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I did some calculations but somehow I feel it's not 100% correct. Could someone have a look please.

Many Thanks

"Task"

A pile driver of mass mh has struck a pile of mass mp and driven the pile D meters into the ground, if the velocity of the strike is V, determine the force due to the resistance in the ground by the following methods:

1. D’Alembers Principle

2. Conservation of energy

V = 3.62m/s

mh = 100kg

mp = 200kg

D = 0.08m

g = 9.81 m/s^2

SOLUTION:

v^2 = u^2 + 2as

where

v = initial velocity

u = final velocity

a = acceleration

s = displacement

transposed the formula to get the acceleration.

Deceleration

a = v^2 - u^2 / 2s

a = 3.62^2 - 0 / 2 * 0.08

a = -81.9 m/s^2

F = ma

F = (200 + 100) * 81.9

F = 24570N

Ground Resistance

R = 300 * 9.81 + 24570

R = 27513N

For the second part I'm trying to work out the Potential and Kinetic energy but then i have no idea what to do next....

K.E = 1/2 mv^2

K.E = 1/2 * 200 * 3.62^2

K.E = 1310.44J

Height of fall

1/2mv^2 = mgh

Transposed to make h the subject

h= 1/2*mv^2 / mg

h = (300 * 3.62^2) / 2+ (200 * 9.81)

h = ~1m

P.E = mgh

P.E = 200 * 9.81 * 1

P.E = 1962J