Centripital Motion: Find Tension & Speed of Bead

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The discussion focuses on calculating the tension in a string and the speed of a bead sliding along it, given a specific setup involving a vertical pole and a rotating string. The bead's mass is 100g, and the string's length is 80cm, with points A and B attached to a pole 40cm apart. The centripetal force acting on the bead is equated to the tension in the string, while the radius at point B is expressed as a function of the angle. The vertical forces must balance the gravitational force acting on the bead. Participants suggest applying Newton's second law to the horizontal components to further analyze the problem.
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1. A 100g bead is free to slide along a 80cm piece of string ABC. Points A and B of the string are attached to a vertical pole 40 cm apart. When the pole is rotated AB becomes horizontal.

I have attached a diagram of the question.

Find the tension in the string?
Find the speed of the ball at point B?

Relevant Equations
F = mv^2/r
a = v^2/r
F = ma

Attempt:
I know that the centripital force acting on the object must be equal to the Tension acting in the horizontal direction. Also the radius of the string when the bead is at point B is a function of the angle. I also believe that the vertical force acting on the string must be equal to the downward force of gravity. Therefore so far I have:

1. radius = 40/tan0
2. a = v^2/(40/tan0) (this is when subbing in for r the above equation)
3. Ty = mg = 0.98

I am not sure where to go from here, or even if I am starting off right. Any help would be appreciated.

Thanks
 

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chopramon said:
1. A 100g bead is free to slide along a 80cm piece of string ABC. Points A and B of the string are attached to a vertical pole 40 cm apart. When the pole is rotated AB becomes horizontal.

I have attached a diagram of the question. Does anybody know how to put the picture of the question directly on this post?

Find the tension in the string?
Find the speed of the ball at point B?

Relevant Equations
F = mv^2/r
a = v^2/r
F = ma

Attempt:
I know that the centripital force acting on the object must be equal to the Tension acting in the horizontal direction. Also the radius of the string when the bead is at point B is a function of the angle. I also believe that the vertical force acting on the string must be equal to the downward force of gravity. Therefore so far I have:

1. radius = 40/tan0
2. a = v^2/(40/tan0) (this is when subbing in for r the above equation)
3. Ty = mg = 0.98

I am not sure where to go from here, or even if I am starting off right. Any help would be appreciated.

Thanks
 
You have the info needed to find the sides and angles of the right triangle.

Apply Newton's 2nd law to the horizontal components.
 
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