Tension Magnitude Calculation for 4.02 m/s Speed & 0.291 kg Mass

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To calculate the tension in the string when the ball is at the top of its circular path, one must consider the forces acting on the ball, including gravitational force and centripetal acceleration. The centripetal acceleration can be expressed as a = v^2/r, where v is the speed (4.02 m/s) and r is the radius (0.95 m). At the top of the path, both gravitational force and the tension in the string act downward, while the centripetal force required to keep the ball in circular motion must also be accounted for. The net force equation can be formulated using Newton's second law, which relates the sum of forces to mass and acceleration. Understanding these relationships is crucial for determining the magnitude of tension in the string.
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Hey everyone, I just need help with a problem that is giving me trouble. I have scoured my physics book and can't find the solution or even a starting point.
First we have a drawing of a circle with mg and ft1 with two arrows pointing down at the top of the circle and at the bottom of the circle it has mg and ft2 with the ft2 arrow pointing up and the mg arrow pointing down. The question is: If its speed is 4.02 m/s and its mass is 0.291 kg, calculate the magnitude of the tension in the string when the ball is at the top of its path. If anyone could help me by just telling me how to figure out the magnitude of tension I'd be forever greatful, thanks.
 
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The sum of forces must provide the centripetal acceleration of the ball..
Don't double post, BTW.
 
Sorry about the repeat. Hmm, I'm still having trouble wrapping my brain around your answer (I'm a rather science-stupid English major) so is there a general formula or something for determining magnitude of tension or what? Thanks.
 
Answer the following:
1) What is the expression for centripetal acceleration?
2) Formulate Newton's 2.law of motion at the moment when the ball is on top.
Which forces act on it, and what are their directions?
 
Ok I know that centripetal acceleration can be written as a=v^2/r (i believe) and Newton's 2nd law states that torque= moment of intertia * angular acceleration. That being said it also states the radius is 95.0 cm. So the centripetal acceleration would be around .17 So the forces acting on the ball attached to the string at the top would be gravity and Ft1, both downward. So would the force be the centripetal acceleration times the mass?
 
This is due tonight and I can't finish it.
 
Whatever has torques to do with Newton's 2.law?
(Torques appear in the moment-of momentum equations, which can be deduced from Newton's 2.law)
You are right about the expression for the centripetal accelerations.
Now write down which forces act upon the ball when it is at the top; the centripetal acceleration are then downwards, WHAT ARE THE DOWNWARDS FORCES ACTING ON THE BALL THEN?
 
The downward forces would be gravity and the centripetal acceleration would they not?
 

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