Elastic collision of particles

[jaeeeger]

Homework Statement

Homework Equations

conservation of momentum, m1v1i+m2v2i=m1v1f+m2v2f

and

conservation of KE, ½m1v1i^2+½m2v2i^2=½m1v1f^2+½m2v2f^2

The Attempt at a Solution

first, i defined my variables. v1i=-v2i, v1f=-0.750v1i, v1f=0.750v2i

I tried isolating V2f using the conservation of momentum equation, getting V2f=[-m1v2i+m2v2i-m1(0.750v2i)]/m2.

Then I use the conservation of kinetic energy equation and plug in my new v2f value. expand it out, then try to simply everything to get an answer for m2. I'm really bad at long and complicated algebra, I often cancel out items I'm not allowed to, and don't cancel out when I should. I've tried around 7-8 times now, all with varying answers, none of them right.

 

[Delphi51]

Welcome to PF, Jaeeeger!
I'm just an old high school teacher - used to keeping the notation simple. It might be worth a try that way. Rather than V2f, I used "W" for the final velocity of the nm.
For conservation of momentum I wrote mv - nmv = -.75mv + nmW (1)
For conservation of energy (cancelling all the 1/2's right off):
mv² + nmv² = m(.75v)² + nmW² (2)
It doesn't looks so bad that way, does it? Cancel all the m's to make it even better. I solved (1) for W and substituted into (2) to get an equation in one unknown.

If you type in your work here (or scan and upload), we will make sure you get it right.
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[NascentOxygen]

I've tried around 7-8 times now, all with varying answers, none of them right.

If you know the correct answer, it is a good idea to provide it so others working along can verify they are on the right track.

 

[jaeeeger]

If you know the correct answer, it is a good idea to provide it so others working along can verify they are on the right track.

The homework is online, I just know if I get it wrong.

Welcome to PF, Jaeeeger!
I'm just an old high school teacher - used to keeping the notation simple. It might be worth a try that way. Rather than V2f, I used "W" for the final velocity of the nm.
For conservation of momentum I wrote mv - nmv = -.75mv + nmW (1)
For conservation of energy (cancelling all the 1/2's right off):
mv² + nmv² = m(.75v)² + nmW² (2)
It doesn't looks so bad that way, does it? Cancel all the m's to make it even better. I solved (1) for W and substituted into (2) to get an equation in one unknown.

If you type in your work here (or scan and upload), we will make sure you get it right.
For the ² symbol, just copy one of mine and paste in your post.
More symbols to copy here: https://www.physicsforums.com/blog.php?b=346

Okay thanks for the help. I'm fairly sure I just screwed up my algebra somewhere, I get n=-1, which is wrong.

I solved (1) for W, then plugged that into the conservation of energy.
My algebra just isn't as hot as it used to be.

 

[Nickie]

I would like to first commend you for attempting to solve this problem using the conservation of momentum and kinetic energy equations. These principles are fundamental in understanding and predicting the behavior of particles in collisions.

To solve this problem, I would suggest breaking it down into smaller steps. First, let's define the variables:

m1 = mass of particle 1
m2 = mass of particle 2
v1i = initial velocity of particle 1
v2i = initial velocity of particle 2
v1f = final velocity of particle 1
v2f = final velocity of particle 2

Next, let's use the conservation of momentum equation to solve for v2f:

m1v1i + m2v2i = m1v1f + m2v2f
Since we know that v1i = -v2i and v1f = -0.750v1i, we can substitute them in the equation:

m1(-v2i) + m2v2i = m1(-0.750v1i) + m2v2f
Simplifying:

-m1v2i + m2v2i = -0.750m1v1i + m2v2f
Combining like terms:

(m2-m1)v2i = (-0.750m1)v1i + m2v2f
Dividing both sides by (m2-m1):

v2i = (-0.750m1/m2-m1)v1i + (m2/m2-m1)v2f

Now, we can use the conservation of kinetic energy equation to solve for v2f:

½m1v1i^2 + ½m2v2i^2 = ½m1v1f^2 + ½m2v2f^2
Substituting in our known values:

½m1(-v2i)^2 + ½m2v2i^2 = ½m1(-0.750v1i)^2 + ½m2v2f^2
Simplifying:

½m1v2i^2 + ½m2v2i^2 = 0.5625m1v1i^2 + ½m2v2f^2
Combining like terms:

(0.5m1