Momentum and Collisions - Mission MC6 Detailed Help

Students of varying mass are placed on large carts and deliver impulses to each other's carts, thus changing their momenta. In some cases, the carts are loaded with equal mass; in other cases they are unequal. In some cases, the students push off each other; in other cases, only one team does the pushing. For each situation, list the letter of the team that ends up with the greatest momentum.


 
The Law of Momentum Conservation:
If an interaction between object 1 and object 2 occurs in an isolated system, then the momentum change of object 1 is equal in magnitude and opposite in direction to the momentum change of object 2. In equation form
 
m1 • ∆v1 = - m2 • ∆v2

The total momentum of the system before the interaction (p1+ p2) is the same as the total momentum of the system of two objects after the interaction (p1' + p2'). That is,  
 
p1 + p2 = p1' + p2'

System momentum is conserved for interactions occurring in isolated systems.


 
The interaction between the two carts (and the students upon them) provides an example of the law of momentum conservation. Before the push-off, both carts have a momentum of 0 units. Thus, the pre-explosion momentum of the system of two objects is 0 units. After the explosion, the total system momentum must still be 0 units. But how can that be? If both carts are moving, how can the system have 0 units of total momentum after the explosion? The answer lies in the fact that momentum is a vector and has a magnitude and a direction (see the Know the Law section). If the direction one cart moves after the explosion is opposite the direction that the other cart moves after the explosion, then one would have positive momentum and the other would have negative momentum. Now answer the question of how can the system of two carts have 0 units of total momentum after the explosion if both objects are moving? There is only way for this to happen and if you think about it you are likely to get at the answer.


 
Many students ponder the importance of which team did the pushing. But don't be fooled! Team A can't push on Team B without the Team B pushing back. It matters not which team exerted the push since for every action there is an equal and opposite reaction. It's automatic! Forces come in pairs as mutual interactions between objects. Thus, the statements concerning which team did the pushing are irrelevant to the question.


 
Momentum as a Vector:
Momentum is a vector and it has a direction. The direction of an object's momentum is in the same direction that the object is moving. An eastward moving object has an eastward momentum.


 

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