Finding tension in string in vertical circle

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SUMMARY

The discussion centers on calculating the tension in a watch chain when swung in a vertical circle. Given a watch mass of 270 g, a chain length of 48 cm, and a speed of 2.3 m/s, the tension was initially calculated as 1.04 N. However, the calculation was incorrect due to misinterpretation of forces acting on the watch when it is closer to the top of the circle. The correct approach requires adjusting the net force equation to account for the gravitational force acting downward and the tension acting upward.

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  • Understanding of circular motion dynamics
  • Familiarity with Newton's second law (Fnet = ma)
  • Knowledge of trigonometric functions in physics
  • Basic principles of gravitational force (weight calculation)
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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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