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Q. In the figure,the ball A is released fom rest,when the spring is at its natural(unstretched) length. For the block B of mass M to leave contact with the ground at some stage,find: the minimum mass of A.

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In the figure, a string passes over a pulley, on one side the string is connected to a spring that is has a block B of mass M attached to it. On the other side a ball A is suspended from the string.

Let the spring constant of the spring be k and the ball A is suspended at a height h from the ground. Also, assume the mass of the spring to be negligible.

As the ball moves lower it pulls the spring upwards with a force equal to Mb*g. By the time the ball reaches the ground an energy equal to Mb*g*h is stored in the spring. This energy is equal to (1/2)*k*x^2 where x is the length by which the spring is elongated. The elongation x is also equal to the height of the ball or h. When the ball reaches the bottom, the elongated spring compresses; if it is able to lift the block B upwards, Mb*g > M*g => Mb > M

This gives the minimum mass of the ball A required for the block A to be lifted off the ground as M.

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