Question concerning two bodies in space

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The discussion centers on calculating the time it takes for two identical spheres, 6mm apart in space, to collide due to gravitational attraction. The gravitational force between the spheres is calculated as 7.12 x 10^-6 N, leading to an acceleration of 7.12 x 10^-8 m/s^2. The original poster considers treating this acceleration as constant despite acknowledging that it changes as the spheres approach each other. There is a debate on whether the initial velocity (v0x) can be assumed to be zero, with some participants suggesting that this assumption is reasonable given the context. Ultimately, the poster decides to proceed with the calculation using the constant acceleration formula, accepting a potential loss of accuracy for a simpler solution.
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Two indentical spheres with radius 15cm and mass 100kg are 6mm apart from echother in space. My problem is to find how long it will take before gravitational attraction will cause the two spheres to come together?

What I have found out so far is:
I have the gravitational force Fg= 7,12*10^-6 N,
and used Newtons 2. law to find the spheres acceleration a=7,12*10^-8 m/s^2

I know the acceleration is not constant, because the gravitational forces increase as the spheres move towards each other. But I think I will neglect this, and treat it as constant.

If I do so, could I use the equation:
X = x0 + v0x +1/2*ax*t^2
t = sqrt((2*x)/ax)= 84269sek ,
x = 0,003m, v0x = 0 m/s, x0= 0 m

I don't know if I can treat v0x as being 0, should it be v0x = a?

Is this way of, or am I on the right track?

all kind of help would be apprciated, thx
 
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Simon316 said:
Two indentical spheres with radius 15cm and mass 100kg are 6mm apart from echother in space. My problem is to find how long it will take before gravitational attraction will cause the two spheres to come together?

What I have found out so far is:
I have the gravitational force Fg= 7,12*10^-6 N,
and used Newtons 2. law to find the spheres acceleration a=7,12*10^-8 m/s^2

I know the acceleration is not constant, because the gravitational forces increase as the spheres move towards each other. But I think I will neglect this, and treat it as constant...

IMO wshful thinking: this needs to be done with calculus. You have already said so in so many words--ie acceleration is not constant.
 
denverdoc said:
IMO wshful thinking: this needs to be done with calculus. You have already said so in so many words--ie acceleration is not constant.


That's true, but the error for this problem will be fairly small. The distance between the centres of the spheres only changes from 306mm to 300mm.

I don't know if I can treat v0x as being 0, should it be v0x = a?

The question doesn't say what v0x was and you have to assume it was something. But assuming "v0x = a" says "a velocity equals an accleration" which doesn't make any sense because they have different units.

I would assume it was 0.
 
Yea I know about calculus, but the question says you get 90%/points for a reasonable answer, and 100% for a correct. I will settle with 90%, and use
X = x0 + v0x +1/2*ax*t^2 (although I'm not sure this is the right way), and use V0x = 0.

Thanks
 

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