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micronat micronat
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9 years ago
Two carts collide, and how do yo know that there is a conservation of momentum?
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wrote...
9 years ago
It is a law, the momentum is always conserved. Do the Math

Don't get mixed up between KE conservation and momentum conservation, they are different.

The Law of conservation of Momentum states that momentum is never lost.

As for the KE conservation, Kinetic Energy is always conserved for an elastic collision. Likewise, KE is not conserved in an inelastic collision

KE stands for Kinetic Energy
wrote...
9 years ago
If you know the mass of each cart and you know the velocity of each cart before and after the (elastic) collision, you can show that

m1vb + m2vb = m1va + m2va

where b indicates before and a indicates after
wrote...
9 years ago
say Pf is the final momentum (momentum of the carts after collision), and Pi the initial momentum (momentum before collision). Pf should be equal to Pi, to withhold to the law for conservation of momentum. since p = mv, put in your values of mass and velocity of each cart and solve. you will see it is conserved with a little bit of error ( dont expect the final and initail values to be exactly equal)
wrote...
9 years ago
Conservation of momentum holds true if the following is true:"The net-impulse due to all external forces equals zero."

How does this become true:
1. There are no forces caused by objects external to the system.  E.G. two astronauts are drifting in deep space toward each other, collide, and either catch each other, bounce off each other, or push against each other.  Gravity is zero and air drag is zero, thus the only forces are the interaction forces of the astronauts.

2. All external forces add up to zero.  For instance: the normal force is equal and opposite to gravity, thus there is a force balance and the objects remain in the horizontal plane.

3. The collision occurs so quickly, that there isn't enough time for the external forces to have a net-impulse.  E.G. two carts are slowing down due to friction, and then have a collision, and travel in opposite directions.  Friction continues to act after the collision.  Friction acts before and after the collision, but since the collision happened quickly, the impulse due to friction during the collision is negligible.

What if the impulse due to external forces isn't negligible? Well, you need to find the net impulse due to external forces, and include that as an extra source of momentum in conservation of momentum equation.  The impulse-momentum theorem proves this.
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