Question about vibrational kinetic energy and potential energy.

[dizzid122]

Homework Statement

You hold up an object that consists of two blocks at rest, each of mass M = 3 kg, connected by a low-mass spring. Then you suddenly start applying a larger upward force, of constant magnitude F = 94 N (which is greater than 2Mg). Some time later, the blocks have moved upward, and the spring stretch has increased.

The heights of the centers of the two blocks are as follows:
Initial and final positions of block 1: y1i = 0.1 m, y1f = 0.2 m
Initial and final positions of block 2: y2i = 0.4 m, y2f = 0.9 m

It helps to show these heights on a diagram. Note that the initial center of mass of the two blocks is (y1i + y2i)/2, and the final center of mass of the two blocks is (y1f + y2f)/2.

(a) Consider the point particle system corresponding to the two blocks and the spring. Calculate the increase in the total translational kinetic energy of the two blocks. It is important to draw a diagram showing all of the forces that are acting, and through what distance each force acts.

(b) Consider the real system corresponding to the two blocks and the spring. Calculate the increase of (Kvib+Us), the vibrational kinetic energy of the two blocks (their kinetic energy relative to the center of mass) plus the potential energy of the spring. It is important to draw a diagram showing all of the forces that are acting, and through what distance each force acts.

Homework Equations

W=fd
K+U (total)= K(trans) + K(vib) + U, etc.
There may be other equations needed, I'm not sure...

The Attempt at a Solution

I got part "a" correct with an answer of 10.56 J. It's part "b" I'm having issue with. Here's what I'm currently thinking.

W=94*.5 (This would give me the total K+U, as block 2 is the part of the system the force is actually affected, it's being pulled up on? maybe?) = 47 J

47-10.56 (the translational kinetic energy)-(9.8*6*.3) (Potential energy of Earth with the system, mgh, with h being the change in height of the center of mass of the system).
=18.8 J. I am however, not very confident in this answer. Any help, especially with a method explaining what to do, would be greatly appreciated, thanks!

 

[Spinnor]

Unless I'm missing something this is a hard problem. It would probably help others if you included a scan of your work that got you the right answer to the first part, then others might better be able to help.

Interesting problem, not feeling very sharp right now.