Chapter 6

# Slide

Take 10 minutes to prepare this exercise.

Then, if you lack ideas to begin, look at the given clue and start searching for the solution.

A detailed solution is then proposed to you.

If you have more questions, feel free to ask them on the forum.

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. A child on a circular slide

## Question

By first using the second law of motion for moments of force, then the conservation of mechanical energy, find the equation of the motion of the child.

### Solution

The second law is : It follows : Mechanical energy of the child : It is conserved : Thus : These equations are the same.

## Question

• Find the velocity of the child as a function of .

• Calculate the maximum speed of the child. Comment on this value.

### Solution

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.

Previous
A few classical applications
Next
Phase portrait of an oscillator