Finding tension in string in vertical circle

AI Thread Summary
To find the tension in the watch chain when swung in a vertical circle, the net force equation is applied, incorporating gravitational force and centripetal acceleration. The attempt at a solution calculated the tension as 1.04 N but was deemed incorrect. The confusion arises from the positioning of the watch in the circle; when closer to the top, the gravitational force should be subtracted from the centripetal force rather than added. Properly accounting for the forces acting on the watch will yield the correct tension value. Understanding the dynamics of circular motion is crucial for solving this problem accurately.
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Homework Statement


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Your niece finds her father's watch. The light watch chain has a length of 48 cm, and the mass of the watch is 270 g. Your niece swings the watch in a vertical circle, maintaining the speed of the watch at 2.3 m/s. Find the tension in the chain when it makes an angle of 43° with respect to the vertical. (Assume the watch is closer to the top of the circle than the bottom. Also assume the radius of the circle is 48 cm.)

Homework Equations



Fnet = ma
a = v^2/r

The Attempt at a Solution


Fnet = ma = T + Wcos(43)
0.270(2.3^2 /0.48) = T + 0.270*9.8*cos(43)
T = 1.04 N

This answer is incorrect. Can someone explain why?
 
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Closer to the top than the bottom. Add or subtract?
 

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