# Force & Newton's 2nd Law Problem

1. Jul 13, 2009

### crono_

Brand new to the forum. My apologies if this problem is already posted on the site. I searched a bit but had no luck.

1. The problem statement, all variables and given/known data
Problem from Cutnell & Johnson PHYSICS 7th Edition. Chapter 4 - Problem #9

Two forces FA and FB are applied to an object whose mass is 8.0 kg. The larger force is FA. When both forces point due east, the objects acceleration has a magnitude of 0.50 m/s2. However, when FA points due east and FB points due west, the acceleration is 0.40 m/s2, due east. Find (a) the magnitude of FA and (b) the magnitude of FB.

2. Relevant equations

F=ma

FA + FB = ma1

FA - FB = ma2

3. The attempt at a solution

I have the text books solution manual, but don't really understand the solution. Any help would be appreciated.

a) Adding equations 1 and 2 gives

FA = m (a1 + a2) / 2

= (8.0 kg) (0.50 m/s2 + 0.40 m/s2) / 2

= 3.6 N

b) Subtracting equation 2 from equation 1 gives

FA = m (a1 - a2) / 2

= (8.0 kg) (0.50 m/s2 + 0.40 m/s2) / 2

= 0.40 N

Ok, the final answers make sense when you plug the numbers into the equations. But I'm curious about why the equations are being added and subtracted from each other? In other words, how / why did the book mix the two equations together at get:

FA = m (a1 + a2) / 2

FA = m (a1 - a2) / 2

Again, probably just simple algebra that I'm looking over...

Thanks for any help!

2. Jul 13, 2009

### LowlyPion

Welcome to PF.

It's a technique for eliminating variables, in this case they are trying to isolate Fa and Fb just in terms of the other variables and not themselves. It is only algebraic cleverness and not physics that calls for that approach. Other more brute force means, maybe not as elegant, could be employed.

3. Jul 13, 2009

### cepheid

Staff Emeritus
HOW did the textbook do it? Because if:

A = B​

and,

C = D​

then,

A + C = B + D​

This just follows from the fact that A and B are interchangeable...whenever you see one, you can substitute it for the other. Likewise for C and D.

I'm not sure if that qualifies as a formal proof, but I don't think you want to go so deep into the math as to question the nature of "equality" rather than merely accepting it and using it ;)

WHY did the textbook do this? Because it allows one to solve the problem.

4. Jul 13, 2009

### PhanthomJay

You mean to say F_B = m(a1-a2)/2. Algebraically, when you add , subtract, multiply, divide, etc 2 equations together, you get a third equation which is equal to the first. Adding or subtracting eliminates one of the unknown variables, alowing you to solve for one of the unknowns.

5. Jul 13, 2009

### crono_

Ok, I definitely need to brush up on the algebra. Thanks for the input everyone. I'm going to have to read and re-read your responses to fully understand what the text book is doing.

Is anyone aware of where I could find information on this method?

Thanks again!

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