Velocity and Direction of Shrapnel After an Object Explodes at Rest

[synergix]

Homework Statement

An object at rest explodes into three pieces of masses 5.00 kg, 10.0 kg and 20.0 kg. The 5.00 kg piece moves west at 30.0 m/s; the 10.0 kg piece moves southwest at 20.0 m/s. What is the velocity of the 20.0 kg piece and what direction is it moving?

Homework Equations

Conservation of kinetic energy

The Attempt at a Solution

My thinking is to use conservation of kinetic energy. I begin by writing out the equation with one mass before and three after. The energy before is zero so I figured that the kinetic energy of the 20.0kg piece would be the negative sum of the other two. it works algebraically and I figured because there is no outside forces acting on the system it should work. I believe that the energy of one piece must be proportional to the others. I am not too sure here though. anyways then to find the angle I treated the other two kinetic energys as vector components and added them to find a resultant vector and then since my 20.0kg piece is equal to the negative of the sum of the othger two energies. I figure that the direction would be the the negative of the direction of the other two if they were to be treated as vector componenets and added togther.

 

[turin]

Homework Equations

Conservation of kinetic energy

No. What is the kinetic energy before the explosion? What is the minimum possible kinetic energy ever?

 

[synergix]

Ok, That makes sense. the energy before the explosion is all potential and we don't have the info to determine what it was soo...Can you help, I really don't know how to go any further with this problem.

 

[turin]

Do you know any other conservation laws? You probably learned another one about the same time that you learned conservation of energy.

 

[synergix]

If two pieces were blown away at known velocities and given momentum, then the other piece must have a velocity and momentum proportional to the other two. Or equal to the other two? it makes sense because if the force caused by the explosion blew these masses away at known velocitties then it would have blown the third piece away with an equal amount of energy or force. i think?

 

[turin]

You are throwing around a lot of buzz-words, but not being very precise about the meaning. In freshman physics the terms "kinetic energy", "velocity", "momentum", "force", "mass", and "energy" have very precise mathematical meanings/relationships, and I would venture to say that most of the trouble students have is with this precision. You need to understand this before you can solve any problems. I ask again, what is the conservation law that you think you need? (it is quite famous).

 

[synergix]

Conservation of momentum

 

[turin]

Yes! Now, what does it mean?

 

[synergix]

Ya I guess I was being pretty imprecise with my vocabulary sorry I'm not trying to act like I know everything. I am just trying to explain my thinking as best as possible.

 

[synergix]

momentum is the product of mass times velocity. Momentum of a system before equals momentum after if no other forces or objects interfere. it means if an object has a low speed but a huge mass then inorder for an object with a small mass to equal the momentum of the object with huge mass it must have a very highspeed. in a collision two objects of equal mass collide, one intially has a speed of 2 one is at rest initially. after they collided they will both have a speed of 1.

 

[turin]

Momentum of a system before equals momentum after if no other forces or objects interfere.

Do any "other forces or objects interfere" in the explosion?

in a collision two objects of equal mass collide, one intially has a speed of 2 one is at rest initially. after they collided they will both have a speed of 1.

Nope. (not a pool player, I guess) What do you think you might be forgetting here? (Well, actually, what you describe could happen, but it doesn't always happen.)

 

[synergix]

No, no other forces or objects interfere. Maybe I forgot to add what I added to the first part if no other objects or forces interefere. umm well it would occur only if the collision was perfectly elastic.

 

[turin]

No, no other forces or objects interfere.

Great. So let's use conservation of momentum. What is the initial momentum? What is the known final momentum? What's missing? You can write this mathematically as a one line problem, and then a one line solution.

umm well it would occur only if the collision was perfectly elastic.

I think you mean "inelastic".

 

[synergix]

Pi=0
0=5.00kg(30.0m/s)+10.0kg(20.0m/s)+20.0kgV
v=350kgm/s/-20kg
v=-17.5m/s

 

[synergix]

if the collision was elastic would the first ball have stopped while the second would have aqcuired the velocity of the first ball? which is usually what pool balls do.

 

[turin]

if the collision was elastic would the first ball have stopped while the second would have aqcuired the velocity of the first ball? which is usually what pool balls do.

If it is hit head on, yes.

 

[synergix]

ok gotcha! and can I treat they other two momenta as componenets of a vector and use them to find the direction of the third piece of shrapnel? this seems unlikely but I am unsure how to proceed.