Question

A spring of negligble mass has force constant k = 1600 N/m. a) How far must the spring be compressed for 3.2 J of potential energy to be stored in it? b) You place the spring vetically with one end on the floor. You then drop a 1.2 kg book onto it from a height of 0.80 m above the top of the spring. Find the maximum distance the spring will be compressed.

I looked at the textbook solution for this question already here on Chegg, but I'm confused how they arrived at the total energy of the system for part (b) of this question. (If it helps, this is Chapter 7, problem 19E for University Physics 13th Edition- you might also see a question on step 5 by anonymous- which is me! haha) Chegg is saying that the total energy in the system is 12.61 J, but why is it 12.61 J? I would think it's 9.41 J because only the gravititational potential energy is present in the system. The way the problem is worded, it sounds like in part (b) that you're placing the spring in a new vertical position, which I interpret it as being placed in a relaxed position (neither stretched or compressed)-it's a scenario different from part (a) where there is not already elastic potential energy present, all there is is gravitational potential energy. How come 3.2 J is being added?

Answer 1

Please go through my solution and ask doubts in comment..we can sort it out

Part a). Has nothing to do with part b