# A body weighing 40N drops freely from a height of 50m and penetrates into the ground by 100cm....

## Question:

A body weighing 40N drops freely from a height of 50m and penetrates into the ground by 100cm. Find the average resistance to penetration and the time of penetration.

## Work-Energy Theorem:

Work-Energy Theorem relates the work done on the object and the kinetic energy of the object according to which the change in the kinetic energy of the object is equal to the work done on the object as both are the form of energies.

Given

Weight of the body is {eq}w=40\ N {/eq}

Height from which the object falls is {eq}H=50\ m {/eq}

Now for the penetration depth:

{eq}h=100\ cm {/eq}

Now from conservation of energy:

{eq}v=\sqrt{2gH}\\ v=\sqrt{2\times 9.81\times 50}\\ v=31.32\ m/s {/eq}

Now for the kinetic energy at impact:

{eq}K.E=\frac{1}{2}mv^2\\ K.E=\frac{1}{2}(\frac{40}{9.81})\times (31.32)^2\\ K.E\sim 2000\ J {/eq}

Now for the resistive force:

{eq}F_r\times 0.1=2000\\ F_r=20000\ N {/eq}

Thus, average resistance to penetration is 20000 N

Now for the time of penetration :

{eq}t=\frac{h}{v}\\ t=\frac{0.1}{31.32}\\ t=0.003\ s {/eq}

Thus, the time for the penetration is 0.003 s