# Newton's Second Law Question

1. Jul 26, 2012

### Slusho

1. The problem statement, all variables and given/known data
A certain force gives object m1 an acceleration of 12.0 m/s2. The same force gives object m2 an acceleration of 3.30 m/s2. What acceleration would the force give to an object whose mass is (a) the difference between m1 and m2 and (b) the sum of m1 and m2.

2. Relevant equations
F=ma

3. The attempt at a solution
I found these two solutions online:
http://www.physforum.com/index.php?showtopic=6754
http://www.jiskha.com/display.cgi?id=1286634662
but I can't follow their math. I tried manipulating the above equation similarly, to no avail.

Any help is greatly appreciated!

2. Jul 27, 2012

### azizlwl

Which part that you do not understand.
Use the formula a=F/m.

3. Jul 27, 2012

### SammyS

Staff Emeritus
Hello Slusho. Welcome to PF !

What are those manipulations? What have you tried?

F = m1a1 and F = m2a2, where a1 = 12.0 m/s2 and a2 = 3.30 m/s2 .

Therefore, $\displaystyle m_1=\frac{F}{a_1}\text{ and } m_2=\frac{F}{a_2}\,.$ Correct?

Now, use all this with F = (m1 + m2)a1+2 to find a1+2 .

4. Jul 27, 2012

### Slusho

I figured it out!

$$F=(\frac{F}{a_{1}}+\frac{F}{a_{2}})a_{1+2}$$
$$\frac{1}{a_{1+2}}=\frac{1}{F}(\frac{F}{a_{1}}+ \frac{F}{a_{2}})$$
$$\frac{1}{a_{1+2}}=\frac{1}{a_{1}}+\frac{1}{a_{2}}$$

Thank you so much for you help! I had to work it several ways for a good half hour until I did it correctly.