Question

Question: A 1.5kg crate falls from a height of 2m onto an industrial spring scale k=1.5×10^5 N/m. At its greatest compression, what is the reading on the scale?

The answer for this question is 3000N. I have to use mgh =(1/2)kx^2 . I checked the solution and it is said that I have to plug in 2 for h.

Can you explain why h=2+x is wrong?

Answer 1

h cannot be equal to 2+x because the potential energy possessed by the crate is equal to mgh. Here h =2. Now this potential energy gets transformed into the potential energy of the spring which appears as it gets compressed by x.  

The potential energy mg(2) gets transformed into the potential energy (1/2)k x^2 and not the potential energy mg(2+x) that gets transformed into the potential energy (1/2)kx^2.

The x part gives rise to the potential energy of the spring while the h=2 part gives rise to the potential energy of the crate.

I hope you are getting what I mean to say. If it is still not clear to you. Let me know. I will try something more.