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To solve for the maximum extension of the spring, use the energy conservation equation for the system that relates its initial energy to its energy when the mass is at its lowest point. What are the constants of the equation and what are the variables?  Compare the height that the mass drops and the amount of stretch in the spring. Can you write one in terms of the other in order to simplify the equation? Compare the stretch of the spring when the mass is hanging in equilibrium and when the mass is at its lowest point after being dropped. When the natural length of the spring and the length of the mass have been accounted for, how much longer should the dropped stretch be than the hanging stretch?

To solve for the maximum extension of the spring, use the energy conservation equation for the system that relates its initial energy to its energy when the mass is at its lowest point. What are the constants of the equation and what are the variables?  Compare the height that the mass drops and the amount of stretch in the spring. Can you write one in terms of the other in order to simplify the equation? Compare the stretch of the spring when the mass is hanging in equilibrium and when the mass is at its lowest point after being dropped. When the natural length of the spring and the length of the mass have been accounted for, how much longer should the dropped stretch be than the hanging stretch?

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*PLEASE SOLVE #3, #4, and #5*

  1. Draw three stages of the motion of the mass on a spring: one with the mass held at the top at rest before it is dropped (spring un-stretched), one with the mass somewhere in the middle of the fall, and one with the mass at rest at the bottom of the fall. Label the relevant physical quantities on your pictures (height, speed, mass, and stretch of the spring) Label the kinds of energy at each stage of the motion of the mass.
  2. For the three pictures, write the energy conservation equation for the system that relates its initial energy to its energy at the point in its motion.
  3. To solve for the maximum extension of the spring, use the energy conservation equation for the system that relates its initial energy to its energy when the mass is at its lowest point. What are the constants of the equation and what are the variables? 
  4. Compare the height that the mass drops and the amount of stretch in the spring. Can you write one in terms of the other in order to simplify the equation?
  5. Compare the stretch of the spring when the mass is hanging in equilibrium and when the mass is at its lowest point after being dropped. When the natural length of the spring and the length of the mass have been accounted for, how much longer should the dropped stretch be than the hanging stretch?
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