Hooke's Law - A spring between 2 masses accelerating to the right.

[CaptainSFS]

Homework Statement

http://pyrofool.googlepages.com/lab25.gif

A 2 kg mass and a 3 kg mass are on a horizontal frictionless surface, connected by a massless spring with spring constant k = 140 N/m. A 15 N force is applied to the larger mass. How much does the spring stretch from its equilibrium length? The masses uniformly accelerate with no oscillations.

Homework Equations

F_spring = -kx (Hooke's law)

The Attempt at a Solution

I haven't the slightest clue how to figure the 2 kg mass in. I know I'm solving for x, but like I mentioned, I don't know what to do with the 2 kg mass. Thanks for any help.

 

[Doc Al]

Hint: What's the acceleration of the system?

 

[CaptainSFS]

so i think the acceleration is 3m/s². so the first mass has a force of 9N and the smaller mass has a force of 6N.

Would I find x for each mass then using Hooke's law and then find the difference between the two? If that's the case would the answer then be 2.14cm?

 

[Doc Al]

so i think the acceleration is 3m/s². so the first mass has a force of 9N and the smaller mass has a force of 6N.

Good. (Note that those are the net forces on each mass.)

Would I find x for each mass then using Hooke's law and then find the difference between the two? If that's the case would the answer then be 2.14cm?

No, it's easier than that. Consider the smaller mass. You know the force that must be exerted on it. So what must be the stretch in the spring to exert such a force?

 

[CaptainSFS]

oh alright. That makes sense. So it's just 6 N / 140 N/m. = 4.29cm. Cool. thanks for your help. :)

 

[compwiz3000]

What happens to the 9N force exerted on the larger mass? How come that doesn't contribute to any extension in the spring?

 

[Doc Al]

What happens to the 9N force exerted on the larger mass? How come that doesn't contribute to any extension in the spring?

The 9N is the net force on the larger mass, not an individual force. The individual forces acting on that mass are the 15N applied force and the tension from the spring.

 

[compwiz3000]

The 9N is the net force on the larger mass, not an individual force. The individual forces acting on that mass are the 15N applied force and the tension from the spring.

So what does this net force do? Does the 15N applied force and the tension from the spring only push the large mass? Does it contribute nothing to the stretch in length?