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..
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M3 edexcel Ex. 4D Q1 (circular motion) watch
- Thread Starter
- 11-06-2006 23:24
- 12-06-2006 12:55
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
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).
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.