# Laws of Motion w/ Friction - Two Forces on Two Boxes

## Homework Statement

A force of 38.64 N pushes and pulls two blocks as shown in the figure below. The vertical contact surfaces between the two blocks are frictionless. The contact between the blocks and the horizontal surface has a coefficient of friction of 0.18.
The acceleration of gravity is 9.8 m/s2.

http://img121.imageshack.us/img121/962/physicsproblem.tif [Broken]

What is the magnitude a of the acceleration of the blocks? Answer in units of m/s2.

## Homework Equations

a = (F - (µm1g + µm2g)) / (m1 + m2)

F = m • g

## The Attempt at a Solution

I've worked on this for a while but still cannot seem to come to the right answer. I submit answers online, so I know the following is either incorrect or not close enough.

There are two contact forces that urge the boxes right:
The push has a horizontal force = 38.64N ➙
The pull has a diagonal force = 38.64 ➚
This force will gives the horizontal force of 38.64cos(50) = 24.84N ➙
as well as a vertical force of 38.64sin(50) = 29.60N ↑

There is also the two opposing forces of friction for each box:
With the vertical force on the right box, m2 must be modified
Its original downward force is 90.16N (m2g) minus the upward force from the pull 29.60N, gives it a new downward force of 60.56N.
Right box µ(m2)g: .18 • 60.56N = 10.9N ←
The left box is still the same
Left box µ(m1)g: .18 • 45.08 = 8.1N ←

Now that I have forces calculated, I put them into the acceleration formula above. (This is where I think I'm messing up.)

a = (38.64N + 24.84N - 10.9N - 8.1N) / (4.6kg + (60.56N/9.8m/s2))

Simplified
a = 44.48N / 10.78kg = 4.13m/s2

And I was told that was incorrect.

That is as right as I think I've been able to get it.
Thanks for any help in advance!

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