Find the speed of the intersection point O of | vedclass

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Question

(A) Let the two wires intersect at point $O$ with an angle $\alpha$ between them. Each wire moves perpendicular to its length with a speed $v$. Consid

Vedclass · Accepted Answer

$v \csc(\alpha /2)$

Vedclass · Answer

(A) Let the two wires intersect at point $O$ with an angle $\alpha$ between them. Each wire moves perpendicular to its length with a speed $v$. Consider the bisector of the angle $\alpha$. Due to symmetry,the intersection point $O$ must move along this bisector. Let the speed of the intersection point be $V$. Consider one wire. The velocity of the intersection point $V$ makes an angle $\alpha /2$ with the direction of the wire's velocity $v$. The component of the velocity of the intersection point $V$ along the direction of the wire's motion must be equal to the speed of the wire,$v$. Therefore,$V \sin(\alpha /2) = v$. Solving for $V$,we get $V = v / \sin(\alpha /2) = v \csc(\alpha /2)$.

Find the speed of the intersection point $O$ of the two wires if the wires start moving perpendicular to themselves with speed $v$ as shown in the figure.

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