Answer to Question #175755 in Classical Mechanics for saddam hussain

Question

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

Answer 1

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 $=(\theta)$

Let tension in the string be F,

Now, applying the force balance equation,

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

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

From equation (i) and (ii)

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

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

$\Rightarrow v^2=rg\tan\theta$

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

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