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# Mechanics M2 - Circular Motion

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1. Struggling on this problem:

A particle of mass m, is attached to one end of a light, inextensible string of length l. The other end of the string is fixed at P. The particle moves in a horizontal circle of radius r at a constant speed v. (In the diagram, the particle is basically following the path of the circular base of a cone, and the point P is the tip of the cone.)

Show that the tension in the string, T, is given by .

What I did do was:

Let the angle between the vertical and string be a.
Equating vertical components:
Equating horizontal componets with centripetal force

As then

Then in order to eliminate the sine's and cosine's:

so from resolving vertical components .

Therefore

But rearranging this to find T doesn't seem to work out, am I heading along the right tracks? Cheers in advance
2. (Original post by marcus2001)
What I did do was:

Let the angle between the vertical and string be a.
Equating vertical components:
Can't see anything wrong with your working but you have over-complicated your approach. Surprisingly, the bit of your working quoted above is pretty much all you need as you can get an expression for cos(a) with a bit of Pythagoras and trigonometry and it works out quite quickly.

You went to a lot of trouble to eliminate the angle but this was in fact something that you knew plenty about in terms of r and l.

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