How Do You Calculate Tension in Wires Holding a Revolving Ball?

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To calculate the tension in the wires holding a revolving ball, a free-body diagram must be drawn, identifying all forces acting on the ball, including gravity and tension. Newton's second law should be applied, separating forces into x and y components for accurate vector addition. The tension in the wires must counteract both the gravitational force and provide the necessary centripetal force for circular motion. If the lower wire is removed, the ball's speed must be increased to maintain the same circular path, as the remaining wire would need to provide the total centripetal force. Understanding the distinction between individual forces and the resultant centripetal force is crucial for solving the problem correctly.
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Homework Statement



Two wires are tied to the 150 g ball shown in the figure. The ball revolves in a horizontal circle at a constant speed of 5.0m/s. gravity is 10m/s2.

attachment.php?attachmentid=40023&d=1318707425.jpg


Draw a free-body diagram and specify any relevant dimensions or angles.

Write expressions applying Newton's second law on the ball.

Calculate the tension in each of the wires.

If we remove the lower wire, but want the ball to revolve in the same path, what must we do to the ball. (i.e. increase decrease speed). Explain

[REALLY NEED HELP ON THIS]
 
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Have you read the board rules? You are expected to attempt the problem yourself and SHOW what you have tried to do.
 
Oh, sorry. I'm in a rush and I actually didn't read it. I attempted to make a freebody diagram, but all I came up with was that the two tensions added up equaled to the force of gravity. I don't think that is right though. I feel like there is supposed to be some sort of centripital force involved, but I don't know where
 
ilovejesus said:
Oh, sorry. I'm in a rush and I actually didn't read it. I attempted to make a freebody diagram, but all I came up with was that the two tensions added up equaled to the force of gravity. I don't think that is right though.
It's not. All three forces, added up using vector addition, equal a. And, it's helpful to separate the forces into x and y components to do the vector addition.

I feel like there is supposed to be some sort of centripital force involved, but I don't know where
a is the centripetal force; it does not get included in the freebody diagram. The freebody diagram should only have forces with identifiable, physical causes -- for example, gravity, rope/string tension, forces applied by people or other objects, friction, normal force, etc. The centripetal force is simply the net result of those forces.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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