Grade 12th PassGeneral Physics
proof of conservation of momentum? please answer fast tommorow is my exam
proof of conservation of momentum? please answer fast tommorow is my exam
1 Answer
Arun
First off momentum = mass x velocity. You can prove the conservation of momentum (i.e. that it stays the same unless a force acts upon a body) from Newton's laws.
Force = mass x acceleration
Acceleration is the change of velocity over time so:
Force = mass x ((velocity1 - velocity2) / time)
Or:
Force = ((mass x velocity1) - (mass x velocity2)) / time
Because mass x velocity is momentum, we can say:
Force = (momentum1 - momentum2) / time
Or:
Force x time = momentum1 - momentum2
Meaning a change in momentum is caused by force multiplied by time. If there is no force (or no time for it to be applied), the left hand side of the equation is zero, meaning momentum1 = momentum2 (and therefore there is no change in momentum).
Therefore, without a force being applied for a period of time, momentum is conserved.
Force = mass x acceleration
Acceleration is the change of velocity over time so:
Force = mass x ((velocity1 - velocity2) / time)
Or:
Force = ((mass x velocity1) - (mass x velocity2)) / time
Because mass x velocity is momentum, we can say:
Force = (momentum1 - momentum2) / time
Or:
Force x time = momentum1 - momentum2
Meaning a change in momentum is caused by force multiplied by time. If there is no force (or no time for it to be applied), the left hand side of the equation is zero, meaning momentum1 = momentum2 (and therefore there is no change in momentum).
Therefore, without a force being applied for a period of time, momentum is conserved.
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