Question

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

Answer 1

knife is dropped from $A$ with $u=0\frac{m}{s}$

From $A$ and $B$

when it strikes the ground at $B$ its velocity is:

$v2-u2=2as$

$v2-0=2\left(g\right)\left(h\right)$

$v=\sqrt{2gh}$

after striking the ground it travels a distance ${}^{\prime \prime }{d}^{\prime \prime }$

in this case $u=\sqrt{2gh}$

$v=0$

$s=d$

therefore, $v2-u2=2as$

$0-2gh=2\left(a\right)\left(d\right)$

$a=-\frac{gh}{d}$

Now, force applied by the ground is $=ma=m(-\frac{gh}{d})=-m\frac{2gh}{2d}$