Momentum Conservation & External Force: Explained with an Example

In summary, when an external force acts on a system, the momentum is no longer conserved because the velocity of the system changes. This can be seen in the example of a billiards table where applying a force causes the ball to move and changes the momentum. The only time momentum is conserved is when there is no external force acting on the system. The conservation of momentum is derived from the equation dP/dt = 0 = F (external), which states that the change in momentum over time is equal to the external force acting on the system. The conservation of momentum holds true as long as all external forces are taken into account.
  • #1
Gurasees
50
1
Why ain't momentum conserved when external force acts on the system?
Please explain with an example.
 
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  • #2
Momentum is the mass of the object times the velocity. Force is defined as the mass of an object times the change in velocity. If the system is exposed to an external force, the velocity of the system changes. Since the velocity of the system changes, so too does the momentum hence it is no longer conserved.

If your system is a single billiards table with one ball and no momentum, applying a force to the table will cause the ball to move.
 
  • #3
Why do you think it should be conserved? Do you know how conservation of momentum is derived?
 
  • #4
weirdoguy said:
Why do you think it should be conserved? Do you know how conservation of momentum is derived?
dP/dt = 0 = F (external). hence P is constant.
 
  • #5
Gurasees said:
dP/dt = 0 = F (external). hence P is constant.
Only time this is true is the case Fexternal = 0, hence no external force.
 
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Likes sophiecentaur and Nugatory
  • #6
Gurasees said:
Why ain't momentum conserved when external force acts on the system?
Momentum is conserved in a system that includes all the sources of your 'external force'.
That is the basis of COM. There is no contradiction or exception.
 

Related to Momentum Conservation & External Force: Explained with an Example

1. What is momentum conservation?

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

2. How is momentum conserved in an example of two objects colliding?

In a collision between two objects, the total momentum of the system before the collision is equal to the total momentum after the collision. This means that the sum of the individual momenta of the two objects before the collision is equal to the sum of their individual momenta after the collision. This is known as the law of conservation of momentum.

3. What is an external force?

An external force is a force that acts on a system from outside of the system. It can change the momentum of the system by either increasing or decreasing its total momentum.

4. How does an external force affect momentum conservation?

An external force can affect momentum conservation by changing the total momentum of a system. If an external force acts on a system, the system's total momentum will change and momentum conservation will no longer hold true. However, the law of conservation of momentum will still apply if the external force can be identified and accounted for in the calculations.

5. Can momentum conservation be violated?

No, momentum conservation is a fundamental law of physics and cannot be violated. In any closed system, the total momentum will always remain constant. If it appears that momentum conservation is not holding true, it is likely due to an external force that was not accounted for in the calculations.

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