How can I simplify this equation by substituting for Vf2?

[jedr]

These two equations are the same:

M1Vf1+M2Vf2=M1Vo1 + 0

After substituting Vf2= M1(Vo1 –Vf1)/M2 in one of the equations above, it is now Vf1=[(M1-M2)/(M1+M2)]V01

The assignment is to show the steps how the first equation becomes the second after substituting for Vf2. I have tried simplifying the equation in numerous ways, but M1 and M2 keep canceling out, and I end up with Vf1=Vf1. Can anybody help?

 

[rock.freak667]

These two equations are the same:

M1Vf1+M2Vf2=M1Vo1 + 0
½M1Vf1 + ½M2Vf2 = ½M1Vo1 + 0

The only thing different is that the second equation is just the first multiplied by 1/2. So you will always end up with something like M1=M1 or similar.

 

[jedr]

Yes, I know that the two equations are the same. I need to substitute Vf2 in either equation to get Vf1=[(M1-M2)/(M1+M2)]V01. It doesn't matter which equation of the two above is used, both were just given to me.

 

[vela]

All three equations are the same. The third one is just the first one solved for v_{f2}.

I think you wanted the velocities to be squared in the second equation.

 

[jedr]

Yes, I forgot the squares but you are misunderstanding what I am asking. The equations are the same, I know that, but I cannot seem to figure the steps to get to the other equation.

 

[vela]

Well, it's hard to understand what you're asking if you don't ask it correctly. Try this. With both equations, collect the v1 terms on one side and the v2 term on the other. Then divide the equation with the squares by the other. Then you'll have a set of two linear equations which you can readily solve while avoiding much algebraic messiness.