Calculating the collusion and loss of energy?

[Matriculator]

Homework Statement

Homework Equations

m₁v_1i+m₂v_2i=m₁v_1f+m₂v_2f

The Attempt at a Solution

I tried doing MV=m₁v_1f+m₂v_2f

I know that the sum of the momentum of the two parts is equal to the the momentum of the the full shell. Since I have two unknowns, I used the conservation of energy. I set used KE=KE₁+KE₂. The kinetic of the full shell equals to the sum of the kinetic energy of the two parts. Since I have two unknowns here too, I used a system of equations solve for v. Am I on the right path? I found two "ms" didn't add up to 5kg. Thank you in advance.

 

[rude man]

It would be helpful if you stated the problem - preferably in its original version. If it's not in English, someone may be able to translate it accurately. Supplementally, give your own translation as best you can.

 

[collinsmark]

Homework Statement

Homework Equations

m₁v_1i+m₂v_2i=m₁v_1f+m₂v_2f

The Attempt at a Solution

I tried doing MV=m₁v_1f+m₂v_2f

I know that the sum of the momentum of the two parts is equal to the the momentum of the the full shell. Since I have two unknowns, I used the conservation of energy.

Don't use conservation of energy. Energy isn't conserved in this problem.

Yes, you will come back to that later when you find the difference in kinetic energies such that you can calculate the energy released. But that comes later.

So go back to your first equation regarding conservation of momentum. That's one of the two equations you will need.

The second equation that you'll need is actually quite simple. What is the sum of the two masses after the explosion? [Hint: it's the same as the shell's mass before the explosion.] Put that in equation form.

I set used KE=KE₁+KE₂. The kinetic of the full shell equals to the sum of the kinetic energy of the two parts.

That's not true for this problem. Additional energy is released as part of the explosion.

But what you can do is find the kinetic energy of the shell before the explosion and compare that to the sum of kinetic energies of the two parts.

I found two "ms" didn't add up to 5kg. Thank you in advance.

According to your attachment, the two masses should add up to 4.5 kg. (not 5 kg).

 

[Matriculator]

Don't use conservation of energy. Energy isn't conserved in this problem.

Yes, you will come back to that later when you find the difference in kinetic energies such that you can calculate the energy released. But that comes later.

O-oh.. ohhh. Wow I feel slow. Thank you very. So it's 410m₁+215m₂=1440 and m₁+m₂=5. I understand this part now(although I'm 85% sure on the former's signage, I'm still loose on signage in physics).

After this to find kinetic energy, I'm thinking of subtracting the kinetic energy of the full shell to the sum of the kinetic energies of the two parts using the new found masses, is that correct? Basically ΔKE=KE_Shell-(KE₁+KE₂).

 

[collinsmark]

O-oh.. ohhh. Wow I feel slow. Thank you very. So it's 410m₁+215m₂=1440

That looks right to me

(Except for the lack of units. But perhaps I'm being nit-picky.)

and m₁+m₂=5.

I think you mean 4.5 kg.

I understand this part now(although I'm 85% sure on the former's signage, I'm still loose on signage in physics).

Everything is going in the same direction for this problem, so the signs look good to me the way you have them.

After this to find kinetic energy, I'm thinking of subtracting the kinetic energy of the full shell to the sum of the kinetic energies of the two parts using the new found masses, is that correct? Basically ΔKE=KE_Shell-(KE₁+KE₂).

Almost right. You can usually expect the energy of the explosion to cause the kinetic energy of the subsequent pieces to be greater overall, compared to the original kinetic energy. And that holds true for this problem too. So what does that tell you about what you need to subtract from the other?

 

[Matriculator]

That looks right to me

(Except for the lack of units. But perhaps I'm being nit-picky.)

Almost right. You can usually expect the energy of the explosion to cause the kinetic energy of the subsequent pieces to be greater overall, compared to the original kinetic energy. And that holds true for this problem too. So what does that tell you about what you need to subtract from the other?

Oh sorry about the unit thing. So I have it backwards? It should be the sum of the potential energy of the two parts minus the kinetic energy of the shell. Could I think of it as the absolute value of the change in kinetic energy, although there's no such convention? Thank you again.

 

[collinsmark]

Oh sorry about the unit thing. So I have it backwards? It should be the sum of the potential energy of the two parts minus the kinetic energy of the shell. Could I think of it as the absolute value of the change in kinetic energy, although there's no such convention? Thank you again.

I don't think potential energy plays a role in this problem.

What I meant in my last post is that explosions tend to increase the kinetic energy of the things around them. So if you want to find the energy released by the explosion, and assuming all of the energy released by the explosion went into increasing the kinetic energy of the two pieces (in addition to what they already had before the explosion, back when the two pieces were a single shell), then...

 

[Matriculator]

I don't think potential energy plays a role in this problem.

What I meant in my last post is that explosions tend to increase the kinetic energy of the things around them. So if you want to find the energy released by the explosion, and assuming all of the energy released by the explosion went into increasing the kinetic energy of the two pieces (in addition to what they already had before the explosion, back when the two pieces were a single shell), then...

Sorry I miswrote that, I meant Kinetic energy. As in ƩKE_Parts-KE_Shell. Thank you for everything by the way.

 

[collinsmark]

I meant Kinetic energy. As in ƩKE_Parts-KE_Shell.

That looks like the correct idea to me.