# Two masses attached by a spring

#### fuddyduddy

This problem was on my test today and I am not sure if my solution is correct.

1. 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.

2. Homework Equations
Fs = -kx
Fnet = ma

3. 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

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#### TSny

Homework Helper
Gold Member
Hello fuddyduddy. Welcome to PF!

Box A (2 kg)
Fnet = ma
a = Fnet/m
a = (4 + Fs)/2
Does the 4 N force act on the 2 kg mass or does it act only on the 8 kg mass?

#### fuddyduddy

It acts on the 8 kg mass, the picture was as such:

[2 kg]--(spring)--[8 kg]--> 4.0 N

And thank you for the welcome! :)

#### TSny

Homework Helper
Gold Member
OK. When thinking about the forces acting on on the 2 kg mass, the force of gravity is an "action-at-a-distance" force (from the earth). All other forces on the 2 kg mass are "contact" forces coming from other objects in contact with the 2 kg mass.

So, if someone pulls on the 8 kg mass to create the 4.0 N force on the 8 kg mass, that pulling force is a contact force on the 8 kg mass, not a force on the 2 kg mass.

So, what should you write for the net horizontal force on the 2 kg mass?

#### fuddyduddy

Okay, I see now! So the net force acting on the 2 kg block is simply the spring force directed to the right. Thank you!

#### TSny

Homework Helper
Gold Member
Yes. Good.

"Two masses attached by a spring"

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