# Homework Help: Mechanical principles using D'lamberts

1. Feb 4, 2010

### Grinter1

First time doin this and i dnt really know how to begin.
1. The problem statement, all variables and given/known data
A pile-driver hammer of mass 150kg falls freely through a distance of 5m to strike a pile of mass 400kg and drives it 75mm into the ground. The hammer does not rebound when driving the pile. Determine the average resistance of the ground. You are required to solve this problem in two ways:
(a)By making use of the principle of conservation of momentum and D'lamberts principle
(b)By making use of the conservation of energy

2. Relevant equations
v=u+at
v2(squared)=u2(squared)+2as
S=ut+0.5at2(squared)
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Feb 5, 2010

### magwas

Be aware that I do not completely understand the question.
The first question is what do they mean in "resistance". The closest thing I can think of is k in Hooke's law:
F = -kx
Actually you would need its integration along x, which gives the stored energy:
$$U=1/2*k*x^2$$
You should check your textbook to figure out whether they mean it.
Now you can compute the energy of the fallen hammer, and have a equation to derive k from the energy stored by ground.
Read the question very carefully to determine how much the hammer have actually gone down.

The problem with this approach that it assumes the "resistance" is along the lines of hooke's law, which holds for elastic, and not for plastic materials. Maybe an approach where we take the force constant would be more physically viable:
$$F=-F_{0}$$
hence
$$U=F_{0}*x$$

Last edited: Feb 5, 2010
3. Mar 25, 2010

### kasot.tope

Well I will work on It and i will send you the answer
but i want you to send me relivent info on D'lamberts principle

4. Mar 25, 2010

### magwas

5. Mar 25, 2010

### kasot.tope

well i dont seems to get the D'lamberts of a thing but i will work on it using consevation of energy method and post it tommorrow is that ok

6. Apr 25, 2010

### sambo1234

Hi I was just wondering if there is any chance you could help me with that question ( a pile hammer of mass 150kg falls freely through a distance of 5M to strike a pile of mass 400kg and drives it 75mm into the ground. The hammer does not rebound when driving the pile determine the average resistance of the ground)

kind regards

Sam

7. Apr 25, 2010

### sambo1234

a pile hammer of mass 150kg falls freely through a distance of 5M to strike a pile of mass 400kg and drives it 75mm into the ground. The hammer does not rebound when driving the pile determine the average resistance of the ground