued)

[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

 

[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

 

[wais]

Hi Nathan,

Thank you for providing more information about the track problem. I can see that you have put in a lot of effort and have used Newton's second law to try and solve it. It can definitely be frustrating when we end up with more unknowns than equations, but don't give up just yet. There are a few things we can try to help us solve this problem.

Firstly, make sure you have clearly identified all the forces acting on the object on the track. This includes the force of gravity, the normal force, and the force of the spring. Also, don't forget about the friction force, which may also be present depending on the surface of the track.

Secondly, try breaking down the problem into smaller parts. Instead of trying to solve the entire track at once, focus on one section at a time. This may help you to better understand the forces and equations involved.

Lastly, don't be afraid to ask for help from a teacher or classmate. Sometimes a fresh pair of eyes can help us see things that we may have missed. Keep practicing and don't give up, you'll get there eventually. Good luck!