# (Problem 6) Fragments of explosion

1. Jun 1, 2014

### gcombina

Why is the answer D for the following question?
A stationary bomb explodes in gravity-free space breaking into a number of small fragments. Which one of the following statements concerning this event is true?
A. Kinetic energy is conserved in this process.
B. The fragments have equal kinetic energies.
C. The sum of the kinetic energies of the fragments must be zero.
D. The vector sum of the linear momenta of the fragments must be zero.
E. The velocity of any one fragment must be equal to the velocity of any other fragment.

My attempt:
C : I think this answer could be correct because all the fragments net force is zero, so basically they have all the potential energy and kinetics is gone.
E : If the velocity is "0" of all fragments then the velocity of fragment A is equal to the velocity of fragment B, C , etc.....right???? because all fragment have the SAME velocity which is 0.

2. Jun 1, 2014

### Nathanael

Why would the velocity be zero? Something exploded into a bucnh of little pieces and they all go flying off in various directions at various speeds. Where does zero velocity come in to play?

I do not quite understand what you're trying to say. What sort of potential energy do they have? Why is kinetics gone?

Momentum is conserved. If the momentum was zero before the explosion, it will be zero after the explosion (for the WHOLE system).

If one piece is exploded off in some direction, then another piece will go flying in the opposite direction with an equal momentum.

3. Jun 1, 2014

### Nick O

C: This is not possible, because kinetic energy is always a positive scalar.

K = $\frac{m|v|^{2}}{2}$

If K is never negative*, and the particles are moving (which they are - the bomb exploded!), then the sum of the energies can never be zero!

E: No, this is not the case. The sum of the velocities is unknown. If the bomb explodes into two pieces flying in opposite directions, one piece being twice as large as the other, then the speed of the smaller piece will be twice that of the larger piece.

The answer is D because the law of conservation of linear momentum requires that the momentum of the bomb before the explosion (which was 0, because it wasn't moving) be the same as the combined momentum of the pieces that fly apart after the explosion.

*My electrical science professor said that you get negative energy when you have Satanic power (P=dE/dt), but that's neither here nor there :p

4. Jun 6, 2014

### gcombina

I got it! the velocity of the stationary bomb was zero so the momentum was zero and based on the law of conservation of linear momentum then after the explosion, the momentum is at well zero