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A child, supposed to be a material point G of mass , slides on a circular slide of radius from the position where its velocity is zero until the position where he leaves the slide.
Forces of friction are neglected.
The second law is :
It follows :
Mechanical energy of the child :
It is conserved :
These equations are the same.
Find the velocity of the child as a function of .
Calculate the maximum speed of the child. Comment on this value.
By integrating the motion :
We deduce :
We can also multiply by and integrate the equation :
This is the same expression as .
This velocity is quite high : luckily, frictions help to reduce this speed and allow the child not to hurt himself.