Need help with an energy-related question

[nehcrow]

Homework Statement

In a fireworks explosion two fragments are ejected horizontallly back-to-back as the shell explodes 200m above the ground. One fragment (A) has a mass of 0.5kg while the other (B) has a mass of 1.0 kg.

(a) If the total energy of the system before the explosion is 1.0kJ and 80% of the energy is converted into the kinetic energy of the fragments, what are the speeds with which the fragments are ejected? Clearly specify which fragments corresponds to which speed.

Homework Equations

Ug = m*g*h
K = (1/2)*m*v^2

The Attempt at a Solution

I can't figure out how much kinetic energy is distributed to each fragment

Your help is much appreciated!

 

[ideasrule]

I think "total energy" refers to total kinetic energy, so you don't need to consider potential energy.

Start off by writing out the equation for the conservation of momentum. That'll give you one equation. The other equation comes from the conservation of energy: the total kinetic energy should equal 0.8kJ.

 

[nehcrow]

Thanks a lot! I get it now... conservation of momentum, why didn't I think of that :P

 

[nehcrow]

Sorry to bother you again but you could you mind setting up the equations?
I'm still not getting the right answers :(

 

[nehcrow]

BUMP, need help ASAP

 

[gneill]

You'll have to show some of your work before we can see how you're going wrong. We can't do the work for you...

 

[-Fady-]

I'm stuck on the same question. please tell me where I made an error.

momentum conservation equation, initial is 0 and final is $$-.5v_1+v_2$$

so $$v_2 - 0.5v_1=0$$ ??

and energy equation gave me $$v_1+v_2=32.6599$$ ?.

Any help would be much appreciated.

 

[gneill]

I'm stuck on the same question. please tell me where I made an error.

momentum conservation equation, initial is 0 and final is $-.5v_1+v_2$

so $v_2 - 0.5v_1=0$ ??

and energy equation gave me $v_1+v_2=32.6599$ ?.

Any help would be much appreciated.

So from momentum conservation you've found that v1 = 0.5*v1, or if you prefer, v1 = 2*v2. That's fine.

Can you show how you worked with the "energy equation" to result in what you've written?

 

[-Fady-]

I equated $$800 J=\dfrac{1}{2}mv^2$$

$$m=1.5kg$$ and $$v=v_1+v_2$$. Is that right? then just rearranged.

Thanks for the help.

 

[gneill]

Not quite. You want to add the kinetic energies of individual pieces together. So

$$KE = \frac{1}{2}m_1 v_1^2 + \frac{1}{2}m_2 v_2^2$$

 

[-Fady-]

You are a legend. Thanks so much.

such a stupid error on my part, but I guess now I'll never make that error :)