Tangential movement in a waterslide

[Fibo112]

Yes. Can you write your equations in terms of that angle plus a perturbation, then make the small angle approximation?

I am still stuck...I don't know what equations you are referring to.

 

[haruspex]

I am still stuck...I don't know what equations you are referring to.

Re-derive your acceleration equation in post #1, but this time do not make any small angle approximations. Use the energy equation to substitute for v in that.

 

[Fibo112]

This is as far as I get...I would appreciate it if you could tell me your solution so I can see what I am missing.

 

[haruspex]

This is as far as I get...I would appreciate it if you could tell me your solution so I can see what I am missing.

Ok. Now use your energy equation to substitute for v².
When you have done that, write a as the sum of the equilibrium angle and a small angle perturbation.

Offline for the next four hours.

 

[Fibo112]

The solution to this problem is given as a''-ga/r+v^2/rR=0. Can someone please tell me how they would arrive at this solution so I can see which part I don't understand.

 

[Fibo112]

It is question 1d incase I am explaining something wrong and somebody understands german