I have a vertical spring of spring constant k with a pan on thetop. I place a bo

Question

I have a vertical spring of spring constant k with a pan on thetop. I place a box of mass M on it and let it move to theequilibrium position a distance d below the unstretched position ofthe spring. I then push it down until the position of the panis 3d below the equilibrium position and release it fromrest. The spring will accelerate the box upward and the boxwill rise up off the pan. If all the energy stored in thespring was transferred to the box how high will it rise above theunstretched position? (Give the answer in terms ofd.)

I have a vertical spring of spring constant k with a pan on thetop. I place a box of mass M on it and let it move to theequilibrium position a distance d below the unstretched position ofthe spring. I then push it down until the position of the panis 3d below the equilibrium position and release it fromrest. The spring will accelerate the box upward and the boxwill rise up off the pan. If all the energy stored in thespring was transferred to the box how high will it rise above theunstretched position? (Give the answer in terms ofd.)

Explanation / Answer

I place a box of mass M on it and let it move to the equilibriumposition a distance d below the unstretched position of thespring. so Mg = kd I then push it down until the position of the pan is 3d below theequilibrium position so the spring is compressed by 3d + d = 4d the energy stored in the spring is k(4d)2/2 =8kd2 that was transferred to the gravitational potential energy Mgh so 8kd2 = Mgh = kdh h = 8d that is the height from the lowest position, or 8d - 4d = 4dfrom the unstretched position. answer: 4d

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