Relaxed spring between two carts

[um20018]

Homework Statement

A 2.0-kg cart and an 8.0-kg cart are connected by a relaxed, horizontal spring of spring constant300 N/m. You pull the 8.0-kg cart with some constant horizontal force. The separation between the carts increases for a short time interval, then remains constant as you continue to pull and the spring is stretched by 0.100 m.
I need to find out what pulling force was exerted on the 8kg cart.

Homework Equations

The Attempt at a Solution

 

[NascentOxygen]

Hi um20018. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

I need to find out what pulling force was exerted on the 8kg cart.

So how will you go about it? What equations will you need?

 

[um20018]

Knowing that F=k*deltaX I figure that the spring is stretched with a force of 30N. But that answer doesn't seem to be right. I know it must have something to do with the other mass at the end of the spring but I don't know how that would relate.

 

[gneill]

Consider a Free Body Diagram of the smaller cart first. What force is acting on it? What's the resulting acceleration of that cart? Can you conclude anything about the acceleration of the system as a whole (once the spring stretching has stabilized as described)?

 

[um20018]

The force acting on the smaller cart is from the spring, and equals 30N. The acceleration of that cart would be 15 m/s^2. The acceleration of the system after the spring stretching has stabilized would be, I think, the same as just the small block because the system would be moving as a whole.

 

[gneill]

The force acting on the smaller cart is from the spring, and equals 30N. The acceleration of that cart would be 15 m/s^2. The acceleration of the system after the spring stretching has stabilized would be, I think, the same as just the small block because the system would be moving as a whole.

Right. So what force do you need to apply to the whole system to make it accelerate at that rate?