I seriously this is a different language to me- Conservation of Momentum

[teggenspiller]

Homework Statement

my notes say this:
Conservation of momentum in one deminsion
m1(v1initial-v1final) = m2(v2i-v2f) equation 1

Conservation of Kinetic Energy:
mass1*(v1^2initial - v1^2final) = mass2(v2^2in - v2^2fin) equation 2

Then is says: on the left hand side of the equality for equation 2, we can use the identity that x-squared minus y-squared, equals the quantity of x-y time x+y

Homework Equations

(x^2-y^2)=(x-y)(x+y)

The Attempt at a Solution

Can anyone tell me how all these equations are related, or how to remember them, or think of something so this makes more sense. I am just getting lost in all the equations, how can I remember them?

thnaks so much.

 

[Peter G.]

Do you know Newton's Law's of Motion? You can derive the Conservation of Momentum for example from those. If you do so, I think you understand what the formula means and it would make things easier for you. For example:

Conservation of Momentum says: In an isolated system, the momentum is conserved, this means:

Imagine a collision between a ball, A, and another ball, B.

In a collision, a ball hits another. When they do so, clearly, there's an acceleration, a change in velocity - one ball will start moving faster and the other one, slower - so, Newton's First Law tells us that there is a resultant force acting.

Newton's Second Law tells us that the resultant force is equal to the rate of change in momentum:

F = (mv - mu) / t

Newton's Third Law tells us that, if ball A exerts a force F on ball B, then ball B exerts a force - F on ball A - that is a force equal in magnitude and opposite in direction.

So, mv_a - mu_a / t = -mv_b + mu_b / t (both t's are equal, so they cancel out leaving us with:)

mv_a - mu_a = -mv_b + mu_b

mv_a + mv_b = mu_a + mu^b

Meaning, the total momentum before is equal to the total momentum after?

Those that make things clearer for the first equation?

 

[teggenspiller]

wait wait, what does 'u' mean?? momentum. why is the variable for it 'p' in the notes?

 

[Peter G.]

Sorry, u is initial velocity. The balls, throughout the collision, change momentum, because they change their velocity, not their mass. The v represents the velocity after the collision, the final velocity of the balls, and u the velocity before the collision, the initial velocity.

p is momentum, = mv

Impulse is the rate of change in momentum:

Change in Momentum = (mv - mu)

Rate of Change in Momentum (Impulse) = F x t = (mv - mu)

so F = (mv - mu) / t, just a simple rearrangement for Impulse - another way of writing Newton's Second Law: F = ma.

 

[teggenspiller]

i just don't get how it has anything to do ith Newtons law. and since it does, as you say, i don't get how to relate it to it without someone having to tell me. i know some people just 'get' this stuff nad some dont. i just can't imagine myself reading this nad being like OH HEY THIS IS TOTALLY NEWTONS 2nd LAW WRITTEN IN ANOTher FORM.

 

[Peter G.]

I see. Sometimes it's hard for anyone, not just for you. I'm not any great physicist, I am just a student too and I have just learned this!

I'll try and show you how F = (mv - mu) / t is just another form of F = ma:

So, you are familiar with F = ma

All we are doing here is substituting the value of a for the meaning of acceleration: The definition of acceleration is the rate of change in velocity.

An object is traveling say, at 10 m/s. It accelerated to 20 m/s in 2 seconds. Acceleration is change in velocity over time: (20 - 10) / 2 = 5 m/s²

All we did above is, we got the final velocity, 20 m/s, and subtracted the initial velocity, 10 m/s, from the final velocity and divided by the time it took for that to happen. Simply to see how much it changes velocity in 1 second.

So, in a case like the one above, to find acceleration we do: (v - u) / t

acceleration = (v - u) / t

If acceleration is equal to the expression above, don't you think it is fair to say that, whenever we see a, we can change the letter a for that expression?

That's what we are doing, look:

F = ma
F = m (v - u) / t
F = (mv - mu) / t

Does that help?

 

[teggenspiller]

oh wow. yes it indeed is ma. didnt see that coming

 

[Peter G.]

Cool! Happy you got it