Tom Mattson Posted February 21, 2005 Share Posted February 21, 2005 The law of conservation of momentum states that the total momentum of a system is constant unless it is acted upon by a net external force. We consider only external forces because all internal forces cancel out, thanks to Newton's third law. The conservation law itself is derived from Newton's second law, as follows. Newton's 2nd: [math] \sum_{i=1}^N \mathbf{F}_{i}^{ext}=\frac{d\mathbf{p}}{dt} [/math] Now if the vector sum of all the external forces is zero, then dp/dt=0 and therefore p is constant. Link to comment Share on other sites More sharing options...
albertlee Posted February 21, 2005 Author Share Posted February 21, 2005 thx Tom, but what is the so-called "system" in this case??? If it helps, can any one provide an example in reality related to the law of consercation of momentum?? thx Albert Link to comment Share on other sites More sharing options...
swansont Posted February 21, 2005 Share Posted February 21, 2005 thx Tom' date=' but what is the so-called "system" in this case??? If it helps, can any one provide an example in reality related to the law of consercation of momentum?? thx Albert[/quote'] The system is whatever you define it to be. If there is no net external force, only internal ones, then momentum will be conserved. An object drops to the earth and collides. If you define the system to be just the object, momentum is not conserved because the force of gravity is present. But if you define the system to be the object + the earth, then momentum is conserved, though changes in the motion of the earth will be tough to see. Link to comment Share on other sites More sharing options...
jordan Posted February 21, 2005 Share Posted February 21, 2005 Real World Example: You have two billiard balls, one has a mass of 100kg and the other 50kg. You roll the 100kg ball at a speed of 100m/sec. It collides with the 50kg ball. After the collision it is going 50m/sec. What is the speed of the 50kg ball after the collision? You know that p=mv. So for the first ball pi=100kg*100m/sec or 1x104N. You also know that after the collision it is moving 50m/sec. So pf=100kg*50m/sec or 5x103N. The only thing that allows you to solve for the second ball (since the only thing you know is it's mass) is that there are no external forces so momentum is conserved. This tells you that since the initial momentum of the system was 1x104N, the final momentum must also be 1x104N. So far we have the final momentum of the 100kg ball as 5x103N, leaving a difference of 5x103N. So then, back to p=mv. For the 50kg ball in the end, 5x103N=50kg*v. Therefore v=100m/sec. Without the Law Of Conservation of Momentum, there would be no way to calculate the final velocity of the second ball with the given information. Link to comment Share on other sites More sharing options...
albertlee Posted February 21, 2005 Author Share Posted February 21, 2005 Newton's third law describes about force, what does have to do with conservation of momentum?? Secondly, in a system of conservation of momentum, there should be no external forces, but what internal forces??? Albert Link to comment Share on other sites More sharing options...
Tom Mattson Posted February 21, 2005 Share Posted February 21, 2005 Albert, I already answered those questions in my last post. Did you miss it? Link to comment Share on other sites More sharing options...
albertlee Posted February 22, 2005 Author Share Posted February 22, 2005 Well, I cannot understand your mathematical symbols..... Does it have to be that "hard"??? Link to comment Share on other sites More sharing options...
Tom Mattson Posted February 22, 2005 Share Posted February 22, 2005 Well' date=' I cannot understand your mathematical symbols..... [/quote'] Well, there's really no other way to say it. The derivative dp/dt merely denotes the rate of change of momentum with respect to time. If the sum of external forces is zero, then the rate of change of momentum with respect to time is zero. And if the momentum doesn't vary with time, then it's a constant, and hence conserved. As for your question about internal forces, I answered that one in words: The internal forces cancel each other out, which is what Newton's third law says. Link to comment Share on other sites More sharing options...
swansont Posted February 22, 2005 Share Posted February 22, 2005 As for your question about internal forces, I answered that one in words: The internal forces cancel each other out, which is what Newton's third law says. It might be better say they balance, since they act on different objects. For internal forces, any momentum lost by one object is gained by another. Link to comment Share on other sites More sharing options...
Tom Mattson Posted February 22, 2005 Share Posted February 22, 2005 What's the difference between "balancing" and "canceling out"? The vector sum of the internal forces is zero. It is understood that the action-reaction pairs act on different objects, with the reference to Newton's third law. Link to comment Share on other sites More sharing options...
albertlee Posted February 22, 2005 Author Share Posted February 22, 2005 As for your question about internal forces' date=' I answered that one in words: The internal forces cancel each other out, which is what Newton's third law says.[/quote'] But in a closed system of momentum, the internal forces only cancel out like what Newton's third law, when the force of the object equals to, for eg, air resisitance maybe the case should be when there is no force, or, the internal forces cancel each other out, right?? Albert Link to comment Share on other sites More sharing options...
Tom Mattson Posted February 23, 2005 Share Posted February 23, 2005 But in a closed system of momentum' date=' the internal forces only cancel out like what Newton's third law, when the force of the object equals to, for eg, air resisitance[/quote'] In that case you have a choice to make. 1. Define the system to include the both the moving object and the air. In that case, the frictional force that acts on the moving object is balanced by the net force that the object exerts on the air molecules. These internal forces cancel out, a la Newton's 3rd. Provided no other net force acts on the object or the air, the momentum of the object+air system will be conserved. 2. Define the system to include the moving object but to exclude the air. In that case, the frictional force that acts on the object counts as an external force, and the momentum of the system is not conserved. Link to comment Share on other sites More sharing options...
albertlee Posted February 23, 2005 Author Share Posted February 23, 2005 Sometimes I feel that many exercise questions, when describing the system, is quite unclear for eg, it just says the momentum of object A is x kgm/s, but not telling whether the internal forces are canceled out, or there is actually no force, like Newton's first law Albert Link to comment Share on other sites More sharing options...
Primarygun Posted February 23, 2005 Share Posted February 23, 2005 In these exercises, friction is always neglected unless the mass of earth is given. Link to comment Share on other sites More sharing options...
Tom Mattson Posted February 23, 2005 Share Posted February 23, 2005 for eg' date=' it just says the momentum of object A is x kgm/s, but not telling whether the internal forces are canceled out, or there is actually no force, like Newton's first law [/quote'] They don't have to tell you what forces are present in order for the value of the momentum to make sense. All they need to tell you is from what reference frame the momentum takes on that value. And even then, it could be not stated but just assumed to be some obvious "lab frame". You are supposed to be able to determine the forces (both internal and external) acting on the system from the description of the system itself. That you should have learned before getting to momentum. In these exercises' date=' friction is always neglected unless the mass of earth is given. [/quote'] Huh? That's not true at all. You don't need the mass of the Earth, you need the mass of the moving object and the coefficients of friction for the object and any surfaces against which it might be moving. Link to comment Share on other sites More sharing options...
albertlee Posted February 23, 2005 Author Share Posted February 23, 2005 thx a million to you guys!!! Eventually..... Link to comment Share on other sites More sharing options...
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