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Problem 6.13: A compressed spring is stretched

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A cart sits on a track. A compressible spring is connected to the cart and to a barrier at the end of the track. At t = 0 s, the spring is compressed 0.5 m from its unstretched position, and you have to push on the cart to keep it in equilibrium. Then, by applying a varying force, you allow the spring to relax and then cause it to stretch while maintaining equilibrium during the entire process. The spring constant is 50 N/m. The frictional force of the track on the cart is negligible. Treat the cart as a point particle (position is given in meters and time is given in seconds). Restart.

  1. What is the work done by the force of your hand on the cart during the interval between t = 0 and when the spring is fully stretched?
  2. What is the work done by the spring on the cart during this same interval?
  3. What is the total work done on the cart during this interval?
  4. What must the force of your hand on the cart be to keep it in equilibrium when the spring is fully compressed?
  5. What must the force of your hand on the cart be to keep it in equilibrium when the spring is fully stretched?
  6. Why is the work done by your hand on the cart not equal to the product of this force component [calculated in part (e)] and the displacement of the cart?

Illustration authored by Aaron Titus and placed in the public domain.

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