Solve 1D Explosion Problem: Find Mass, Speed, Force & Momentum

[venceslau]

Homework Statement

An object with total mass mtotal = 8.6 kg is sitting at rest when it explodes into two pieces. The two pieces, after the explosion, have masses of m and 3m. During the explosion, the pieces are given a total energy of E = 48.0 J.

1) What is the speed of the smaller piece after the collision?
2) What is the speed of the larger piece after the collision?
3) If the explosion lasted for a time t = 0.028 s, what was the average force on the larger piece?
4) What is the magnitude of the change in momentum of the smaller piece?
5) What is the magnitude of the velocity of the center of mass of the pieces after the collision?

Homework Equations

Ek = P^2/2m
Ek = 0.5*m*v^2
ΔP = Pf - Pi
F = ΔP/Δt

The Attempt at a Solution

m1 (smaller piece) should be 1/4 of mtotal, so m1=2.15 kg
m2 (larger piece) should be 3/4 of mtotal, so m2=6.45 kg

We're told the pieces are given a total of 48 J, I simply assumed that 1/4 of that energy goes to m1 and the other 3/4 to m2. This is probably where I am going wrong.

From there I solved for velocity using Ek and mass:
v1 = sqrt(2*Ek/m1) = sqrt(2*12/2.15) = 3.341 m/s

Also tried assuming each piece was given a total of 48 J:
v1 = sqrt(2*Ek/m1) = sqrt(2*48/2.15) = 6.682 m/s

Also tried assuming each piece was given a total of 24 J:
v1 = sqrt(2*Ek/m1) = sqrt(2*24/2.15) = 4.7249 m/s

I don't quite understand what I may be doing wrong, some insight would be very much appreciated.

Thanks in advance.

 

[haruspex]

I simply assumed that 1/4 of that energy goes to m1 and the other 3/4 to m2. This is probably where I am going wrong.

You're right - that's wrong.
Use conservation of momentum to figure out how the energy is shared.

 

[Spinnor]

I think you should assume that the initial momentum is zero and that the sum of the final momentum is zero.

The last question does not seem to make sense in terms of what was qiven,

"5) What is the magnitude of the velocity of the center of mass of the pieces after the collision? "

Should that be,

5) What is the magnitude of the velocity of the center of mass of the pieces after the explosion?
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[venceslau]

You're right - that's wrong.
Use conservation of momentum to figure out how the energy is shared.

I think you should assume that the initial momentum is zero and that the sum of the final momentum is zero.

The last question does not seem to make sense in terms of what was qiven,

"5) What is the magnitude of the velocity of the center of mass of the pieces after the collision? "

Should that be,

5) What is the magnitude of the velocity of the center of mass of the pieces after the explosion?
----------

Thank you both for your replies. Spinnor, I agree with you, the wording on that last question is definitely incorrect, thanks for pointing that out.

Now, I am not so sure how I would go about using conservation of momentum to find out how the energy would be shared between the different pieces.

If I setup m1V1=m2V2, I still have two unknowns...

 

[Spinnor]

Thank you both for your replies. Spinnor, I agree with you, the wording on that last question is definitely incorrect, thanks for pointing that out.

Now, I am not so sure how I would go about using conservation of momentum to find out how the energy would be shared between the different pieces.

If I setup m1V1=m2V2, I still have two unknowns...

But you also have an equation for the total kinetic energy is 48J. Two equations, two unknowns, you are set.

 

[venceslau]

But you also have an equation for the total kinetic energy is 48J. Two equations, two unknowns, you are set.

Thank you Spinnor, I finally got it!

I appreciate your help.

Cheers