Momentum Conservation Between Two Masses

[Greatness]

I have been studying momentum and began believing that I understood it, but I began thinking...

Between two objects of the same mass, the first object will collide with another object (let's say the second object is not moving) and the momentum, in an isolated system, will be transferred, stopping the first object. However, why is this? Why is half of the momentum not transferred to object 1 and another to object 2?

 

[Nugatory]

You are right that momentum would be conserved if half the momentum ended up with each object (after the collision, they're both moving at speed v/2). But we also have to conserve energy, and in the elastic collision that you are describing no kinetic energy is lost to heat or crushing and deforming the colliding masses, so the kinetic energy after the collision has to be equal to the kinetic energy before.

Kinetic energy is given by ##E=\frac{mv^2}{2}##, and there's only one solution that conserves this quantity as well as the momentum ##p=mv## and that's the one in which the first object stops dead and the second ends up with all the momentum.

 

[Astrum]

I have been studying momentum and began believing that I understood it, but I began thinking...

Between two objects of the same mass, the first object will collide with another object (let's say the second object is not moving) and the momentum, in an isolated system, will be transferred, stopping the first object. However, why is this? Why is half of the momentum not transferred to object 1 and another to object 2?

In this situation, as has already been pointed out, the KE has to stay the same (elastic collision). But keep in mind that the total momentum of the system is always conserved, in elastic and inelastic collisions.

 

[nasu]

Between two objects of the same mass, the first object will collide with another object (let's say the second object is not moving) and the momentum, in an isolated system, will be transferred, stopping the first object. However, why is this? Why is half of the momentum not transferred to object 1 and another to object 2?

In a plastic (or completely inelastic) collision of two ball of equal mass this is how the momentum is distributed. They each have half of the original momentum. And they move together.
Conservation of momentum alone is not sufficient to determine the redistribution of momentum after collision.

 

[PJC01]

I can understand your confusion about the transfer of momentum between two objects. Momentum is a fundamental concept in physics that describes the quantity of motion an object has. In an isolated system, such as the scenario you described, the total momentum must remain constant before and after the collision. This is known as the law of conservation of momentum.

When two objects collide, there are various factors at play that determine how the momentum is transferred between them. One important factor is the mass of the objects. In a collision between two objects of equal mass, the momentum will be evenly distributed between them. This means that both objects will experience a change in velocity, with one slowing down and the other speeding up.

Additionally, the direction of the momentum also plays a role in how it is transferred between objects. In the scenario you described, the first object is colliding with the second object from a specific direction. This means that the momentum will primarily be transferred in that direction, resulting in the first object coming to a stop and the second object gaining momentum.

It is also important to note that momentum is a vector quantity, meaning it has both magnitude and direction. This means that even though the two objects may have the same mass, the direction of their momentum may be different due to their initial velocities.

In conclusion, the transfer of momentum between two objects is dependent on various factors such as mass, direction, and initial velocities. The law of conservation of momentum ensures that the total momentum remains constant in an isolated system, even if it is distributed differently between the objects involved in a collision. I hope this helps clarify any confusion you may have had about momentum conservation between two masses.