A 100 {\ m g} block slides back and forth on a frictionless surface between two

Question

A 100 { m g} block slides back and forth on a frictionless surface between two springs. The left-hand spring has 110 { m N/m} and its maximum compression is 17 { m cm}. The right-hand spring has 280 { m N/m}.
1)Find the maximum compression of the right-hand spring.
2)Find the speed of the block as it moves between the springs.

Explanation / Answer

potential energy in compressed spring = .5*k*x^2 for max. compression left spring P.E = .5*110*.17^2 = 1.5895 J for max. compresion right spring P.E = .5*280*x^2 conservation of energy ==> .5*280*x^2 = 1.5895 x = sqrt(.011353) = .1065 m max. compression of right spring = 10.65 cm max speed of block ==> .5*.100 * v^2 = 1.5895 ==> v = 5.638 m/s speed of block in between springs = 5.638 m/s

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