Conservation of Energy and Momentum Lie

[arbitrator]

Conservation of Energy and Momentum "Lie"

Homework Statement

Each marble on a Newtonian demonstrator has a mass m, and the 1st marble hits the others with a velocity v.
1. Using the law of conservation of momentum - determine the velocities for:
a. Two marbles moving up
b. Three marbles moving up
c. Four marbles moving up
2. Using the law of conservation of energy - show that the scenarios a-c violate this law.
3. Describe the "lie" in stating that these laws apply and can solve problems.
(assume there is no air resistance and that the marbles are perfectly elastic)

Homework Equations

W_in + PE_i + KE_i = W_out + PE_f + KE_f ( KE and PE are kinetic and potential energy respectivley)
m₁v₁ = m₂v₂

The Attempt at a Solution

So far I have worked through numbers 1 and 2, here is an example of my work:
Using conservation of momentum
a) mv₁ = mv₂ + mv₂
mv₁ = 2mv₂
v₁ = 2v₂
Using conservation of energy
a) 0.5mv₁² = 0.5mv₂² + 0.5mv₂²
0.5mv₁² = mv₂²
mv₁² = 2mv₂²
v₁² = 2v₂²
v₁ = (2)^1/2v₂
Note: because the mass of each marble is the same, I use m for all the masses; because the velocities of the 1st marble and the other marbles are different, I use v with a subscript to indicate which velocity it is
So I've found that when I use each law to find the velocity of the other marbles, I get different results. My task is to find out why and my teacher instructed me to use the internet. Using what I've learned so far won't help, since all we've covered is motion, forces, energy, and momentum.

 

[Chi Meson]

Well you're off to a good start. The rest of the assignment is totally conceptual. It helps if you say or write out a few statements: "Conservation of momentum is never violated," and "Conservation of energy is never violated." (let's ignore quantum fluctuations for now).

For any situation, both of these laws must be satisfied, not one or the other. In the "http://www.walter-fendt.de/ph14e/ncradle.htm" " demonstration, what is the outcome that will satisfy both laws at the same time?

And what do your mathematical "disagreements" ( in a, b, and c ) say about the possibility of those outcomes?

 

[arbitrator]

In the "Newton's Cradle" demonstration, what is the outcome that will satisfy both laws at the same time?

Would these outcomes be the number of marbles that move up when 1 marble hits the series of marbles? In that case the outcome would be 1 marble moving up when 1 marble hits the series.

But if we change the problem to say that a marble with a mass of m hits a marble with a mass of 2m. As far as the two laws apply, is this problem the same as the original?

conservation of momentum
mv₁ = 2mv₂
v₁ = 2v₂

conservation of energy
0.5mv₁² = 0.5*2mv₂²
mv₁² = 2mv₂²
v₁² = 2v₂<sup>2[/SUP
v₁ = 21/2v₂

The velocities are the same as those calculated in the original problem, but still unequal. I'm not sure if I'm thinking along the right lines, but is there some sort of kinetic energy transfer? So that when using the law of coservation of energy I should instead write it as: KE_i = KE_f + W_out rather than KE_i = KE_f because the kinetic energy of the 1st marble and more massive marble is not the same? If so then what is the W_out?</sup>