Question

Prove that for a conical pendulum tan theta= v squre/ rg

Answer 1

Answer:

 

When viewed from above, the path taken by a conical pendulum's bob is circular.   

 



 

Freebody diagrams can help us understand the forces acting on the bob.

 

          

 

Vertically, the pendulum bob is in dynamic equilibrium,

 

T cos(θ) = mg.

 

However, the horizontal component of the tension, T sin(θ), supplies an unbalanced force towards the center of the circle. This is the source of the centripetal force that allows the bob to follow its circular trajectory.

 

T sin(θ) = mv2/r

 

Solving these equations simultaneously by dividing T sin(θ) by T cos(θ) yields,

 

y: T sin(θ) = mv2/r

x: T cos(θ) = mg

 

tan(θ) = v2/rg

 

This result is true for all horizontal conical pendulums for which the angle, θ, is measured from the pendulum's position of vertical equilibrium.

Answer 2

Explanation:

So read this then u will get derivation of tan theta = vsquare/ rg

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