Conservation of Momentum - BOMB EXPLOSION question

[gcombina]

Homework Statement

QUESTION 1 :A stationary bomb explodes in space breaking into a number of small fragments. At the location of the explosion, the net force do to gravity is 0 Newtons. Which one of the following statements concerning the event is true?
a) Kinetic energy is conserved in the process
b) The fragments must have equal kinetic energies
c) The sum of the KE's of the fragments must be 0
d) The vector sum of the linear momenta of the fragments must be zero
e) The velocity of anyone fragment must be equal to the velocity of any other fragment

Homework Equations

mv (before) = mv (after)

The Attempt at a Solution

a) mv (before) = mv (after), velocity before is 0 and velocity after is 0 therefore, the KE is NOT conserved
b) there is NO KE as the bomb was stationary so it was zero velocity
c) KE must always be positive so it can NOT be 0
d) YES
e) The velocities of these fragments are zero, therefore the velocity of one fragment can be equal to other fragment so I don't understand this question

 

[haruspex]

a) mv (before) = mv (after), velocity before is 0 and velocity after is 0

The velocity of what is zero after? There are many independently moving fragments.
If you mean the average velocity (weighted according to mass), you can't use that for finding the KE of an ensemble.

 

[gcombina]

The velocity of what is zero after? There are many independently moving fragments.
If you mean the average velocity (weighted according to mass), you can't use that for finding the KE of an ensemble.

I thought that because it said "stationary bomb" then the velocity was zero before it exploted

 

[haruspex]

I thought that because it said "stationary bomb" then the velocity was zero before it exploted

Sure, but you wrote that it is also zero afterwards.

 

[gcombina]

Sure, but you wrote that it is also zero afterwards.

right cause the conservation of momentum, am I right? velocity is zero before and its zero after

 

[haruspex]

right cause the conservation of momentum, am I right? velocity is zero before and its zero after

The momentum is zero before and after, but in the after condition the mass is made of many small parts. You can only use $\frac 12 mv^2$ for KE when the m is a rigid body (and you would have to add in rotational energy too. If it is an ensemble then you must sum the energies over the rigid components.

 

[gcombina]

The momentum is zero before and after, but in the after condition the mass is made of many small parts. You can only use $\frac 12 mv^2$ for KE when the m is a rigid body (and you would have to add in rotational energy too. If it is an ensemble then you must sum the energies over the rigid components.

wow, i don't understand you. Which option are you trying to explain to me? option a) or option e)?

 

[haruspex]

wow, i don't understand you. Which option are you trying to explain to me? option a) or option e)?

It relates to your reasoning on all except d), but does not necessarily change your answer. For instance, in a) you got the right answer, that KE is not conserved, despite apparently reasoning that it would be.

 

[haruspex]

I assume that the bomb explodes and the parts fly and then remain on the ground

What ground? The question only concerns the instants before and after the explosion.