Conservation of Momentum: Solving For Velocity After Collision

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Discussion Overview

The discussion revolves around the conservation of momentum in a collision scenario involving two pucks of different masses and velocities. Participants explore the implications of momentum conservation when the pucks collide and stick together, raising questions about the resulting velocity of the combined mass.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions why the final velocity after the collision is -v/2, suggesting that -2v seems more intuitive if the smaller mass's momentum cancels out the larger mass's momentum.
  • Another participant agrees that the momentum of the smaller mass cancels out an equal momentum of the larger mass, stating that the total momentum after the collision is -2mv, leading to the conclusion that the final velocity must be -v/2 when divided by the total mass of 4m.
  • A different participant provides calculations showing how momentum is conserved, noting that the initial momentum of the system is -2mv and that the new mass is 4m, which leads to the conclusion that the new velocity must be -v/2 to maintain momentum conservation.
  • One participant expresses confusion about the implications of having a new velocity that seems to suggest an increase in momentum, questioning how this aligns with the principle of conservation of momentum.

Areas of Agreement / Disagreement

Participants generally agree on the principle of conservation of momentum but express differing interpretations and calculations regarding the final velocity after the collision. The discussion remains unresolved as participants explore various perspectives and calculations.

Contextual Notes

Some participants' calculations depend on specific assumptions about the initial conditions and the definitions of momentum. There are unresolved aspects regarding the interpretation of momentum changes and the implications of the collision dynamics.

hemmi
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I'm currently reading Understanding Physics by Asimov and am stuck on an example he gives regarding conservation of momentum.

Suppose one puck was moving to the right at a given speed and had a momentum of mv, while another, three times as massive, was moving at the same speed to the left and had, therefore, a speed of -3mv. If the two stuck together after a head-on collision, the combined pucks (with a total mass of 4m) would continue moving to the left - the direction in which the more massive puck had been moving - but at half the original velocity (-v/2).

What I don't understand is, why half the velocity? -2v makes sense to me if the momentum of the small mass "canceled out" an equal momentum of the larger mass, but -1.5v doesn't make sense. I'm obviously missing something, I just don't know what. Thanks!
 
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hemmi said:
I'm currently reading Understanding Physics by Asimov and am stuck on an example he gives regarding conservation of momentum.



What I don't understand is, why half the velocity? -2v makes sense to me if the momentum of the small mass "canceled out" an equal momentum of the larger mass, but -1.5v doesn't make sense. I'm obviously missing something, I just don't know what. Thanks!


If the new velocity is -2v, then the new momentum is (4m)(-2v)=-8mv,right? But how could it have more momentum than initially given unless an external force acts?

But if no external force acts, then the momentum must be the same as it was initially given.
Initial momentum is -2mv. So if the new mass is 4m, then the new velocity must be -v/2 so that the new momentum is (4m)(-v/2)=-2mv.
 
Momentum is a vector so it can be + or - depending on direction.
p=mv m is mass in Kg and v is velocity (vector) in ms^-1 so p is momentum in Kgms^-1.
If no units are given then its just the same except it would be something like u ms^-1.
p = mv = 1*3 = 3
p = mv = 3*-3 = -9 3+-9 = -6
v = -6/4 (add up momentum and masses) = -1.5ms^-1
I think this is correct. The thing to rember is that momentum is always conserved.
 
hemmi said:
What I don't understand is, why half the velocity? -2v makes sense to me if the momentum of the small mass "canceled out" an equal momentum of the larger mass,
The momentum of the small mass does "cancel out" an equal momentum (in the opposite direction, of course) of the larger mass. The total momentum is now -2mv. To find the new speed you must divide by the mass of the entire system, which is now 4m. So: Vf = (-2mv)/4m = -v/2, in other words: half the original speed v.
 

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