Question

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

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

Answer 1

Answer: (B)

$mg(\frac{h}{s})$

Answer 2

Velocity at the time when knife edge strikes wooden floor is $\sqrt{2gh}$ . The velocity of $\sqrt{2gh}$ is reduced to zero in a distance $s$. If $F$ is the average retardation, then by work-energy theorem, we have $0-\frac{1}{2}mv^{2}=-Fs$ $\Rightarrow$ $F=mg\frac{h}{s}$