A knife edge of mass .m. is dropped from...

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.

Text Solution

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(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)`

An open knife edge of mass M is dropped from a height .h. on a wooden floor. If the blade penetrates a distance .s. into the wood, the average resistance offered by the wood to the blade is :

`Mg(1+(h)/(s))`

`Mg(1-(h)/(s))`

`Mg(1+(h)/(s))^(2)`

An open knife edge of mass M is dropped from a height h on wooden floor. If the blade penetrates a distance s into the wood, the average resistance offered by the wood to the blade is

`Mg(1+(h)/s)`

`Mg (1-(h)/s)`

`Mg (1+(h)/s)^2`

An open knife edge of mass M is dropped from a height 'h' on a wooden floor. If the blade penetrates a distance 's' into the wood, the average resistance offered by the wood to the blade is :

`Mg`