Can Conservation of Linear Momentum Estimate Velocities When External Forces Act?

[hangover]

Conservation of linear momentum holds if no external net force acts on the system. Therefore we use them to calculate the velocities of objects after collison.
However, my professor said that we can use the princple of Conservation of linear momentum to estimate the velocities of objects when there is external net force acting.
For example, pulling a string which is connected with a block. No friction and string has mass and it is loose at first. We can estimate the "initial" velocity of the block by Conservation of linear momentum:
(Mass of string)times(velocity string)=(Mass of block+Mass of string)times(initial velocity block)
He said that the conservation of linear momentum holds for an infinismal of time.
It is because Ft=mv-mu, when t is very small, even though there exists F, no impulse, then the momentum is conserved.
Is that right? Also interestingly, the answer of this approach is quite similar to that considering the block as individual objects,then F=ma, then v=at, then take t as 1sec.
Thx

 

[eljose79]

Thank you for sharing your thoughts on the principle of Conservation of linear momentum. Your professor is correct in saying that we can use this principle even when there is an external net force acting on the system.

The key idea behind the Conservation of linear momentum is that the total momentum of a system remains constant, regardless of any external forces acting on it. This means that if there is an external force acting on the system, it will result in a change in the momentum of one or more of the objects in the system, but the total momentum of the system will still remain the same.

In the example you mentioned, pulling a string connected to a block, the external force of pulling the string will result in a change in the momentum of the block. However, the momentum of the string will also change in the opposite direction, such that the total momentum of the system (block + string) remains the same. This allows us to use the principle of Conservation of linear momentum to estimate the initial velocity of the block.

As for your question about the time interval, it is correct that the principle of Conservation of linear momentum holds for an infinitesimal amount of time. This is because, in reality, there is no such thing as an instantaneous change in velocity or momentum. However, for practical purposes, we can consider the time interval to be very small, such as 1 second, and still use the principle to estimate velocities.

I hope this helps clarify your understanding of the Conservation of linear momentum. It is indeed a very useful principle in physics and is applicable in various situations, as your professor pointed out.

 

[astrokreng]

Yes, your professor is correct. The principle of conservation of linear momentum can be used to estimate velocities in cases where there is an external net force acting on the system, as long as the time interval is very small. This is because in such a short time interval, the change in momentum due to the external force is negligible compared to the total momentum of the system. Therefore, the conservation of linear momentum still holds.

The approach your professor described, using the conservation of linear momentum to estimate velocities in the case of a string connected to a block, is a valid application of the principle. In this case, the string and the block can be considered as a single system, and the conservation of linear momentum can be used to calculate the initial velocity of the block.

It is interesting to note that the result obtained from this approach is similar to that obtained by considering the block and string as separate objects and using Newton's second law (F=ma) to calculate the acceleration and velocity of the block. This is because both approaches are based on the fundamental principles of conservation of momentum and Newton's laws of motion, and they are both valid ways of analyzing the system.

Overall, the conservation of linear momentum is a powerful principle that can be applied in various situations to understand and predict the behavior of objects in motion. It is important for scientists to understand and use this principle in their research and experiments to accurately describe and explain the physical world.