# Momentum of a System and External Forces

• gibberingmouther
In summary, Pearson is telling me that the external forces on a system whose momentum we're studying will not affect whether we can obtain a decent approximation of the momenta of the objects using the conservation of momentum principle.
gibberingmouther
So Pearson is telling me that, basically, the ratio of internal to external forces and the briefness of the time interval is what determines whether the external forces on a system whose momentum we're studying will affect whether we can obtain a decent approximation of the momenta of the objects using the conservation of momentum principle.

Specifically, in a car collision situation where the drivers are pushing their breaks when the cars hit: "The collision between the cars involves brief forces that are much stronger than the forces of friction exerted on the cars by the road. Thus if we apply conservation of momentum to a very thin “slice” of time surrounding the collision, the total momentum of the two cars will not change very much and will be approximately conserved."

This makes intuitive sense to me, that the tiny force of rolling friction for say a pool ball collision isn't going to affect momentum conservation much. But I'm trying to find a F(internal)/F(external) expression of some kind to mathematically back up this idea, and I can't find anything.

Does J = F(net average) * delta t = delta p have any bearing on this?

I mean, in the sense of the fact that the breaking won't have a huge impact on the cars' velocities, this makes sense, but I'm looking for a mathematical expression to back it up. Is there one?

The very fact that cars do not simply bounce off each other without any deformations shows you that car crashes are usually not described by elastic scattering processes. This would be great since then crashes wouldn't damage the cars at all ;-))).

[Edit: This argument is wrong. Momentum is indeed conserved in the inelastic collision, but of course not energy. @hilbert2 is right!]

Last edited:
But isn't the elasticity of a collision related to the conservation of energy, not that of momentum?

That's indeed true.

hilbert2
Thanks for correcting.

gibberingmouther said:
But I'm trying to find a F(internal)/F(external) expression of some kind to mathematically back up this idea, and I can't find anything.

The ratio between braking distance and crush zone should be a good approximation.

gibberingmouther

## What is momentum?

Momentum is a physical quantity that describes the motion of a system. It is defined as the product of an object's mass and velocity.

## What is the law of conservation of momentum?

The law of conservation of momentum states that in a closed system, the total momentum remains constant. This means that the initial momentum of a system will be equal to the final momentum, even if external forces act on the system.

## How do external forces affect the momentum of a system?

External forces can change the momentum of a system by causing it to accelerate or decelerate. If the external force is in the same direction as the system's velocity, the momentum will increase. If the external force is in the opposite direction, the momentum will decrease.

## What is an elastic collision?

An elastic collision is a type of collision in which the total kinetic energy of the system is conserved. This means that the objects involved in the collision bounce off each other without any loss of energy.

## How can momentum be calculated?

Momentum can be calculated by multiplying an object's mass by its velocity. The formula for momentum is p = m * v, where p is momentum, m is mass, and v is velocity. It is important to note that momentum is a vector quantity, meaning it has both magnitude and direction.

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