Elastic Collision Problem: Solving for Velocities with Conservation of Momentum

[Jordash]

Homework Statement

Two elastic balls, one with mass m = 50 g and the other with mass M = 3m experience a head-on elastic collision after initially traveling in opposite directions at the same speed v = 15 m/s.

Use the conservation of momentum strategy to obtain symbolic expressions and numerical values
for the velocities of the two balls after the collision. (One of the answers is 3E1.)

Homework Equations

Mi1Vi1+Mi2Vi2=Mf1Vf1+Mf2Vf2

The Attempt at a Solution

Well I know that the initial Velocities are going to be the same so

M1+M2(Vi)=M1Vf1+M2Vf2

Would be correct

I'm not sure how you would solve this problem because you are looking for 2 unknowns?

Thanks for any help

 

[LowlyPion]

What else is also conserved in an elastic collision?

http://en.wikipedia.org/wiki/Elastic_collision#One-dimensional_Newtonian

 

[Jordash]

The Kinetic Energy is conserved

So I guess KEi=KEf

or

KEi=1/2M1Vi1^2+1/2M2Vi2^2
KEf=1/2M1Vf1^2+1/2M2Vf2^2

Where would I go from there?

 

[LowlyPion]

Weren't you complaining about having 2 unknowns?

So don't you have 2 equations?

 

[Jordash]

I'm reading this:
http://en.wikipedia.org/wiki/Elastic_collision#One-dimensional_Newtonian

I'm confused on what the 'u' means under one dimensional Newtonian, does it just mean velocity?

Thanks

 

[LowlyPion]

I'm reading this:
http://en.wikipedia.org/wiki/Elastic_collision#One-dimensional_Newtonian

I'm confused on what the 'u' means under one dimensional Newtonian, does it just mean velocity?

Thanks

They use v' interchangeably with u to represent velocities after collision.

 

[Jordash]

Ok, I used this equation:

Vi1+Vi2=Vf1+Vf2
Vi1-Vi2=Vf1-Vf2

which would mean

15m/s + -15m/s=Vf1+Vf2
0=Vf1+Vf2
or
Vf1=-Vf2

and

15m/s- -15m/s=Vf1-Vf2
15+15
30m/s=Vf1-Vf2

30m/s=Vf1-Vf1

what am I doing wrong?

 

[LowlyPion]

One mass is 3 times the other.

 

[Jordash]

Oh yeah, good point

 

[Jordash]

I'm trying to take that into account but I'm still lost I think it's because I'm really rusty on Algebra

 

[LowlyPion]

I'm trying to take that into account but I'm still lost I think it's because I'm really rusty on Algebra

Also try using the equations at the link I supplied.

Kinetic energy ... you know that ½mv² thing is also conserved.
Momentum is conserved.

Write them out carefully and solve..