a hammer of mass M falls from a height h repeatedly to drive a pile of mass m into ground. the hammer make the file penetrate in the ground and goes with it up to a distance D in single blow. opposition Force to penetration is given by
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Explanation:
(M+m)d
m
2
gh
+(M+m)g
Using law of conservation of total momentum, we get
(M+m)v=M
2gh
or v=
M+m
M
2gh
Let opposition to penetration be F then
Total work done = change in K.E.
i.e. F=
2
1
(M+m)
d(M+m)
2
(M
2
2gh)
+(M+m)g
=
(M+m)d
M
2
gh
+(M+m)g
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