Posted by **Lindsay** on Monday, December 17, 2007 at 9:02am.

Two 2.160 kg crystal balls are 0.870 m apart in the vertical direction. Calculate the magnitude of the gravitational force they exert on a 8.80 g marble located 0.260 m horizontally out from the center of a line that intersects the centers of the balls. (For your own knowledge, determine the direction of the force.)

I feel like I'm close to understanding this, but I still don't quite get it. Do I have to calculate the mag. of grav. force the crystal balls exert on each other first?

- Physics -
**drwls**, Monday, December 17, 2007 at 9:14am
<<Do I have to calculate the mag. of grav. force the crystal balls exert on each other first? >>

No, just calculate the forces between the 0.0088 kg ball and either of the 2.160 kg balls, using the universal law of gravity. The value of R, from the small marble to either ball, is

sqrt(0.435^2 + 0.260^2)= 0.5068 m

The force vectors are the same in magnitude but act in different directions. The vertical components of the two forces (with the upper and the lower ball cancel. The gravity force vectors make an angle of arctan 0.435/0.260 = 59.1 degrees with the horizontal axis of symmetry. Only the horizontal components of the gravitaional force are additive.

- Physics -
**Lindsay**, Monday, December 17, 2007 at 9:26am
(6.67E-11)(2.16)(0.0088) / (0.5068)^2 = 4.94E-12 N

Is that correct?

- Physics -
**drwls**, Monday, December 17, 2007 at 10:31am
That is the force between the mabloe and one ball. For the net force with two balls, multiply by twice the cosine of the angle I calculated

- Physics -
**Lindsay**, Monday, December 17, 2007 at 10:36am
Oh you're right, I forgot that step.

So 5.07E-12 N is the net force with both balls.

- Physics -
**:]**, Tuesday, April 5, 2011 at 12:30am
if you scuff electrons from your hair onto comb, are you positively or negatively charged? how bout the comb?

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