Dynamics Problem

  • #1
A car moves around an ellipse with the equation
[tex]\frac{x^2}{60^2} + \frac{y^2}{40^2} = 1 [/tex]
-60<x<60
-40<y<40

The car keeps a constant speed of 60 km/h.

I have to find the minimum acceleration experienced by the passengers of the car.

---------

I am nearly sure that my solution contains the right process. However, they may be an error in calculation throughout. If anyone could check my answers, I would strongly appreciate it.

There is no tangential acceleration. Therefore, acceleration = normal acceleration. Normal acceleration = [tex]\frac{v^2}{p} [/tex]
Where:
[tex]p = \frac{(1+ (dy/dx)^2)^\frac{3}{2}}{|d^2y/dx^2|} [/tex]

After manipulation, I end up with a function for a:

[tex]a = 2400*(v^2)*(\frac{180^2-9x^2}{(180^2-5x^2)(60^2-x^2)})^\frac{3}{2} [/tex]

Afterwards, I diffentiated this 'a' function and found its roots. x=0, x=42.43, and x=60. Then, i calculated the accelerations as needed.

Please tell me where I have gone astray!
 

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