# Sign convention problem in momentum calulations

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1. Sep 18, 2016

### Fariaz Haque

1. The problem statement, all variables and given/known data
Particle A has a mass of 1kg and velocity 2x10^8m/s to the right and collides with a stationary particle B that has a mass of 4kg. after the collision, particle A moves to the left with a velocity(v) and particle B moves to the right with a velocity of 1x10^7 m/s. calcuate the value of 'v'.
i get a value of 1.6x10^8 for v but shouldnt it be -1.6x10^8 as it is moving to the left?

The thing is, in other collisions where two objects moving towards each other collide and then move apart after the collision, the answer justifies the direction just fine. for example...

An example: Particle C has a mass of 1kg and velocity 2x10^8 m/s to the right and collides with particle D that has a mass of 4kg and is moving to the left at 1.5x10^8 m/s. after the collision, particle C moves to the left with a velocity(v) and particle D moves to the right with a velocity of 2x10^7 m/s. calcuate the value of 'v'.
solution: (2x10^8 x 1) + [4 x (-1.5x10^8) ] = (1x v) + (4x 2x10^7)
v= -0.48x10^9(here the answer justifies the direction)

2. Relevant equations:
momentum before collision= momentum after collision

3. The attempt at a solution
momentum before collision= momentum after collision
(2x10^8 x 1) + (4x0) = (1xv) + (1x10^7 x 4)
v= 1.6x10^8

2. Sep 18, 2016

### kuruman

This looks like a relativistic collision because the projectile particle travels at (2/3)c. Are you studying relativity?

3. Sep 18, 2016

### Fariaz Haque

nope... just a simple momentum question that was given at school...

4. Sep 18, 2016

### haruspex

Quite so. Both particles will move to the right. There must be an error in the question.

5. Sep 19, 2016

### Fariaz Haque

Indeed. Asked my teacher today and verified the problem! :)

6. Sep 19, 2016

### hmmm27

Context.

Left at 7m/s
Left, at -7m/s (note comma)

can mean the same thing. The first one is 7m/s leftwards, the second is -7m/s along an implied left-to-right horizontal axis (x) - the "left" is semi-redundant.

On the other hand proofreaders don't get paid much, so best not to make them work too hard if it can be avoided.

Last edited: Sep 19, 2016