# Conservation of Momentum: Union & Separation Law

• azizlwl
In summary, the conservation of momentum states that the total momentum of a system remains constant over time. However, at the end of the swing in a ballistic pendulum test, the velocity is zero and thus the momentum is also zero. This is because momentum is transferred into the stand and then into the Earth. The conservation of momentum only applies during and after union/separation of items and not in other instances. This law only holds when there is no external force present. In solving problems such as a ballistic pendulum, conservation of momentum is necessary because a lot of energy is expended during the process. This is due to the fact that the collision between the bullet and the pendulum is inelastic and kinetic energy is not conserved. Thus,
azizlwl
In a ballistic pendulum test, the mv is added to the system and that total remains constant over time. This what conservation of Momentum states. But at the end of the swing velocity is zero. Thus no momentum. What is conserved here?

As in energy total energy always remains the same. In momentum its nor true even in ordinary motion with resistance, the velocity decreases thus momentum.
To me it is just a Law of Union/Separation. After Union/Separation its not use/applicable.

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The momentum is transferred into the stand and then into the earth.

Thank you aziz and khashishi ,I agree with both of your answers with what everyone may know that momentum is conserved.With a rule that states that "momentum before is equal to momentum after".
If anyone is inquiring about energy then the rules that YES energy is also conserved but in a different form.

YES it is.The rules states that momentum before is equal to momentum after.√

Thank you. I mean here i see the Conservation of Momentum only applies to union and separation of items. In other instances other laws apply. When a body moves, it follows the Newton's first Law. When a body moves and changes direction or/and magnitude, Newton 2nd law is used and sometimes we use KE and PE, conservation of energy.

Thus COM only applies only JUST before the union/separation and JUST after that.
Conservation law should be at any instances/places.

Conservation of momentum holds only as long as there is no "exernal" force. The force of gravity is an external force.

Khashishi said:
The momentum is transferred into the stand and then into the earth.

Yes. As the pendulum rocks back and forth, the Earth rocks back and forth in the opposite direction. Momentum is always conserved, at all times.

HallsofIvy said:
Conservation of momentum holds only as long as there is no "exernal" force. The force of gravity is an external force.

Thank you
I agree that with no external force, means there's no change in momentum. Total sum of momentum remains constant.
I still cannot figure out why we need conservation of momentum in solving eg. ballistic pendulum.
Initial mv=final mv then we get velocity. Then KE to PE.
Why not just KE incoming bullet to PE without resorting to COM if we assume no energy expended in the process(I've been making this error frequently). Conservation of energy is intuitively easy for accept.

azizlwl said:
Thank you
I agree that with no external force, means there's no change in momentum. Total sum of momentum remains constant.
I still cannot figure out why we need conservation of momentum in solving eg. ballistic pendulum.
Initial mv=final mv then we get velocity. Then KE to PE.
Why not just KE incoming bullet to PE without resorting to COM if we assume no energy expended in the process(I've been making this error frequently). Conservation of energy is intuitively easy for accept.

But a lot of energy is expended in the process. When the bullet collides with the pendulum, it sticks to the pendulum, and that's an inelastic collision. Kinetic energy is not conserved. Most of the kinetic energy of the bullet is turned into heat and a little of it is turned into sound.

ok now i understand why we have to resort to COM.

In a collision,

$mv_{in}=mv_{out}$ where no external forces involve.

$KE_{in}\geq KE_{out}$

So applying COM is the most ideal transformation for a collision.

## 1. What is the Conservation of Momentum: Union & Separation Law?

The Conservation of Momentum: Union & Separation Law is a fundamental principle in physics that states that the total momentum of a closed system remains constant over time, regardless of any internal changes or interactions within the system.

## 2. How is the Conservation of Momentum: Union & Separation Law applied?

The Conservation of Momentum: Union & Separation Law is applied in various areas of physics, including mechanics, fluid dynamics, and thermodynamics. It is used to analyze and predict the motion and interactions of objects and systems.

## 3. What is the difference between the Union and Separation aspects of the law?

The Union aspect of the Conservation of Momentum: Union & Separation Law refers to the principle that the total momentum of a system is conserved when two or more objects come together to form a larger system. The Separation aspect refers to the principle that the total momentum of a system is also conserved when a larger system breaks apart into smaller objects.

## 4. Is the Conservation of Momentum: Union & Separation Law always applicable?

Yes, the Conservation of Momentum: Union & Separation Law is a universal law that applies to all closed systems, regardless of size, shape, or type of interaction. It is one of the most fundamental principles in physics.

## 5. Can the Conservation of Momentum: Union & Separation Law be violated?

No, the Conservation of Momentum: Union & Separation Law has been extensively tested and has been found to hold true in all observed scenarios. It is considered a law of nature and cannot be violated under normal circumstances. Any apparent violations can be explained by external factors, such as external forces or energy loss.

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