# What is conserved in the system?

• PhyIsOhSoHard
In summary, In an inelastic collision between two balls attached to a rod, the mechanical energy is not conserved due to a decrease in kinetic energy. The conservation of momentum depends on whether the second ball can be considered an external force. The moment of inertia may also affect the rotation of the rod. It is safe to assume that there is conservation of angular momentum about the center of mass, as the added weight of the second ball balances out the uneven weight distribution and maintains angular momentum during rotation.
PhyIsOhSoHard

## Homework Statement

A ball is attached to a rod at one end. The rod rotates about a point at the other end.
A second ball hits the first ball with a horizontal velocity u, and then the two balls travel together with the same horizontal velocity v. The collision is inelastic.

What is conserved in the system after the collision?
The mechanical energy? Horizontal momentum? Angular momentum about the CM? Or angular momentum about the rod's axis?

## The Attempt at a Solution

I do not believe the mechanical energy is conserved. Since this is an inelastic collision the kinetic energy after the collision is less than before, thus the mechanical energy is not conserved.

I'm not sure if the momentum is conserved. In my book it says the momentum is conserved if the external forces can be neglected but I'm not sure if the second ball is an external force or not?

Are there OTHER external forces of roughly equal magnitude acting upon the second ball+pendulum system that actively prevents some type of motion to occur? (Hint: Look at the ceiling for a clue!)

arildno said:
Are there OTHER external forces of roughly equal magnitude acting upon the second ball+pendulum system that actively prevents some type of motion to occur? (Hint: Look at the ceiling for a clue!)

The moment of inertia? It makes it harder for the rod to rotate around the point on the ceiling?

Is it correct to assume that there is conservation of angular momentum about the CM? Since the added weight (when the two ball join together) thus balance out the uneven weight by moving the center of mass thus the rotation has angular momentum conservation?

The angular momentum about the CM is not conserved because the two balls travel together with the same horizontal velocity v, so the distance between the CM and the axis of rotation changes.

The only thing that remains constant in this system is the angular momentum about the rod's axis. This is because there are no external torques acting on the system, so the total angular momentum must be conserved. This means that the sum of the angular momentum of the two balls before the collision must be equal to the angular momentum of the two balls after the collision. The angular momentum about the rod's axis is calculated by multiplying the angular velocity of the system by the moment of inertia about the rod's axis. Since the angular velocity and moment of inertia do not change during the collision, the angular momentum about the rod's axis remains constant.

## 1. What do scientists mean by "conserved" in a system?

When scientists refer to something being "conserved" in a system, they are referring to a physical quantity that remains constant over time. This means that the quantity cannot be created or destroyed, but can only change form or be transferred between different parts of the system.

## 2. Why is conservation important in science?

Conservation is important in science because it allows us to make accurate predictions and understand the behavior of a system. By identifying what is conserved in a system, we can better understand how energy, matter, and other physical quantities are transferred and transformed within the system.

## 3. What are some examples of conserved quantities in a system?

Some common examples of conserved quantities in a system include energy, momentum, and mass. For example, in a closed system, the total amount of energy will remain constant even if it is transferred between different forms, such as kinetic energy and potential energy.

## 4. How do scientists determine what is conserved in a system?

Scientists determine what is conserved in a system by using the principles of conservation laws, which are based on fundamental physical laws and theories such as Newton's laws of motion and the laws of thermodynamics. They also use experimental evidence and mathematical models to validate their findings.

## 5. Can anything be conserved in a system?

No, not everything can be conserved in a system. In order for something to be conserved, it must follow certain fundamental laws and principles. For example, the law of conservation of energy states that energy cannot be created or destroyed, but the law of conservation of unicorns does not exist because unicorns do not follow any known physical laws or principles.

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