A knife edge of mass .m. is dropped from a height .h. on to ground. On reaching the ground it pierces through a distance .s. and stops finally. Find the resistance force offered by the ground and also the time of penetration, retardation during penetration.

Explanation

(i) The potential energy at the height P.E = mgh , Let resistance be R, then mgh `- (R - mg)s`
`R = (mgh)/(s) + mg = mg (1 + (h)/(s))`
(ii) Velocity on reaching the ground `v = sqrt(2 gh)` and stops finally after penetrating through a distance .s.
`rArr ((v+0)/(2))`t = s , where .t. is the time of penetration `vt = 2s , t = (2s)/(v) = (2s)/(sqrt(2gh))`
(iii) From third equation `v^(2) - u^(2) = 2as , 0^(2) - (sqrt(2gh))^(2)` = 2as retardation `= - a = (2gh)/(2s) = (gh)/(s)`