The block of mass m1 shown in figure (12−E2) is fastened to the spring and the block of mass m2 is placed against it. (a) Find the compression of the spring in the equilibrium position. (b) The blocks are pushed a further distance (2/k) (m1 + m2)g sin θ against the spring and released. Find the position where the two blocks separate. (c) What is the common speed of blocks at the time of separation?
Figure
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Explanation:
(a) In equilibrium condition, . Thus, the compression of the spring is .
(b) We know that . When the blocks are pushed further distance against the spring and released, they become separated at P=0. So,
Therefore, . This shows that the blocks will get separated when the springs attain their natural length.
(c) At the time of separation, the total compression is . Therefore, where v is the velocity of the blocks. Thus, on solving, we get the common speed of the blocks .
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