Conservation of Linear Momentum

AI Thread Summary
The discussion focuses on a physics problem involving the conservation of linear momentum after a particle explodes into two pieces. The initial momentum is calculated as 5m x v, and the challenge lies in determining the actual speed of the lighter piece after the explosion. The key point is that the lighter piece moves at 5v relative to the heavier piece, which complicates the calculation. To solve it correctly, speeds must be assessed with respect to the ground rather than relative to each other. The correct answer for the speed of the lighter piece is 4v, derived from properly applying the conservation of momentum principles.
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Homework Statement


A particle of mass 5m moving with speed v explodes and splits into two pieces with masses of 2m and 3m. The lighter piece continues to move in the original direction with speed 5v relative to the heavier piece. What is the actual speed of the lighter piece?


Homework Equations


Momentum = Mass x Velocity


The Attempt at a Solution


The answer is 4v, as stated in the answer sheet, but I've no idea how to get it. Appreciate any help here, thanks!
 
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Start by writing the conservation of linear momentum equation.
 
I've only got: 5m x v = (2m x 5v) + (3m x -1 2/3 v)

Does the problem lie with the term "relative speed"?
 
skunk said:
I've only got: 5m x v = (2m x 5v) + (3m x -1 2/3 v)

Does the problem lie with the term "relative speed"?

Certainly does!
 
skunk said:
I've only got: 5m x v = (2m x 5v) + (3m x -1 2/3 v)

Does the problem lie with the term "relative speed"?
Yes. You should always determine speeds with respect to the ground when using this equation. If the lighter piece is moving at 5v with respect to the heavier piece, and the heavier piece is moving at a speed v2 with respect to the ground, then what is the speed of the lighter piece with respect to the ground, in terms of v and v2?
 

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