pile driver!A pile driver drives a post into the ground. The mass of the pile driver is 2500 kg and it is dropped through?

A pile driver drives a post into the ground. The mass of the pile driver is 2500 kg and it is dropped through a height of 8.0 m on each stroke. If the resisting force of the ground is 4.0 x 10^6 N, how far is the post driven in on each stroke?
Using

v^2 = u^2 + 2as

where v = final velocity (m/s) ; u = initial velocity (m/s) ; a = g = acceleration due to gravity ;
s = distance moved (m)

we can worpile driverk out the velocity of the driver just before it hits the pile.
Since u = zero, then, taking g = 10 m/s^2,

v^2 = 2 * 10 * 8 = 160

The kinetic energy of the driver is given by
KE = (1/2) m v^2 = (1/2) * 2500 * 160 = 200 000 J

This must be equal to the work done by the pile as it moves into the ground.

Work done by pile = F * distance

Since the resisting force is the force that has to be overcome, we can say

pile driver Work done by pile = 4.0 * 10^6 * X
So,

200 000 = 4.0 * 10^6 * X

X = 200 000 / 4.0 * 10^6 = 0.05 m or 5 cm
Post is driven 4.905cm each time. Simply equate the kinetic energy of the pile once it reaches the ground (= mgh) to the Work Done by the ground (=Force applied * distance driven into ground).

Distance = 4.905 cm

:)