Finding tension in string in vertical circle

In summary, the conversation discusses finding the tension in a watch chain when it is swung in a vertical circle by a child. Using the equations Fnet = ma and a = v^2/r, the tension is calculated to be 1.04 N. However, this answer is incorrect because the watch is closer to the top of the circle than the bottom, requiring a different calculation.
  • #1
greenglasses
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Homework Statement


[/B]
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


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

This answer is incorrect. Can someone explain why?
 
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  • #2
Closer to the top than the bottom. Add or subtract?
 

1. How do you find tension in a string in a vertical circle?

The tension in a string in a vertical circle can be found by using the equation T = mv^2/r, where T is the tension, m is the mass of the object, v is the velocity, and r is the radius of the circle.

2. What factors affect the tension in a string in a vertical circle?

The tension in a string in a vertical circle is affected by the mass of the object, the velocity of the object, and the radius of the circle. As any of these factors increase, the tension in the string will also increase.

3. How does the tension in a string change as the object moves through the vertical circle?

The tension in a string in a vertical circle will change depending on the position of the object in the circle. At the top of the circle, the tension will be at its highest point, while at the bottom of the circle, the tension will be at its lowest point. As the object moves through the circle, the tension will vary continuously.

4. What happens to the tension if the object's mass or velocity changes?

If the mass or velocity of the object changes, the tension in the string will also change accordingly. An increase in mass or velocity will result in an increase in tension, while a decrease in these factors will result in a decrease in tension.

5. Why is it important to calculate the tension in a string in a vertical circle?

Calculating the tension in a string in a vertical circle is important because it helps us understand the forces acting on the object. It also allows us to ensure that the string is strong enough to support the object and prevents it from breaking or becoming too loose, which could be dangerous for the object and those around it.

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