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I have a multiple choice non-uniform circular motion problem that I am trying to solve, but somehow I keep getting an answer that is not one of the possible answers. Here it is:

A 0.30kg mass attached to the end of a string swings in a vertical circle (R=1.6m) as shown [ In the diagram, x = theta ]. At an instant when x=50, the tension in the string is 8.0N, what is the magnitude of the resultant force on the mass at this instant?

a) 5.6N

b) 6.0N

c) 6.5N

d) 5.1N

e) 2.2N

http://img468.imageshack.us/img468/716/physdiag5xc.png [Broken]

So.. firstly, I established that the resultant force on the mass is the sum of the net radial force and the net tangential force. The net radial force is equal to [ Tension - Gravity in the Y direction ], and the net tangential force is equal to Gravity in the X direction. So...

Fnet = Sum of Radial Forces + Sum of Tangential Forces

Fnet = (T - mgcosx) + (mgsinx)

Using this formula, I get Fnet= 8.4N ?? What could I be doing wrong here?

Then I thought.. if I just take the tangential force, that is equal to mgsinx = 2.25..which is pretty close to E. Can this be what is meant by resultant force?

I hope someone can help me find my mistake in solving this problem, and point me toward the right solution. Thanks in advance!

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# Non-Uniform Circular Motion

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