A mortar fires a shell of mass m at speed v0. The shell explodes at the top of its trajectory (shown by a star in…
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Question “A mortar fires a shell of mass m at speed v0. The shell explodes at the top of its trajectory (shown by a star in…”
A mortar fires a shell of massm
at speed
v0.
The shell explodes at the top of its trajectory (shown by a star in
the figure) as designed. However, rather than creating a shower of
colored flares, it breaks into just two pieces, a smaller piece of
mass
15m
and a larger piece of mass
45m.
Both pieces land at exactly the same time. The smaller piece lands
perilously close to the mortar (at a distance of zero from the
mortar). The larger piece lands a distanced
from the mortar. If there had been no explosion, the shell would
have landed a distancer
from the mortar. Assume that air resistance and the mass of the
shell’s explosive charge are negligible.
(Figure
1)
Find The distance d
from the mortar at which the larger piece of the shell lands. Solve
d in terms of r.
Answer
Concepts and Reason
The conservation of momentum is the basis for this question.
First, determine the linear momentum for two fragments. Then, add the sum of the two masses to the momentum prior to explosion. Finally, solve for the distance between the mortar and the larger fragment.
Fundamentals
Consider a particle of mass , m that explodes into two masses #media_tag_0$ as well as
As follows is the momentum of an object of mass , m moving at velocity
:
p indicates the momentum of an object.
Here is the velocity of an object as it travels d during t:
v indicates the velocity of an object.
Find the expression to describe the larger fragment of an object.
Here is the
momentum of smaller mass:
r refers to the mortar’s position at the center of mass, t indicates the time it took for the fragments of the mortar to reach the ground after the explosion, and
represents the velocity of the smaller fragment.
The negative sign meant that the smaller fragment moved backwards following the explosion.
Here is the momentum of a larger mass:
indicates the velocity of the smaller fragment, and the distance between the mortar and the larger fragment.
The momentum
is the momentum of the object prior to explosion.
refers to the angle formed by initial velocity
compared with horizontal.
The horizontal component of velocity,
The linear momentum of the shell’s shell is,
The system’s momentum is conserved because no external force is exerting any influence on it.
is the distance from where the larger shell pieces land.
Conclusion
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