What is the Resultant Force on a Mass in Non-Uniform Circular Motion?

AI Thread Summary
The discussion revolves around calculating the resultant force on a mass in non-uniform circular motion, specifically a 0.30kg mass swinging in a vertical circle. The user initially struggles with the correct formula, mistakenly combining radial and tangential forces without proper separation. After clarification, they realize the need to use Pythagoras to combine the perpendicular and parallel forces, leading to a resultant force calculation of 6.11N for the perpendicular component and 2.25N for the parallel component. This correction helps them understand the proper approach to solving the problem. The conversation highlights the importance of correctly separating and combining forces in physics problems.
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Hi,
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

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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I think we'd need a diagram..
 
Diagram included now.
 
Usually once you separate the Forces into components parallel to
and perpendicular to the motion, KEEP THEM SEPARATE!

HERE, you're asked to combine them, using Pythagoras.

I get F perp = 6.11 N , and F parallel = 2.25 N
 
Ahhhhh... That clears it all up! Thanks a lot :).
 
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