Really general question regarding basic Momentum

[AJKing]

My instruction material keeps talking about how "The Law of Conservation of Momentum" is only applicable in isolated systems, without friction or other dissipative forces.

However, in the same breath it will go on to say that Momentum is always conserved in collisions.

Would someone mind describing this in a little more depth?

And, while I'll surely read any materials you link me to on the matter, my entire course is sans human contact, so communicating would be rad :).

 

[bjd40@hotmail.com]

momentum is always conserved in collisions. we do not consider dissipative forces here only because when we calculate speed or velocity to compute momentum we actually consider its value just before and just after collision. here friction does not come into play. if we do consider the speed before or after a time interval before or after collision and use it to compute the momentum to verify or use the conservation of momentum principle there should not be any frictional loss, such that the speed remains same until the collision takes place. that is why the term 'without friction' is used.

 

[tiny-tim]

Hi AJKing!

… Momentum is always conserved in collisions.

Yes, https://www.physicsforums.com/library.php?do=view_item&itemid=53"

(and https://www.physicsforums.com/library.php?do=view_item&itemid=313")

This is because "collision" is always understood to mean that the change can be assumed to happen in an infinitesimally short time, and so the https://www.physicsforums.com/library.php?do=view_item&itemid=75" by any ordinary force (such as friction or gravity) can be assumed to be zero.​

eg when two bodies collide in mid-air, there are no external impulses (and only one external force, that of gravity) … external to the two-body system, that is … so momentum in all directions (and also angular momentum) is conserved.

when one body hits a fixed object, and bounces off, or rotates around it, the impulse from the fixed object is external to the one-body system, so the momentum of the body is not conserved, although the angular momentum about the point of contact will be conserved, since the impulse has no moment about that point

 

[sankalpmittal]

Hi AJKing! Yes, https://www.physicsforums.com/library.php?do=view_item&itemid=53"

(and https://www.physicsforums.com/library.php?do=view_item&itemid=313")

This is because "collision" is always understood to mean that the change can be assumed to happen in an infinitesimally short time, and so the https://www.physicsforums.com/library.php?do=view_item&itemid=75" by any ordinary force (such as friction or gravity) can be assumed to be zero.​

eg when two bodies collide in mid-air, there are no external impulses (and only one external force, that of gravity) … external to the two-body system, that is … so momentum in all directions (and also angular momentum) is conserved.

when one body hits a fixed object, and bounces off, or rotates around it, the impulse from the fixed object is external to the one-body system, so the momentum of the body is not conserved, although the angular momentum about the point of contact will be conserved, since the impulse has no moment about that point

Yeah , if external force is neglected then total momentum before collision is same as after the collision

m₁u₁+m₂u₂=m₁v₁+m₂v₂

Or p₁=-p₂

 

[rwisz]

The Law of Conservation of Momentum states that in a closed and isolated system, the total momentum before an event (such as a collision) is equal to the total momentum after the event. This means that the total amount of momentum in the system remains constant and is not affected by any internal forces or external forces such as friction.

In real-world situations, it is difficult to find truly isolated systems without any dissipative forces such as friction. However, the concept of conservation of momentum still holds true in these situations, but with some modifications. In the case of collisions, we can still apply the law of conservation of momentum, but we have to take into account the external forces such as friction that may act on the system. This means that the total momentum of the system may change, but the total amount of momentum before and after the collision will still be equal.

To understand this concept in more depth, it is important to understand the difference between elastic and inelastic collisions. In an elastic collision, the total amount of kinetic energy is conserved, meaning that the objects involved bounce off each other without losing any energy. In this case, the law of conservation of momentum applies without any modifications. However, in an inelastic collision, some of the kinetic energy is lost due to dissipative forces such as friction, and therefore the total momentum of the system may not be conserved. In this case, we have to take into account the external forces and the loss of kinetic energy when applying the law of conservation of momentum.

I hope this explanation helps to clarify the concept of conservation of momentum and its applicability in real-world situations. If you would like to further explore this topic, I would recommend reading about the different types of collisions and their effects on momentum, as well as the concept of impulse and how it relates to momentum. Additionally, there are many online resources and videos available that can provide more detailed explanations and examples of momentum and its conservation.