A mass of 0.4 kg hangs motionless from a vertical spring whose length is 0.95 m

Question

A mass of 0.4 kg hangs motionless from a vertical spring whose length is 0.95 m and whose unstretched length is 0.65 m. Next the mass is pulled down to where the spring has a length of 1.10 m and given an initial speed upwards of 1.4 m/s. What is the maximum length of the spring during the motion that follows?

Explanation / Answer

initally .4*9.8=k*.3 =>k=13.07 N/m conservation of energy we get .5*.4*1.4^2+.5*13.07*.45^2-.4*9.8*.45=.5*13.07*x^2-.4*9.8*x =>6.535x^2-3.92x=-4.866*10^-2 =>x=.58716m so maximum length of string is l max=.65+.58716 l max=1.23716 m

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