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Assuming a bob attached to a string is given a horizontal velocity u when it is at the bottom, what would be the height at which the tension of the bob would be zero (i.e the bob leaves the circular path). I know that the cos component of weight should be equal to the centripetal force, but I cannot formulate an equation for it. Any suggestions?

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  • $\begingroup$ Do you mean "string"? If "spring" it will not be a circular path. $\endgroup$ – Ben51 Jan 7 '18 at 5:15
  • $\begingroup$ Yeah😅! I meant a string $\endgroup$ – Roshan Surana Jan 7 '18 at 7:10
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I'm assuming that you're looking for the radius needed to achieve velocity v:

$F=ma$

$F_G + F_T = m v^2 / r$

$mg = mv^2 / r$

$g= v^2/r$

$r = v^2/g$ blue is bob, green is string, red are forces

The radius needed is velocity (tangent to acceleration) squared divided by gravity acceleration

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