A 9.40 kg mass suspended from a spring with spring constant, k= 975.0 N/m, exten

Question

A 9.40 kg mass suspended from a spring with spring constant, k= 975.0 N/m, extends it to a total length of 0.410 m. Find thetotal length of the spring when a 13.20 kg mass is suspended fromit. I understand that I have to use Hooke's law and simpleharmonic motion, but I'm still at a loss... A 9.40 kg mass suspended from a spring with spring constant, k= 975.0 N/m, extends it to a total length of 0.410 m. Find thetotal length of the spring when a 13.20 kg mass is suspended fromit. I understand that I have to use Hooke's law and simpleharmonic motion, but I'm still at a loss...

Explanation / Answer

Start with the equation for a stretched spring: F = k*x where x is the amount stretched. But it's hanging, so F=m*g then x = m * g / k, x = (9.40 kg)*(9.8 m/s2) / (975.0 N/m) x = 0.0945m Then the rest length, L is L = 0.410 m - 0.0945 m L = 0.3155m The amount stretched with the 13.2kg mass, y, is: F = m*g = k*y y = m*g/k y = (13.2kg)(9.8m/s2) / (975 N/m) y = 0.1327m So the total length with the new mass is: Total Length = y + L Total Length = 0.1327 + 0.3155 Total Length = 0.4482m

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