# Confusion about conservation of energy vs. momentum

• B
Gold Member

## Main Question or Discussion Point

Hello,

A dude I'm discussing momentum and kinetic energy with says this:
"Place two masses in deep space, the only gravitational attraction is from each other.
One of the masses is ten kilograms and the other is one kilogram.
From Newton's Third Law we know that the mutual attraction is equal in both directions.
From F = ma we know that the acceleration of the one kilogram will be ten times greater than the acceleration of the 10 kilograms.
After a period of time the one kilogram will be moving 10 times faster than the 10 kilograms. When the one kilogram is moving one meter per second the 10 kilograms will be moving .1m/sec.

Then ½ *10kg *.1 m/sec * .1 m/sec = .05 joules
And ½ * 1 kg * 1 m/sec* 1 m/sec = .5 joules

Energy is not conserved
."

This guy say that if you have a 10kg steel ball, here at earth, that is pushed into motion at 0.1m/s and spend all its momentum to put a 1kg. steel ball into motion, the 1kg ball would have a velocity of 1m/s, but with that mass and velocity, the kinetic energy is 10 times greater than the kinetic energy of the 10kg ball before impact.
Why does he say that energy isn't conserved? I assume it must be a misunderstanding in how he calculate the results, even he is right about conservation of momentum.

Vidar

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phinds
Gold Member
2019 Award
Why does he say that energy isn't conserved?
Why don't you just ask him?

mjc123
Homework Helper
First question: What is the change in gravitational potential energy?
Second question: That doesn't happen, because it violates energy conservation. Set up equations to express the conservation of momentum and energy, and solve for v1 and v2. There are only two possible solutions; one is the initial condition and the other is the condition after collision. You cannot arbitrarily specify that the first ball must "spend all its momentum" to put the other ball in motion.

Hello,

Then ½ *10kg *.1 m/sec * .1 m/sec = .05 joules
And ½ * 1 kg * 1 m/sec* 1 m/sec = .5 joules

Energy is not conserved
."
Energy conservation does not mean that the two balls must have the same energy.
"Conservation" of some quantity in Physics means that the value of the quantity at some time t1 is the same as the value as another time, t2.
If you calculate the total energy of the system when it starts moving and at a later time, they will have the same energy. You need to consider potential energy of the system and the sum of the kinetic energies to get the total mechanical energy.