Question #175755

Find the velocity V, the period T, of a conical pendulum of mass M attached to a string of length L making angle teta with vertical


1
Expert's answer
2021-03-29T07:12:22-0400

Given,

Velocity of the pendulum =v

Period of oscillation =T

Mass of the conical pendulum = M

Length of the string = L

Angle with the vertical direction =(θ)=(\theta)

Let tension in the string be F,



Now, applying the force balance equation,

Fsinθ=mv2r...(i)F\sin\theta = \frac{mv^2}{r} ...(i)

Fcosθ=mg...(ii)F\cos\theta = mg...(ii)

From equation (i) and (ii)

FsinθFcosθ=v2rg\Rightarrow \frac{F\sin\theta}{F\cos\theta }=\frac{v^2}{rg}


tanθ=v2rg\Rightarrow \tan\theta=\frac{v^2}{rg}

v2=rgtanθ\Rightarrow v^2=rg\tan\theta


v=rgtanθ\Rightarrow v=\sqrt{rg\tan \theta}

Hence, the velocity of the conical pendulum will be rgtanθ\sqrt{rg\tan\theta} .


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