How does -9.2*m/s + 3.6 Kg become 2.6m/s?

[superjoebob]

Homework Statement

The problem is that there are a bunch of physics equations were they end up with a number like 9.2 (then the dot that means times i think) and then m/s. How do I convert a number with both mass and speed attached to it to just a single number?

Homework Equations

none that I know of

The Attempt at a Solution

Ive got nothing

I also forgot to mention that m/s isn't a variable, its an empty thing that just seems to be attached to my numbers

 

[dranseth]

Can you post an example..?

 

[superjoebob]

a child rolls a superball of mass of 0.025kg at a speed of 2.3m/s and it collides head on with a ball of 0.020kg. What are the new speeds of the 2 balls after collision?

m1=0.025
m2=0.020
v1=2.3m/s
newv1=?
newv2=?

There is no friction or any other force acting, its completely 1 dimensional. The collision is elastic.

Its a textbook example.

near the end it says

"0=-9.2kg*m/s + 3.6 kg*newv2, or newv2=0

Since newv2=0 corresponds to no collision, we must have:

0=-9.2kg*m/s + 3.6kg*newv2
newv2=+2.6m/s"

how do they get that!?

 

[Snazzy]

They took the 9.2 to the left hand side and divided by 3.6 to get "newv2". It's algebra.

 

[superjoebob]

but that comes out with negative 2.6, how does it become posotive?

 

[Snazzy]

It doesn't come out negative.

0 = -9.2 + 3.6x

When solving for x, you get a positive number.

 

[superjoebob]

because x moves left of the = sign?

 

[Snazzy]

Yes. You should refresh on your algebra skills before you attempt to do physics questions.

 

[superjoebob]

ok it all makes sense now :) thanks Snazzy. Its not that I don't know algebra its just that that random m/s threw me off

 

[BryanP]

Doesn't matter which one moves. In the end after the algebra is done, you have two positive numbers.

Dividing by two positive numbers will yield to another positive number.

It changes sign because in order to solve for 'x', you need to isolate that term so you can perform multiplication by 1/3.6 .

Therefore:

0 = -9.2 + 3.6x
9.2 + 0 = 9.2 + (-9.2) + 3.6x
9.2 = 9.2 + (-9.2) + 3.6x ------ additive identity a + 0 = a
9.2 = 0 + 3.6x ----- additive inverse a + (-a) = 0
9.2 = 3.6x ---- additive identity
(1/3.6)*9.2 = (1/3.6)*3.6x
2.55 ~= (1/3.6)*3.6x
2.55 ~= 1*x -------- multiplicative inverse a/a = 1
2.55 ~= x ------- multiplicative identity 1*a = a

That's pretty much the algebra behind it. I mean I'm not sure that you were clear with that based off your replies though.