Elastic conservation, explosion.

[medicle]

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.

 

[Doc Al]

What's the total momentum?

Set up conservation equations for horizontal and vertical components.

 

[Fewmet]

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 teh velocity from that.

 

[medicle]

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?

 

[medicle]

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

 

[medicle]

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?

 

[gneill]

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.

 

[medicle]

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

 

[gneill]

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.

 

[medicle]

i jumped around using a couple different avenues of approach.