Project ForgeThe rod AB, of length 1 m, is connected to two sliders at each end through pins. The sliders can slide along QP and QR, two rails from a common point Q making equal 60° angles with the line QR, such that triangle QAB is equilateral with side 1 m at the instant shown. If the velocity VA of the slider at A is 2 m/s along QP, the velocity of the midpoint of the rod at this instant is __________ m/s.
Explanation
Set Q at the origin, QR along the x-axis, QP at 60°. Let A=t(cos60°,sin60°), B=(b,0). The rigid-rod constraint |AB|=1 with the equilateral geometry (t=b=1 at this instant) gives, after differentiating the constraint, ḃ=-ṫ. Since |ṫ|=|VA|=2, Ȧ=2(0.5,0.866)=(1,1.732) and Ḃ=(-2,0). Midpoint velocity = (Ȧ+Ḃ)/2 = (-0.5, 0.866), magnitude = 1.0 m/s.
Source: GATE ME 2016 Set-2 (2016)
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