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UMath1

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- Thread starter UMath1
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UMath1

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- #2

A.T.

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In an isolated system as seen from an inertial frame of reference.conservation of momentum dictates that momentum is still conserved.

- #3

UMath1

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wouldn't this meet both those criteria

- #4

BvU

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- #5

A.T.

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What is your isolated system?wouldn't this meet both those criteria

- #6

UMath1

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The car and the tree

- #7

BvU

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Plus the earth underneath - or else the tree would fall over

- #8

UMath1

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Right. The car, tree, and earth underneath.

- #9

UMath1

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So how is momentum conserved?

- #10

BvU

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(just as much as when you accelerate from standstill for this unhealthy experiment, only in the opposite direction)

- #11

UMath1

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- #12

BvU

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The parts of the car are welded, screwed, glued etc. together. The sum of their momenta before IS the momentum of the car.

- #13

UMath1

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After the collision, the change is that motion of the parts of the car are in random directions and there is no net motion in any given direction, so the car has no velocity and has all its kinetic energy transformed into heat, the random motion of the microscopic particles making up the car.

My question is that why is momentum not transferred from the macroscopic motion of the car to the random microscopic motions of the particles making up the car like kinetic energy is?

- #14

jbriggs444

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Because momentum is conserved. The earth moves as a result of the collision.My question is that why is momentum not transferred from the macroscopic motion of the car to the random microscopic motions of the particles making up the car like kinetic energy is?

In every single interaction among all the bazillions of particles that constitute the car and the earth, momentum is conserved in that interaction. Momentum is an additive property -- the momentum of the whole is the sum of the momenta of the parts. If the momentum of all of the particles is otherwise randomized, the law of conservation of momentum assures us that there is still a bias in the direction of the original bulk momentum so that total momentum is conserved. ∑mv is conserved.

Kinetic energy is also conserved in every tiny interaction. But there is no direction to kinetic energy. The law of conservation of energy only assures us that Σ½mv

- #15

Nugatory

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My question is that why is momentum not transferred from the macroscopic motion of the car to the random microscopic motions of the particles making up the car like kinetic energy is?

The energy is independent of the direction of motion (no matter what direction a particle is moving, its kinetic energy will be ##mv^2/2##) but momentum is not (a particle moving to the left will have momentum ##-mv## while a particle moving to the right will have momentum ##mv## - the net momentum of the two particles is zero).

Momentum and energy must both be conserved in the collision. Thus, after the collision all the collision fragments will collectively have the same net momentum as the original projectile. Even if the collision were to completely vaporize both objects so all that all that is left is a cloud hot gas, on average a few more particles will be moving more in one direction than the other so there will be some net momentum and the cloud as a whole will be moving. (You can see this in online videos of high-speed projectiles penetrating armor plate - a flare of fast-moving incandescently hot gas bursts out the back side, obviously carrying substantial momentum).

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The car and the tree do not form an isolated system. There is a very large external force exerted on the car-tree system.The car and the tree

What is the mass of the earth? How much would you expect the earth's velocity to change? Do you think this is measurable?Right. The car, tree, and earth underneath.

- #17

UMath1

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No its very insignificant owing to the large mass of the earth.

- #18

UMath1

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- #19

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Yeswouldn't momentum still be conserved if you considered the closed system to be the earth and the car?

Based on the answers you have received so far, what do you think? Can you justify your answer using Newtons 3rd law?Where would the momentum of the car be transferred to then?

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