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Q.7
A small bar resting on a smooth horizontal plane is attached by threads to a point P and by means of weightless pulley, to a weight B possessing the same mass as the bar itself. Besides, the bar is also attached to a point O by means of a light non-deformed spring of lenght l₀ = 50cm and the stiffness K = 5mg/l₀, where m is the mass of the bar. The thread PA having been burned, the bar starts moving. Find its velocity at the moment when it is breaking off the plane.
Ans : 1.7 ms^-1
See Fig. 6

Q.8
A horizontal plane supports a plank with a bar of mass m=1 kg placed on it and attached by a light elastic non-deformed cord of length l₀ = 40 cm to a point O. The coefficient of friction between the bar and the plank equals k=0.20.
The plank is slowly shifted to the right until the bar starts sliding over it. It occurs at the moment when the cord deviates from the vertical by an angle 30^o. Find the work that has been performed at that moment by the frictional force acting on the bar in the reference frame fixed to the plane.
Ans : W = 0.09 Joule
See Fig. 7

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