# D'lamberts Question.

1. Feb 9, 2010

### Grinter1

Could you tell me if i am right please and if im wrong could you point out any mistakes?

A pile-driver hammer of mass 150kg falls freely a distance of 5m to strike a pile of mass 400kg and drives it 75mm in the ground. The hammer doesnt rebound when driving the pile. Calculate the average resistance of the ground. You are required to solve this problem by:
(a)By making use of the principle of conservation of momentum and D'lamberts principle

2. Relevant equations
v=u+at
v2(squared)=u2(squared)+2as
S=ut+0.5at2(squared)
f=m*a

3. The attempt at a solution

a)
Hammer mass=150kg
Falls freely= gravity = 9.81
Distance= 5m
pile mass =400kg
depth= 75mm= 0.075m
no rebound
Average resistance= ???

M1*U1+M2*U1=M3*V1
(150*9.81)+(400*0)=1471.5 m/s

a=v(squared)-U(squared)/2*5
a= 0.981
f=m*a
f=147.15

FR=f-m*a-m*g
FR= -5395.5

2. Feb 9, 2010

### magwas

That French guy have been called D'Alembert.

Your solution is hard to decipher, because you did not define your variables correctly, and it seems
you are switching them in the middle of the solution.
It seems you meant
M1 = 150 kg //hammer mass
U1 = 9.81 m/s^2 //gravitational acceleration on earth surface
M2 = 400 kg //mass of pile
U2 = 0 m/s^2 //acceleration of pile (I guess you meant U2 at the second instance of U1)

so
M1*U1+M2*U2=150 kg * 9.81 m/s^2 + 400 kg * 0 m/s^2 = 1471.5 kg*m/s^2
notice the difference in units between your and my solution!

This far I could go with deciphering your solution. Maybe this could be the cause that you get an answer so hardly.

I would suggest to start over, define your variables, and always write units.
Defining your variables helps you to understand yourself (and others to understand you, but it is secondary)
Imagine when you are in the middle of a lengthy solution. You cannot afford to mix two variables because
they are not defined clearly. And in the beginning even this problem can be lengthy for you.
Writing units helps you to spot errors (And cheating in the exam by coming up with forgotten equations correctly based only on the units of variables involved. Serious scientists also do this, and call it dimensional analysis.).