Answer to Question #216464 in Physics for Msk

Question #216464

A block with mass m is attached to a ceiling by a spring with spring constant k and relaxed length . Initially, the spring is compressed to a length of l / 2 . If the block is released, at what distance below the ceiling will the block be brought to rest (instantaneously, at the lowest point) by the spring?


1
Expert's answer
2021-07-13T10:42:33-0400

From the conservation of energy:


"0.5k(0.5l)^2+mgl=-mgx+0.5k(x)^2\\\\x^2-\\frac{2mg}{k}x-\\frac{2mg}{k}l-\\frac{l^2}{4}=0\\\\x=\\frac{mg}{k}+\\sqrt{\\frac{m^2g^2}{k^2}+\\frac{2mg}{k}l+\\frac{l^2}{4}}"


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