Elastic Collision: Solving Components of the Problem

[harisf]

1. Homework Statement
The problem is in the picture(attached)


2. Homework Equations
I know we have to use
m1v1 + m2v2 = m1v1' + m2v2'
(1/2)m1v1^2 + (1/2)m2v2^2 = (1/2)m1v1'^2 + (1/2)m2v2'^2

3. The Attempt at a Solution
All I know is that it needs to be split up into components.
Please help me out.

 

[tiny-tim]

Welcome to PF!

Welcome to PF!

(please type the question in future … it's much easier to read than having to look at a picture in a separate window)

(and try using the X² and X₂ tags just above the Reply box )

I know we have to use
m1v1 + m2v2 = m1v1' + m2v2'
(1/2)m1v1^2 + (1/2)m2v2^2 = (1/2)m1v1'^2 + (1/2)m2v2'^2
…
All I know is that it needs to be split up into components.

Yes, the first equation is a vector equations, and needs to be split up into two scalar equations.

(You could choose West and North for the component directions, for example.)

So … show us what you get.

 

[davieddy]

Health Warning:

This problem can get very messy unless you translate it into
the reference frame in which the c of m is stationary.

David

 

[tiny-tim]

Health Warning:

This problem can get very messy unless you translate it into
the reference frame in which the c of m is stationary.

David

No, you should be able to do it in the reference frame given.

 

[harisf]

Thanks guys, and yes I will try this question out. I got some help today from a friend, he said that there was no need for NS/EW components. He told me to make a triangle. So therefore the resulting velocity after the collision of the 2amu mass would be v₁'cos10.

2(2km/s) + 1(0m/s) = 2(v₁'cos10) + v₂'
4 - 2v₁'cos10 = v₂' (this will be equation one)

We know kinetic energy is conserved:
2(2km/s)² + 1(0m/s)² = 2(v₁'cos10)² + v₂'²
8 - 2(v₁'cos10)² = v₂'² (our second equation)

Then sub in equations into each other for v₂'.
I have to go for now but I will get back to you guys soon on the problem. Please keep in mind that I am only in grade 12. Thanks again.