Find Mass 2 with Momentum Conservation

AI Thread Summary
In a collision between two hockey players, one weighing 120 kg and traveling at 12 m/s north, and another traveling at 18 m/s south, they slide together at 4 m/s after the impact. The conservation of momentum equation is applied to find the mass of the second player. Initial calculations yielded incorrect results, prompting further algebraic manipulation and consideration of directionality in the final velocity. The discussion highlights the challenge of solving problems with unspecified parameters and emphasizes the importance of critical thinking in physics. Ultimately, the correct mass for the second player is determined to be approximately 140 kg.
Matthew_Maz
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Homework Statement


Hockey player 1 is traveling at a velocity of 12m/s North and hockey player 2 is traveling at a velocity of 18m/s south when they collide head on. after colliding, the hockey players hang onto each other and slide along the ice with a velocity of 4m/s. if hockey player 1 weighs 120 kg, calculate how much hockey player 2 weighs

givens
m1= 120kg
vi1= 12m/s North
vi2=18m/s South
m2=?
vf= 4m/s

Homework Equations


p1+p2=pt
(m1)(vi1) + (m2)(vi2) = (mt)(vft)
(m1)(vi1) + (m2)(vi2)= (m1 + m2) (vft)

The Attempt at a Solution


(m1)(vi1) + (m2)(vi2)= (m1 + m2) (vft)
(120)(12) + (m2)(-18)= (120+ m2) (4)

Not too sure where to go from here... I understand that momentum is conserved, so momentum1 + momentum 2 = momentum total... or if this is even the correct equation? test tomorrow, any help is appreciated. Thanks
 
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Hi Matthew_Maz, Welcome to Physics Forums.

You're doing okay. You just need to solve for m2: a bit of algebra.

Hint: Notice that they didn't specify a direction for vf? What happens to the mass m2 if vf is -4 m/s instead of +4 m/s? Is one result more probable than the other?
 
Im having a crazy brain fog right now and I seriously can't think. Could you please explain to me in words, what algebra needs to be done to solve for m2? And yes, I also notice that they didnt specify a direction for vf which I found quite wierd...
 
Matthew_Maz said:
Im having a crazy brain fog right now and I seriously can't think. Could you please explain to me in words, what algebra needs to be done to solve for m2? And yes, I also notice that they didnt specify a direction for vf which I found quite wierd...
Expand the right side to get individual terms. Gather all the terms involving m2 together on one side,... etc.
 
when I solved using that method I get an answer of 43.64 kg however the answer key says its 140 kg... I've checked this calculation multiple times and I am not sure where I am going wrong
 
Matthew_Maz said:
when I solved using that method I get an answer of 43.64 kg however the answer key says its 140 kg... I've checked this calculation multiple times and I am not sure where I am going wrong
Did you explore the hint that I gave?
 
i tried the hint you gave, It gave me 137.14 kg, which i would assume is the correct answer... Dont you think it's kind of a silly question due to the idea that the direction of the resultant velocity wasnt specified?
 
Matthew_Maz said:
... Dont you think it's kind of a silly question due to the idea that the direction of the resultant velocity wasnt specified?
Not necessarily. It depends upon what experience the question writer was intending to impart. Students should be able to pick up on incompletely specified problems, or at least be able to choose the most suitable result when the data allows for more than one. This situation crops up quite a bit when the equations describing a physics problem have more than one solution. For example, quite often a result may be a root of a quadratic equation. The student should be able to discard unrealistic roots and select the one(s) that fit the problem.
 
gneill said:
Not necessarily. It depends upon what experience the question writer was intending to impart. Students should be able to pick up on incompletely specified problems, or at least be able to choose the most suitable result when the data allows for more than one. This situation crops up quite a bit when the equations describing a physics problem have more than one solution. For example, quite often a result may be a root of a quadratic equation. The student should be able to discard unrealistic roots and select the one(s) that fit the problem.

but in this scenario, without knowing the answer, how would I know which one is correct?
 
  • #10
Matthew_Maz said:
but in this scenario, without knowing the answer, how would I know which one is correct?
You couldn't be 100% sure, but you could make a pretty good assumption based upon the nature of the sport and the given mass of the other player.
 

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