# Mechanical point

# 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.

## 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.

### Hint

### 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.

### Hint

### 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.