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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.
- 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?
- What is the work done by the spring on the cart during this same interval?
- What is the total work done on the cart during this interval?
- What must the force of your hand on the cart be to keep it in equilibrium when the spring is fully compressed?
- What must the force of your hand on the cart be to keep it in equilibrium when the spring is fully stretched?
- 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.