Tangential movement in a waterslide

Click For Summary
The discussion focuses on deriving the tangential equation of motion for a person on a waterslide with a circular curve. Key points include the need to account for both centripetal and tangential forces, as the motion is not purely circular due to the tangential component. Participants emphasize the importance of using energy conservation principles and avoiding small angle approximations unless necessary. The conversation highlights confusion over the correct application of forces and the need for clear derivations to arrive at the correct equations of motion. Ultimately, the solution involves substituting velocity in the acceleration equation and considering perturbations around an equilibrium angle.
  • #31
haruspex said:
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.
 
Physics news on Phys.org
  • #32
Fibo112 said:
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.
 
  • #33
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.
 

Attachments

  • 20170710_104237.jpg
    20170710_104237.jpg
    22.9 KB · Views: 408
  • #34
Fibo112 said:
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.
 
  • #35
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.
 

Attachments

  • 20170710_110712.jpg
    20170710_110712.jpg
    26.4 KB · Views: 408
  • #36
It is question 1d incase I am explaining something wrong and somebody understands german
 

Attachments

Similar threads

  • · Replies 6 ·
Replies
6
Views
2K
Replies
6
Views
4K
Replies
5
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
Replies
17
Views
2K
Replies
90
Views
10K
  • · Replies 11 ·
Replies
11
Views
2K
  • · Replies 18 ·
Replies
18
Views
2K
  • · Replies 11 ·
Replies
11
Views
2K