Find Mass 2 with Momentum Conservation

In summary: If the other player is much more massive than you, then you would expect their momentum to be much greater than yours, and so their answer would be much higher. Conversely, if the other player is much lighter than you, then their momentum would be much less, and so their answer would be lower.In summary, 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.
  • #1
Matthew_Maz
6
0

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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  • #2
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?
 
  • #3
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...
 
  • #4
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.
 
  • #5
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
 
  • #6
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?
 
  • #7
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?
 
  • #8
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.
 
  • #9
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.
 

FAQ: Find Mass 2 with Momentum Conservation

How is mass 2 determined using momentum conservation?

According to the principle of momentum conservation, the total momentum of a closed system remains constant. This means that the initial momentum of mass 1 before a collision must be equal to the final momentum of both masses after the collision. By measuring the initial momentum of mass 1 and the velocity of both masses after the collision, we can use the equation p1 = p2 + p3 to calculate the mass of mass 2.

What are the key variables needed to find mass 2 with momentum conservation?

The key variables needed to find mass 2 are the initial momentum of mass 1 (p1), the final momentum of both masses after the collision (p2 and p3), and the velocity of both masses after the collision. These variables can be measured using various instruments such as a motion sensor or a stopwatch.

Is momentum conservation applicable to all types of collisions?

Yes, momentum conservation is applicable to all types of collisions, including elastic and inelastic collisions. In an elastic collision, both kinetic energy and momentum are conserved, while in an inelastic collision, only momentum is conserved. Regardless of the type of collision, the total momentum of the system remains constant.

Can the mass of mass 2 be negative?

No, the mass of an object cannot be negative. The concept of negative mass does not exist in the scientific community. If the calculated mass of mass 2 is negative, it could be an indication of an error in the measurements or calculations.

Are there any limitations to using momentum conservation to find mass 2?

One limitation of using momentum conservation to find mass 2 is that it assumes a closed system, meaning there are no external forces acting on the masses during the collision. In real-life scenarios, it is challenging to have a completely closed system, so there may be some discrepancies in the calculated mass. Additionally, this method only works for two-body collisions and cannot be applied to more complex systems.

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