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.

A knife edge of mass .m. is dropped from a height .h. on to ground. On

1.	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.
Answer» Solution :(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)`