Gravitational attraction question

AI Thread Summary
The discussion revolves around calculating the velocity of two point masses, each 400 kg, as they move from a distance of 10^14 m to 1000 m apart under mutual gravitational attraction. The user applied the gravitational force equation and integrated it to find the work done, equating it to the change in kinetic energy (ΔKE). There is uncertainty regarding whether to use one or both masses in the kinetic energy formula, leading to a calculated velocity of approximately 7.3226*10^-6 m/s. The user concludes that this value represents the velocity of each mass as they approach each other. The transformation of gravitational potential energy into kinetic energy is also highlighted in the discussion.
physninj
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Homework Statement


two point masses (400 kg) are 10^14 m apart in deep space under no gravitational attraction besides each others. find their velocity when they are 1000 m apart.

Homework Equations


-G (m_1m_2)/r^2=F

The Attempt at a Solution


I integrated the equation above plugging in the 400 kg for m1 and m2 from 10^14 to 1000. I believe this gave me the work required to bring one of them to that distance so i set it equal to ΔKE. This became (1/2)mv_f^2 because they start from rest. Now my question is whether that mass is 400 kg or 800 kg or if I'm on the right track. I just put one of the mass in that then solved and got 7.3226*10^-6. And I think that is the velocity of each of the masses. Anybody care to disagree? Thank you.
 
Physics news on Phys.org
As they come together, their mutual gravitational PE is transformed into the kinetic energy of both masses.
 
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