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# M3 edexcel Ex. 4D Q1 (circular motion) watch

1. A marble of mass m is moving in a horizontal circle round the inside surface of a smooth hemispherical bowl of radius r. The centre of the circle is at a distance r/2 below the centre of the bowl. Find the magnitude of the reaction between the marble and the bowl and the speed of the marble.

Any hints please? Having a massive mental block here..
2. I'll have a go.

First of all, I tried to work out the radius of the circle that the marble is moving around. Looking at the bowl horizontally (and pretending that the bowl is a sphere rather than a hemisphere) gives the following diagram (with x being the required radius).

Using trigonometry, we find

Therefore, .

This thus gives .

Now, considering the forces acting on the marble, and once again looking at the bowl from the side, gives

You know x and , so you can resolve vertically and horizontally to answer your question (or you could just look at the spoiler).

Spoiler:
Show

Resolving vertically gives:

Therefore,
Unparseable or potentially dangerous latex formula. Error 4: no dvi output from LaTeX. It is likely that your formula contains syntax errors or worse.
\large{\mbox{R} = 2mg

Resolving horizontally gives:

Thus
Unparseable or potentially dangerous latex formula. Error 4: no dvi output from LaTeX. It is likely that your formula contains syntax errors or worse.
\large{v^2 = \frac{2\sqrt3 mgx}{2m} = xg\sqrt 3 = \frac{3rg}{2}

And finally
Therefore, the marble's speed is .

Note that it's quite probable that I've made mistakes, but it should give you an idea as to how to do the question (I hope).

EDIT: correcting grammar.
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