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## Homework Statement

A box of mass 2 kg and another of mass 8 kg are attached by a spring with a spring constant of 80 N/m. A 4.0 N force is applied to the 8 kg box. Both of the boxes move with a constant acceleration on a horizontal frictionless surface. Find the acceleration.

## Homework Equations

Fs = -kx

Fnet = ma

## The Attempt at a Solution

Here is where I'm not sure if I am right or if my classmate is right. He did this:

total mass of system = 10 kg, total applied force = 4.0 N

4 = (10 kg)(a)

**a = 0.4**

What I did was find the Fnet of the 8 kg box and the 2 kg box respectively and set the accelerations as equal. I think this is where I kind of went off the rails - I pictured it as the spring pulling in on both of the boxes, meaning the Fnet of the 8 kg box is 4 - Fs and the Fnet for the 2 kg is 4 + Fs.

Box A (2 kg)

Fnet = ma

a = Fnet/m

a = (4 + Fs)/2

Box B (8 kg)

a = Fnet/m

a = (4 - Fs)/8

Then set them equal: (4 + Fs)/2 = (4 - Fs)/8

Cross multiply to get: 32 + 8Fs = 8 - 2Fs

10Fs = -24

**Fs = -2.4 N**

When I plug in these numbers into the free body diagrams it all seems to work out, but that might be circular logic - I get an acceleration of

**0.8 m/s^2**

Please help! :(