Questions about conservation of momentum

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In a closed system with no external forces, momentum is conserved during collisions, meaning the total momentum before and after the collision remains constant. If one object accelerates while another moves at a constant speed, an external force is present, which affects momentum conservation. During a collision, forces act on the objects, but according to Newton's third law, the total change in momentum is zero. The momentum conservation equation m1u1 + m2u2 = m1v1 + m2v2 applies only when no external forces are acting. Thus, understanding the conditions of external forces is crucial for analyzing momentum in collisions.
sgstudent
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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 :smile:
 
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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 :smile:

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).
 

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