Uniform Circular Motion: Solving for String Tension

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Homework Help Overview

The problem involves uniform circular motion, specifically calculating the tension in a string at different points in the vertical circular path of a ball. The scenario includes a ball of mass 4 kg being swung in a circle with a radius of 1.5 m at a constant speed of 10 m/s.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the equations for tension at the bottom and top of the circular path, questioning the correctness of the original poster's approach. There is an exploration of the forces acting on the ball at these points, particularly how tension must counteract gravitational force while providing centripetal acceleration.

Discussion Status

Some participants have provided guidance on the reasoning behind the equations for tension, and there is an ongoing exploration of the calculations involved. The original poster has attempted to verify their calculations, but no consensus on the correctness of the final numerical answer has been reached.

Contextual Notes

Participants emphasize the importance of showing working steps in the calculations, and there is a mention of the need to consider both gravitational and centripetal forces when determining tension.

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Homework Statement



A ball of mass 4 kg on a string of length 1.5 m is being swung in a circle in the vertical plane at a constant speed of 10 m/s. Find the tension in the string at the bottom and top of the balls path

Homework Equations



ƩF = m(v^2/r)

The Attempt at a Solution


This is how I attempted to solve this problem, but my answer is not correct.
Is it correct that the tension in the string at the bottom is: T = m(v^2/r) + mg
And at the top: T = m(v^2/r) - mg
 
Last edited:
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Please show your working - not just some answers.

Consider:
T = m(v^2/r) + mg

This is saying that, at the bottom of the path, the tension has to overcome gravity and still have enough left over to give a centripetal force... the net force points upwards.
Does that make sense?
 
Yes; so the tension at the bottom would be, T = (4*(10)^2)/1.5 + 9.8*4 = 217 N. Is this correct?
 
I don't check arithmetic.
But you appear to have answered your own question.
 

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