Circular Motion - Finding Tension

AI Thread Summary
To find the tension in the string of a ball revolving in a vertical circle, the net force equation Fnet=ma is applied. At the top of the circle, the tension plus the weight of the ball equals the centripetal force required for circular motion. The calculated centripetal acceleration is approximately 24.62 m/s², leading to a tension of about 4.44 N at the top. For the bottom of the path, a similar analysis with a free body diagram is recommended to determine the forces acting on the ball. Understanding these concepts is crucial for solving both parts of the problem effectively.
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Homework Statement


A ball on the end of a string is cleverly revolved at a uniform rate in a vertical circle of radius 65.0 cm, as shown in Fig. 5-33. Its speed is 4.00 m/s and its mass is 0.300 kg.
(a) Calculate the tension in the string when the ball is at the top of its path.
(b) Calculate the tension in the string when the ball is at the bottom of its path.

Homework Equations


Fnet=ma
v^2/r=a


The Attempt at a Solution


This is for my quiz review packet which is unfortunately due tomorrow, and I'm confused about how to solve this problem.
I'm thinking that since this problem involves tension I'm going to need the equation Fnet=ma.
To find A first I take the velocity 4m/s and put it to the power of 2, so its (16m/s)/radius= centripetal acceleration)
In this case 16/.65=a so 24.62m/s is the acceleration
Fnet at the top of the circle is mg+t (.300)(9.81)+t
2.94300+X=.300*24.62
2.94300+x=7.38600
4.44300=x

If this is right I know how to do the second part.
 
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To start, draw a free body diagram of both situations to see all the forces acting on the objects and how they're acting. Then come up with a Fnet statement, by looking at all the forces.
 
That is right.
 
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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