Tangential movement in a waterslide

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Homework Help Overview

The discussion revolves around the dynamics of a person navigating a curved waterslide, specifically analyzing the tangential equation of motion for the angle of inclination as they move along a circular segment. The problem involves concepts from mechanics, including centripetal force and the effects of gravitational force on motion in a curved path.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants explore the relationship between centripetal force and the normal force acting on the person in the slide. There are attempts to derive the tangential equation of motion and to linearize it using small angle approximations. Questions arise regarding the validity of equating forces and the implications of the normal force in relation to work done.

Discussion Status

The discussion is ongoing, with participants providing guidance and questioning each other's reasoning. Some participants express confusion about the derivation of equations and the application of energy conservation principles. There is a recognition of the need for additional relationships between variables, and various interpretations of the problem are being explored.

Contextual Notes

Participants note that the mechanical energy conservation may depend on the orientation of the normal force and its relationship to the velocity of the person in the slide. There is also a discussion about the applicability of small angle approximations, indicating that the angle may not be consistently small throughout the motion.

  • #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.
 
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  • #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.
 

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  • #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.
 

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  • #36
It is question 1d incase I am explaining something wrong and somebody understands german
 

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