Why is my momentum equation giving an incorrect force?

[k_squared]

Homework Statement

There are two boxes, sitting right next to each other. Call the box on the left "box A" and the box on the right "Box B". A 50 pound force starts pushing A into B. Find their speed at 5 seconds, and how much force Box B puts on Box A. Box A weighs 100 pounds, Box B is 50 pounds and the coefficient of kinetic friction is 0.25.

Homework Equations

(mv)_1 + (integral of force with repsect to time) = (mv)_2

The Attempt at a Solution

First, I solved for their speed and acceleration using basic equations of motion (It is in fact 13.4 ft/s. This implies an acceleration of 2.68 ft/s.) Then, I solved for the force that Box B places on box A. My attempt goes like this:

F_(b on a) * 5 = (50/32.2)*13.4. This yields and answer of 4.1 lbs. However, by doing F_(b on a)-(50(0.25))=(50/32.2)(2.68) I get the correct answer, (because of Newton's third law.)

Why does my first equation not yield the correct answer? Thanks for any help!

 

[gneill]

Why does my first equation not yield the correct answer?

Is your F_(b on a) the only force acting on block B? The change in momentum (or impulse) will be due to the net force acting on the block.