I believe I have the first part worked out: U=mgh --> U=980 K+U=0 --> K= -980 -9

Question

I believe I have the first part worked out:
U=mgh --> U=980 K+U=0 --> K= -980
-980=.5(20)(v^2) --> v=9.9 m/s
But I have no idea where to go on the second part.

Explanation / Answer

Mass, m = 20 kg Height, h = 5 m Spring constant, k = 4000 N/m ---> From the law of conservation of energy, Potential energy at the highest point = Kinetic energy just before hitting the platform m g h = (1/2) m v^2 Hence, v = sqrt ( 2 g h ) = sqrt ( 2 * 9.8 * 5 ) = 9.9 m/s ---> Potential enegy of spring = Gravitational potential energy at the starting point (1/2) k x^2 = m g h 0.5 * 4000 x^2 = 20 * 9.8 * 5 2000 x^2 = 980 x^2 = 98 / 200 Hence, x = 0.7 m

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