Creative Commons License Copyright © Michael Richmond. This work is licensed under a Creative Commons License.

Work done by the (changing) force of a spring

Joe finds a spring in an old junkyard. It looks pretty stiff. He attaches one end to a wall, leaving the right end free. When the spring is at rest, its length is L(rest) = 1.5 m.

Joe then pulls on the right end with a force of F = 400 N. The spring stretches, so that its new length is L(stretched) = 1.8 m.



  Q:  What is the force constant k of the spring?










The answer

Joe gets risky. He hangs the spring vertically from the ceiling, then climbs up on top of a bookcase, next to the spring. He grabs onto the bottom of the spring, and then steps off the bookcase.



  Q:  Just as his foot leaves the bookcase, what
           is Joe's kinetic energy?







Joe is an ordinary guy of mass m = 60 kg. Joe starts to fall downward, and the spring begins to stretch.



  Q:  After Joe has fallen D = 0.2 m, 
 
           how much work has gravity done on Joe?

           how much work has the spring done on Joe?

 
  Q:  At this moment, what is Joe's velocity?







Joe keeps falling, and the spring keeps stretching.



  Q:  At what distance D1 will the force of gravity 
           have the same size as the force of the spring?
 
  
  Q:  At this position, what will Joe's velocity be?









Joe keeps falling, and the spring keeps stretching.



  Q:  At what distance D2 will Joe's kinetic energy
           finally become zero?
 






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Creative Commons License Copyright © Michael Richmond. This work is licensed under a Creative Commons License.