Question

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

• A. $Mg$
• B. $Mg(1+\frac{h}{s})$
• C. $Mg\left(\frac{1-h}{s}\right)$
• D. $Mg(\frac{1+h}{s}{)}^2$

Answer 1

Answer: (B)

$Mg(1+\frac{h}{s})$

Let $F$ be the resistance force of wooden plank.It will be acting opposite to the weight of body therefore , resultant force opposite to motion
$=F-Mg$
Velocity of fall $=\sqrt{2gh}$
$Workdone=(F-Mg)s=kineticenergy$
$=\frac{1}{2}M(\sqrt{2gh}{)}^2$
$F=\frac{Mgh}{s}+Mg$
$=Mg(1+\frac{h}{s})$