I have a spring, with a spring constant k=50 N/m, and a metalwasher of mass m=10

Question

I have a spring, with a spring constant k=50 N/m, and a metalwasher of mass m=100 grams. If I compress the spring 10 cmdown and use it to launch the washer into the air, how high willthe washer go? I thought I knew how to do this but I got it wrong so couldsomeone tell me the right way to do it. I have a spring, with a spring constant k=50 N/m, and a metalwasher of mass m=100 grams. If I compress the spring 10 cmdown and use it to launch the washer into the air, how high willthe washer go? I thought I knew how to do this but I got it wrong so couldsomeone tell me the right way to do it.

Explanation / Answer

Spring constant t k = 50 N / m

Mass m = 100 g = 0.1 kg

Compression x = 10 cm = 0.1 m

Maximum eleastic potential energy of the spring P = ( 1/ 2)kx^ 2

According to law of conservation of energy , kinetic energy atequilibrium position

        K = P

( 1/ 2) mv ^ 2 = ( 1/ 2) kx^ 2

                  v = x  [ k / m]

                    = 2.236 m / s

So, required height from equilibrium position H = v ^ 2/2g

                                                                              = ( 2.236) ^ 2 / 19.6

                                                                               =0.255 m

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