hammer of the mass 500 gram fall from the height of the 20 and the strikes on the ground on the nail the nails enter into the ground with the acceleration of the 0.5 metre per second square find how much that penetrated in the soil
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Answer:
When the hammer strikes the nail, both of them will go together. So, the collision can be treated as inelastic.
So just after the hammer strikes the nail (which is initially at rest), their velocity will become
v=
M+m
M×u+m×0
=
M+m
Mu
So their kinetic energy after collision will become
2
1
(M+m)(
M+m
Mu
)
2
=
2(M+m)
M
2
u
2
After the penetration, the nail and the hammer come to rest. So their kinetic energy is zero.
So the work done W=∣ΔK∣=∣K
f
−K
i
∣=
2(M+m)
M
2
u
2
It penetrated a m.
While penetration, assuming the resistive force f to be constant, work done by the force W=fa
∴fa=
2(M+m)
M
2
u
2
∴f=[
m+M
M
2
]
2a
u
2
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