Calculate Tension in a String: Ball at Top & Bottom

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In summary, the conversation discusses the calculation of tension in a string when a ball is at the top and bottom of a vertical circle based on its speed and mass. The equation F=ma is used, with the correct equation for the bottom of the path being FsubT - mg = mv^2/r. The conversation also mentions difficulties in finding the correct answer and receiving help from others.
  • #1
Hisui
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Homework Statement



A ball at the end of a string is revolved at a uniform rate in a vertical circle of radius 72cm. If its speed is 4m/s and its mass is 0.300kg, calculate the tentsion in the string when the ball is (a) at the top of its path and (b) at the bottom of its path.

Homework Equations



F=ma, and variations thereof to include the sum of all forces

The Attempt at a Solution



I got (a) by using mg+FsubT=m(v^2/r) and I came up with 6.66N-2.94N=3.72N, but for some reason I can't get (b). I'm doing this for practice for an exam, so I'm doing the problems that have the answers in the back so that I can check myself, and the answer for (b) is supposed to be 9.61N, but I can't figure out how to get there.

The equation that I'm using for (b) is mg-FsubT=m(v^2/r), because that looked right from my free body diagram (with x reference frame point down), but I keep ending up with 2.94N-6.66N=-3.72N ...

This is obviously not right... the answer is positive and 3x the magnitude on top of it, so... I don't know what I'm doing wrong. Any help is greatly appreciated.
 
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  • #2
"mg-FsubT=m(v^2/r)"

your signs/directions are wrong here.

If you take upwards positive... downwards negative...

FsubT - mg = mv^2/r

now solve for FsubT
 
  • #3
Excellent. Many thanks.
 

1. What is tension in a string?

Tension in a string is the force that is exerted on the string, either by an external force or by the weight of an object attached to the string.

2. How is tension calculated in a string?

Tension in a string can be calculated using the equation T = mg + ma, where T is the tension, m is the mass of the object attached to the string, g is the acceleration due to gravity, and a is the acceleration of the object.

3. What factors affect the tension in a string?

The tension in a string can be affected by the weight of the object attached to the string, the acceleration of the object, and the length and stiffness of the string.

4. How does the position of the object affect the tension in a string?

The position of the object can affect the tension in a string because the tension will be greater at the top of the string where the weight of the object is pulling down, and less at the bottom where the weight is pulling up.

5. Can tension in a string be negative?

No, tension in a string cannot be negative. It is always a positive value as it represents the force exerted on the string.

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