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Dynamics - Connected motion of sliders

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Please see the attached file.

The sliders A and B are connected by a light rigid bar of length .5m. and move with out friction in the horizontal slots shown. (both slots lie on the horizontal plane there is no weight force involved)

For the position where Xa = .4m the velocity of A ,Va = .9 m/s to the right.

Find the acceleration of each slider( A and B) and the force in the bar at the instant shown (Xa = .4m)

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The expert examines the connected motion of sliders. Step by step solution provided.

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Please refer attachment.

At any instant let the position of piston A be x and that of piston B be y.

Then, x2 + y2 = 0.52 ..............(1)
_________
At the given instant x=0.4m. Hence, y = √0.25 - 0.16 = 0.3 m

Differentiating (1) with respect to time we get :

2x dx/dt + 2y dy/dt = 0 ...

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