Question
An open knife edge of mass m is dropped from a height h on a wooden floor. if the blade penetrates a dist s into the wood , the avg. resistance offered by wood to blade. ANS mg(1+h/s)
Joshi sir comment
velocity at the time of strike of the knife at the wood = √(2gh)
now equation for penetration on the wood is R-mg = ma here R is reaction by the wood
so R = m(g+a)
here it is given that s is the distance penetrated by the knife on the wood so 02 = (√2gh) - 2as so a = 2gh/2s = gh/s
on taking this value of a
we get R = m(g+gh/s) = mg(1+h/s)