Question

Consider a mass ' m ' attached to a spring of length ' l ' performing vertical circle.
Find an expression for :

( 1 ) velocity at any point
( 2 ) tension at any point
( 3 ) minimum velocity at the lower - most point for a vertical circle

Answer 1

The tension on the string is equal to the centripetal force on the mass.

The tension on the string is equal to the centripetal force on the mass.Centripetal force on the string :

$centripetal \: force \: = \frac{m {v}^{2} }{r}$

radius is length of the string which is " l ".

radius is length of the string which is " l ".Substitute r in the above equation we get,

$centripetal \: force \: = \frac{m {v}^{2} }{l}$

From the above equation we can get the value of velocity at any point,

$v = \sqrt{ \frac{TL}{m} }$

At the lowest point the tension is balanced by the weight of the body.

At the lowest point the tension is balanced by the weight of the body.Weight of the body is mass × gravitational pull

At the lowest point the tension is balanced by the weight of the body.Weight of the body is mass × gravitational pullWeight = mg.

At the lowest point the tension is balanced by the weight of the body.Weight of the body is mass × gravitational pullWeight = mg.Therefore, the tension is " mg "

At the lowest point the tension is balanced by the weight of the body.Weight of the body is mass × gravitational pullWeight = mg.Therefore, the tension is " mg "Substituting the value of F in the above equation we gget

$</strong></p><p><strong>[tex]v \: = \sqrt{ \frac{mgL}{m} }$

Hope this helps you.

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