Homework Help: Ciruclar motion and gravitation question

1. Mar 5, 2006

chazgurl4life

Q:Two objects attract each other gravitationally with a force of 3.3 10-10 N when they are 0.25 m apart. Their total mass is 4.0 kg. Find their individual masses.

Now my professor only told us to use F= Gm1m2/r2
Force in this case would be the 3.3e-10 Newtons, the radius squared = 0.0625 m and G is a the gravitational constant 6.67e-11 N so when i solve for m1 and m2 the larger mass come out to 4.2 kg and thats impossible

2. Mar 5, 2006

arildno

Hence, you haven't done your arithmetic right.

3. Mar 5, 2006

Hootenanny

Staff Emeritus
How did you solve for m1 and m2?

4. Mar 5, 2006

arildno

You have:
$$m_{1}m_{2}=\frac{r^{2}F}{G}$$
withe the condition $$m_{1}=4-m_{2}$$
you get a quadratic equation to solve for $m_{2}$

5. Mar 5, 2006

Hootenanny

Staff Emeritus
That's how I would do it.

6. Mar 5, 2006

chazgurl4life

ok so what i come up with is :

4m-m2^2=.25^2(3.3e-10)
---------------
6.67e-11

so when i solve i get :(Mass 2)^2-4(mass2)-.309 m=0
but when i solve for mass to i get 4.02 kg.. what am i doing wrong?

7. Mar 5, 2006

Hootenanny

Staff Emeritus
You should get:
$$4m_2 - m_{2}^{2} = \frac{r^2 \cdot F}{G}$$

8. Mar 5, 2006

arildno

First of all:
DO NOT ENTER NUMBERS BEFORE THE VERY LAST MOMENT!! :grumpy:

You have:
$$m_{2}(4-m_{2})=\frac{r^{2}F}{G}$$
which you rewrite as:
$$m_{2}^{2}-4m_{2}+\frac{r^{2}F}{G}=0$$

This has the solutions:
$$m_{2}=\frac{4\pm\sqrt{16-\frac{4r^{2}F}{G}}}{2}$$
This yields ALWAYS positive answer(s), in so far as the solution exists.

Note that the sum of your two solutions equals 4. What does that mean?

Last edited: Mar 5, 2006
9. Mar 5, 2006

chazgurl4life

thank you very much.:-)..i realize where i was going wrong.

So after my calculations mass 1 =.078 kg and mass 2= 3.92 kg

10. Mar 5, 2006

arildno

I haven't the slightest idea what plug&chug would yield. Your numbers sort of add up to 4, though, which isn't bad at all..

11. Mar 5, 2006

Hootenanny

Staff Emeritus
plug&chug?

12. Mar 5, 2006

arildno

Plug into the formula, chug out the answer..

13. Mar 5, 2006

Hootenanny

Staff Emeritus
ahhhh... It's all starting to make sense...