Conservation of Linear Momentum

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Homework Help Overview

The problem involves the conservation of linear momentum in the context of an explosion where a particle of mass 5m splits into two pieces of masses 2m and 3m. The lighter piece moves with a speed of 5v relative to the heavier piece, and the task is to determine the actual speed of the lighter piece.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of the conservation of linear momentum equation and question the interpretation of "relative speed." There are attempts to set up the momentum equation based on the given masses and speeds.

Discussion Status

Some participants are exploring the implications of relative speed in their calculations and are questioning whether their interpretations align with the problem's requirements. Guidance has been offered regarding the need to determine speeds with respect to the ground.

Contextual Notes

There is a focus on the term "relative speed" and its impact on the momentum calculations. Participants are considering how to express the speed of the lighter piece in relation to the heavier piece and the ground.

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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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