Question

why a small bullet fired from a gun does create a big impact?

Answer 1

because of the Newtons 3 law ,,,, which states that every action had an equal and opposite reaction

Answer 2

When a bullet with mass m leaves a gun with a velocity v, the gun must have an equal-but-opposed momentum MV, where M is the mass of the gun and V is the recoil velocity, or
mv+MV=0
m
v
+
M
V
=
0
. If there are two possible gun sizes, M1
M
1
and M2
M
2
, each will have a recoil velocity V1
V
1
and V2
V
2
. If, for instance, M2=2M1
M
2
=
2
M
1
,
M1V1=M2V2
M
1
V
1
=
M
2
V
2
and
V1=2V2
V
1
=
2
V
2
Why does this matter? Consider kinetic energy. Let K1
K
1
be the kinetic energy of M1
M
1
, and K2
K
2
is that of M2
M
2
. Then
K1K2=M1V122M2V222=M1M2(V1V2)2=1222=2
K
1
K
2
=
M
1
V
1
2
2
M
2
V
2
2
2
=
M
1
M
2
(
V
1
V
2
)
2
=
1
2
2
2
=
2
So the lighter gun has twice the kinetic energy of the heavier gun and this shows up in two ways. First, since both guns need to stop in about the same distance, the force applied to the lighter gun must be greater than that applied to the heavier. By Newton's First Law, this means that the lighter gun pushes harder on the hand or shoulder of the shooter. Second, the duration of acceleration must be smaller for the lighter gun, since
S1=a1t122=V1t12=S2=a2t222=V2t22
S
1
=
a
1
t
1
2
2
=
V
1
t
1
2
=
S
2
=
a
2
t
2
2
2
=
V
2
t
2
2
and
V1t1=V2t2
V
1
t
1
=
V
2
t
2
or
t1t2=V2V1=12
t
1
t
2
=
V
2
V
1
=
1
2
So not only is the recoil force greater for the lighter gun, it lasts a shorter time and is therefore "sharper".