Hi, Please, need help, and step by step. Thank You A 263 - g block is dropped on

Question

Hi,
Please, need help, and step by step. Thank You A 263 - g block is dropped onto a vertical spring with force constant k = 2.52 N/cm. The block sticks to the spring, and the spring compresses 11.8 cm before coming momentarily to rest. While the spring is being com pressed, hoVv much work is does (a) by the force of gravity and (b) by the spring9 (c) What was the speed of the block just before it hit the spring? (d) If this initial speed of the block is doubled, what is the maximum compression of the snags? Ignore friction

Explanation / Answer

        Given that the mass ofblock is m = 0.263 kg        Spring constant is k = 2.52N/m        compressed length of springfrom relaxed position is x = 0.118 m ---------------------------------------------------------------------------      (a) Work done by gravity is Wg= m g x                                                         = ------------ J      (b) Work done by spring is Ws =(1/2)kx2          =---------- J    (c) Apply conservation of energy just beforeblock strike the spring and at compressed position    (1/2)m v2 = (1/2)kx2 - mgx       v2 =kx2 / m - 2gx       v = [ kx2 / m - 2gx ]1/2             =----------- m/s    (d) If the speed is doubled Apply conservation of energy just before blockstrike the spring and at compressed position    (1/2)m (2v)2 = (1/2)kx2 - mgx                     slove for x = ---------- m

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