Consider a wedge rod system in which rod of length L is moving vertically downwards without tilting with constant speed v. The situation at t = 0 is shown in the figure. The surface of the wedge is parabolic and has an equation y = x2. Find the speed of wedge at t = 0. (Assume that the contact between the rod and wedge is not lost).

Engineering

Physics

Constrained Motion

Question

Consider a wedge rod system in which rod of length L is moving vertically downwards without tilting with constant speed v. The situation at t = 0 is shown in the figure. The surface of the wedge is parabolic and has an equation y = x². Find the speed of wedge at t = 0. (Assume that the contact between the rod and wedge is not lost).

$\frac{v}{2 L}$

$\frac{v}{L}$

$\frac{2 v}{L}$

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$\frac{dy}{dt} = 2 x \frac{dx}{dt}$

$\Rightarrow \frac{dx}{dt} = \frac{v}{2 x}$

at t = 0

$v_{ω} = \frac{v}{2 L}$