Question

Question:

A block is hung vertically from a spring of force constant 50N/m and slowly lowered to equilibrium, stretching the spring by 0.1m.

If instead of being lowered slowly to equilibrium, the block --still attached to the spring-- was released from rest and allowed to fall, which of the following would happen?

Answer:

A) It would descend 0.1m and remain at that position

B) It would descend 0.1m and reverse its direction of motion

C) It would descend 0.2m and remain at that position

D) It would descend 0.2m and then reverse its direction of motion

E) It would descend more than 0.2m and then reverse its direction of motion

I actually have to solution for this question. What I want to know is how slowly lowering to equilibrium and just releasing the block is different. What is the purpose of this question? Why does it matter if it was slowly lowered or not?

Answer 1

The answer to the first question is option D. This is due to the conservation between gravitational energy from the equilibrium point and the potential energy of the stretched spring.

Now the second question's answer has to do a lot with kinetic energy and inertia.

From Newton's first law we know that object in motion wants to stay in motion. So if we suddenly release the block gravity will accelerate it and the block will have significant kinetic energy when it reaches the equilibrium point.
At this moment, due to inertia, the block flies past this point and starts to loose kinetic energy because the spring is stretching and tries to pull the block back to equilibrium. The block eventually stops and starts to move back, gains kinetic energy again, flies past the equilibrium point again, goes to its initial position again, and everything replays again and again. This creates an oscillatory motion.

But when the block is being lowered slowly, it doesn't gain kinetic energy, so it doesn't fly past the equilibrium and stays there. The gravitational and the pull from the spring stays equal and block doesn't move.

The purpose of this question is to test your knowledge of conservation of energy and concept of inertia.

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You can better understand this if you do the experiment hands-on. Get a rubber band and something heavy (the rubber band should be able to support its weight though). Now do this experiment above. You'll get a better "feel" of the theory if you do that.