Frictional Forces and Acceleration: Solving for Horizontal Component

[Pyae]

Homework Statement

Two blocks are accelerated across a horizontal frictionless surface as shown. Frictional forces keep the two blocks from sliding relative to each other, and the two move with the same acceleration. F = 1.2 N and M = 1.0 kg

Homework Equations

what is the horizontal component (frictional force) of the force of the large block on the small block?

The Attempt at a Solution

 

[JaredJames]

If the acceleration is the same, then the force must change given the masses are different.

Given F = ma

For the lower block, F₁ = 2M*a

For the upper block, F₂ = M*a

Where M = 1.0kg and F₁ = 1.2N

Given a is equal, you can rearrange the two and solve for F₂

Please note you are really supposed to supply an attempt at the solution.

Jared

 

[Pyae]

I know the answer is 0.4 N to the right. I don't know how it gets. But here's what I'm thinking.

i think the given F applies to both blocks, so

F= ma
1.2 = 3M * a
a = 0.4

then F1 = ma = 1 * 0.4 = 0.4 N

I don't know if it makes sense. Can someone give idea and guidance on how to solve this problem?