Moving Blocks Connected by a spring

[Deadsion]

Homework Statement

Moving blocks connected by a spring
Two identical 0.13 kg blocks (labeled 1 and 2) are initially at rest on a nearly frictionless surface, connected by an unstretched spring whose stiffness is 225 N/m, as shown in the upper diagram. Then a constant force of 8 N to the right is applied to block 2, and at a later time the blocks are in the new positions shown in the lower diagram. At this final time, the system is moving to the right and also vibrating, and the spring is stretched.

Homework Equations

KE= (1/2)mv^2
U= (1/2)kx^2

The Attempt at a Solution

What is the final translational kinetic energy of the real system?
What is the final vibrational kinetic energy of the real system?

I'm a little lost on how to find the two different kinetic energies since the problem doesn't give a final velocity. I found that the final total kinetic energy is .595 joules and that the total final potential energy is .045 joules, but i don't know to separate the two kinetic energies.

 

[tiny-tim]

Welcome to PF!

Hi Deadsion! Welcome to PF!

Hint: Call the positions of the two blocks x1 and x2.

Then x1 - x2 helps you find the PE, and x1 and x2 individually give you the KE.

And the work done is … ?

 

[Deadsion]

Thanks!
I found the work to be .64 joules and i used W=deltaK, but this gives me the total kinetic energy, and I'm trying to find the two different kinds of kinetic energy, Translation and vibrational.

 

[tiny-tim]

… but this gives me the total kinetic energy, and I'm trying to find the two different kinds of kinetic energy, Translation and vibrational.

Hi Deadsion!

I'm not sure what "vibrational KE" is … what definition are you using?

Anyway, given x1 and x2 (and its average, x3), there must be an expression for vibrational KE in terms of x1 x2 and x3.

 

[Deadsion]

Well there isn't any equation for finding the vibrational energy in my book, but this problem had a first part to it where it asked for the the translational kinetic energy for the blocks as a point particle system, which doesn't have the vibrational energy, which i found was the same for both the particle system and the real system, .55125 J. I figured this would work for finding the Vibrational Kinetic energy, but its wrong.
.55125+KEV=.64
KEV=.08875J

 

[tiny-tim]

How did you get the translational KE?

I expect they're defining vibrational KE as being total KE minus KE of the centre of mass … can't you get the latter from x1 and x2?

 

[Deadsion]

I used the center of mass. The CM moves .07 and the amount of force applied is 8N, so the work done is .56 Joules, and since the initial KE is 0, the final KE is .56J.
Oh i accidentally put the wrong trans KE...