# When the conservation of linear momentum is violated

• fog37
In summary, the conservation of linear momentum applies when the net external force is negligible and is valid for perfectly elastic, partially elastic, and totally inelastic collisions. For perfectly elastic collisions, the mechanical energy is also conserved. In the case of an inelastic collision where the system does not move and the total final momentum is zero, there is a violation of the conservation of momentum due to the dissipation of mechanical energy in crushing the cars. However, in laboratory experiments, it is important to calculate the total momentum before and after the collision to account for any external forces that may affect the conservation of momentum. Inelastic collisions involve sticking, deformation, and loss of mechanical energy, but the conservation of total momentum should still hold as long as the
fog37
Hello Forum,

The conservation of linear momentum is applicable when the net external force is zero or negligible compared to the internal forces. This principles is applicable to perfectly elastic, partially elastic and totally inelastic collisions.
But only for perfectly elastic collisions the mechanical energy (KE+PE) is conserved.

That said, what happens when two cars collide in a crash in an inelastic collision and the system does not move, i.e. total final momentum is zero? There is clearly a violation of the conservation of momentum, correct? All the mechanical energy is dissipated into crushing the cars. That said, I thought that the conservation principle applied to inelastic collision without problem, regardless of the deformation and loss of mechanical energy involved...

Thanks,
fog37

fog37 said:
what happens when two cars collide in a crash in an inelastic collision and the system does not move, i.e. total final momentum is zero?

In that case, before the collision, the two cars must have momenta that are equal in magnitude and opposite in direction. The vector sum of the two initial momenta is zero.

(This ignores effects from friction between the cars and the road, of course.)

Thank you.

So, total momentum before the collision is equal to total momentum after the collision (as long as the external forces don't eat up too much of the momentum). That is why, in laboratory experiments, it is important to calculate the total momentum right before the collision and right after the collision. Otherwise the total momentum will start changing, due to the presence of friction (external force acting for a long enough time).

Inelastic collisions imply sticking between the objects involved in the collision, deformation, loss of mechanical energy. The deformation requires energy (hence the loss of mechanical energy). But the conservation of total momentum should still be valid (if the net external force is zero).

thanks,
fog37

## 1. What is the conservation of linear momentum?

The conservation of linear momentum is a fundamental law of physics that states that the total momentum of a closed system remains constant over time. This means that the total amount of motion in a system will not change unless acted upon by an external force.

## 2. How can the conservation of linear momentum be violated?

The conservation of linear momentum can be violated if there is an external force acting on the system, causing a change in the total momentum. This can happen in situations such as collisions, explosions, or when an object is acted upon by an unbalanced force.

## 3. What are the consequences of violating the conservation of linear momentum?

If the conservation of linear momentum is violated, it means that the laws of physics are not being followed and the total momentum of the system is not conserved. This can lead to unexpected and often chaotic behavior in the system, making it difficult to predict the outcome of a situation.

## 4. Can the conservation of linear momentum be violated in everyday life?

Yes, the conservation of linear momentum can be violated in everyday life, for example in car accidents or sports where objects collide with each other. However, in most cases, the violation is very small and not noticeable, as the external forces involved are typically much smaller than the total momentum of the system.

## 5. How is the conservation of linear momentum used in science and engineering?

The conservation of linear momentum is a crucial principle in many areas of science and engineering, including mechanics, thermodynamics, and fluid dynamics. It is used to analyze and predict the behavior of complex systems, such as rockets, satellites, and even the entire universe. Without this law, it would be much more difficult to understand and manipulate the physical world around us.

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