How Do You Calculate the Speed of Two Masses Attracting in Space?

AI Thread Summary
To calculate the speed of two attracting masses in space, the conservation of energy equation is essential, considering both kinetic and gravitational potential energies. The initial and final energies must account for both masses, as each contributes to the total kinetic energy. It is important to remember that momentum is also conserved, which means both masses will have the same speed as they approach each other. The gravitational constant (G) is given as 6.67x10^-11, and the equations should reflect the total energy before and after the masses move closer. Understanding these principles will help clarify the calculation process.
arydze2
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Two baseballs, each with a mass of 0.158 kg, are separated by a distance of 400 m in outer space. If the balls are released from rest, what speed do they have when their separation has decreased to 270 m? Ignore the gravitational effects from any other objects.
I keep on using the conservation of energy equation, but nothing seems to give, I feel like I'm missing a step, Please help...
This is what I've done so far
Ei=Ef
1/2mvi^2-(Gm1m2/ri)=1/2mvf^2-(Gm1m2/rf)
if this is the right equation...
KEi obviously = 0, how to I get rid of the mass(m) in the KEf, I can't cancel it out since there are 2 masses involved, am I right?
value for G = 6.67x10^-11
Thanks for the help.
 
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That is the right equation, except that the KE is the sum of the individual kinetic energies of the two balls. You also don't have to cancel out the mass (which is equal for both balls) since it is given.
 
Since you haven't mentioned it and said you feel like you are missing something (ie, maybe you have two velocities to solve for with one equation), don't forget conservation of momentum.
 
Yes,both total mechanical energy & momentum are conserved...Therefore they have the same speed in modulus...

Daniel.
 
arydzse2,

Yes, you're missing a step. Actually you're skipping it, and that's getting you confused.

Write the equations for total energy (both masses) before and after. Ei=? Ef=?
 
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