Elastic conservation, explosion.

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Homework Help Overview

The problem involves a bomb that explodes while sliding on a frictionless pond, with a focus on the conservation of momentum. The scenario includes a 0.5 kg bomb moving west at 2 m/s, which after the explosion, results in a 0.2 kg piece moving south at 4 m/s. The objective is to determine the components of the remaining 0.3 kg piece.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the conservation of momentum and attempt to set up equations for both horizontal and vertical components. There are attempts to use trigonometric relationships and vector diagrams to find unknown values. Some participants express uncertainty about their methods and seek clarification on the principles involved.

Discussion Status

The discussion includes various approaches to the problem, with some participants providing diagrams to illustrate momentum before and after the explosion. While there is no explicit consensus, guidance has been offered regarding the use of vector components and the importance of understanding the conservation principles.

Contextual Notes

Participants mention a lack of sufficient information and express confusion about their calculations and methods. There is an acknowledgment of the need for clarity in the principles of momentum conservation and vector analysis.

medicle
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Homework Statement


.5kg bomb sliding west frictionless pond at 2 m/s. after explosion .2kg piece moves south at 4.m/s what are the components of the .3 kg piece.

Homework Equations


I attempted to use mv1cos+mv2cos=2mvf mv1sin -mv2 sin=2mvf

The Attempt at a Solution


using v2=v1sin1/sin2 but I am not doing something right as I do not have enough information. any help would be appreciated.
 
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What's the total momentum?

Set up conservation equations for horizontal and vertical components.
 
medicle said:

Homework Statement


.5kg bomb sliding west frictionless pond at 2 m/s. after explosion .2kg piece moves south at 4.m/s what are the components of the .3 kg piece.


Homework Equations


I attempted to use mv1cos+mv2cos=2mvf mv1sin -mv2 sin=2mvf



The Attempt at a Solution


using v2=v1sin1/sin2 but I am not doing something right as I do not have enough information. any help would be appreciated.

I recommend getting the principle straight in your head first and let the math follow from that. The law of conservation of momentum tells you that the total momentum before the explosion equals the total momentum after the explosion.

I assume you are OK with vector triangles. Can you draw the right triangle that where the the momentum before the explosion is perpendicular to the momentum of the 0.2 kg piece? Do you see how to get the momentum of the 0.3 kg piece in the triangle? You can then use simple trig to find the unknown momentum and algebra to get the velocity from that.
 
you will have to excuse my ignorance. if I draw the right triangle I would get two sides..5(2) and .2(4) a^2+b^2=c^2 gives me 1.28 which is the magnitude of the hypotenuse correct?
 
so 1.28=.3v v=4.26 how do I achieve an x and y component from there.knowing that the answer is vx=3.3 vy=2.7
 
1/2mvi^2/1/2mv1f^2+1/2m2=v2f^2 vf=.77 ?

2+.77=2.7 vy=2.7

4-.77=3.23 vx=3.23??
is that really how you do this?
 
The idea is to have the sum of the momenta of the pieces after the explosion equal the momentum of the single body before. Momentum is a vector quantity, and as such can be broken out in terms of X and Y components. Choosing the X and Y axes suitably can simplify the resulting equating of before-event and after-even momentum components. The sum of the X-components of the momenta must be the same before and after, and similarly for the sum of the Y-components.

Attached is a a pair of diagrams representing the before and after views of the momenta for the bodies involved. Perhaps you can spot from the diagram how you might go about working out the unknown values from the given known ones.
 

Attachments

  • Fig25.gif
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roger, thank you for the help. I believe i stumbled my way through the problem, with a little guidance. You all are great.
 
medicle said:
roger, thank you for the help. I believe i stumbled my way through the problem, with a little guidance. You all are great.

Glad to help. The reason I posted the diagram was that from what I could make out, the methodology by which you arrived at a solution was a bit dubious (of course it could just be that I didn't follow it appropriately). I thought that the diagram might make determining the appropriate steps more straightforward.
 
  • #10
i jumped around using a couple different avenues of approach.
 

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