# Questions about conservation of momentum

• sgstudent
In summary, "No external force" means that all objects travel at constant velocity between collisions and the vectorial sum of the momenta of all the objects is the same before and after the collision, assuming the only interaction is collisions.
sgstudent
What does having no external force on a closed system mean? For example if I have 2 objects colliding. One travels at a constant speed while the other travels with a constant acceleration. In this case is an external force being applied on the system?

If so, only the m1u1+m2u2=m1v1+m2v2 can be used if the two objects have a constant velocity?

Also, during the collision won't there be a force being applied on the object? So how would momentum be conserved? During the collision the formula F=change in mv/time is used. So is the conservation only after this collision?

Thanks for the help

An object can't accelerate without some applied force. Momentum isn't conserved if you have an external force on the system. Actually, the change in total momentum is equal to the external force.

Khashishi said:
An object can't accelerate without some applied force. Momentum isn't conserved if you have an external force on the system. Actually, the change in total momentum is equal to the external force.

Oh, you mean the change in momentum is equal to the external force multiplied by the duration of it?

So if there is an external force, how will the collision be like? Or are we unable to solve for the final velocities.

Thanks :)

sgstudent said:
What does having no external force on a closed system mean? For example if I have 2 objects colliding. One travels at a constant speed while the other travels with a constant acceleration. In this case is an external force being applied on the system?

If so, only the m1u1+m2u2=m1v1+m2v2 can be used if the two objects have a constant velocity?

Also, during the collision won't there be a force being applied on the object? So how would momentum be conserved? During the collision the formula F=change in mv/time is used. So is the conservation only after this collision?

Thanks for the help

If the only interactions that you are considering are collisions, then "no external force" means that all objects travel at constant velocity between collisions.

During the collision, you're certainly right that there are forces involved. But Newton's third law implies that the total change in momentum due to a collision is zero. So the vectorial sum of the momenta of all the objects is the same before and after the collision. (Assuming once again that the only interaction is collisions).

Having no external force on a closed system means that there are no forces acting on the system from outside. In your example, the two objects colliding would be considered a closed system if there are no external forces acting on them. This means that the total momentum of the system will remain constant before and after the collision.

In the case where one object travels at a constant speed and the other with constant acceleration, there is no external force being applied on the system. This is because the acceleration of the second object is caused by the interaction with the first object, and not by an external force.

The equation m1u1+m2u2=m1v1+m2v2 can be used regardless of whether the objects have constant velocity or not, as long as there are no external forces acting on the system.

During the collision, there will be a force being applied on the objects. However, this force is internal to the system and does not affect the conservation of momentum. The formula F=change in mv/time is used to calculate the force during the collision, but it does not affect the overall conservation of momentum.

The conservation of momentum holds true before, during, and after the collision. This means that the total momentum of the system will remain constant throughout the entire process, as long as there are no external forces acting on the system.

## 1. What is conservation of momentum?

Conservation of momentum is a fundamental principle in physics that states that in a closed system, the total momentum remains constant. This means that the total amount of momentum before a collision or interaction is equal to the total amount of momentum after the collision or interaction.

## 2. Why is conservation of momentum important?

Conservation of momentum is important because it helps us understand and predict the behavior of objects in motion. It is a fundamental law of nature that applies to all objects, from small particles to large celestial bodies. It is also the basis for many important concepts in physics, such as Newton's laws of motion and the principle of impulse and momentum.

## 3. How is conservation of momentum related to Newton's third law?

Newton's third law states that for every action, there is an equal and opposite reaction. This means that when two objects interact, they exert equal and opposite forces on each other. Conservation of momentum is related to this law because it shows that the total momentum of the system is conserved, even when there are equal and opposite forces acting on the objects.

## 4. Is conservation of momentum always true?

Yes, conservation of momentum is always true in a closed system where there are no external forces acting on the objects. In real-world situations, it may seem like momentum is not conserved because there may be external forces at play, such as friction or air resistance. However, these forces can be accounted for and the total momentum of the system can still be conserved.

## 5. How is conservation of momentum applied in real-world scenarios?

Conservation of momentum is applied in many real-world scenarios, such as collisions between objects, rocket propulsion, and sports. For example, in a car crash, the total momentum of the car and any other objects involved in the collision will remain constant. This can be used to calculate the velocities of the objects before and after the collision. In rocket propulsion, the conservation of momentum is used to explain how a rocket can move forward by expelling gas in the opposite direction. In sports, the conservation of momentum is used to analyze the movements of athletes and objects, such as a baseball being hit by a bat.

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