# Homework Help: 2 Q's on average resistance of ground, d'alembert's principle and energy conservation

1. Mar 15, 2012

### Manners

hi there, i was wondering if anybody could help me with some problems i am having great difficulty getting my head around at the minute, any help would be greatly appreciated.

1. The problem statement, all variables and given/known data

The first question is:
A piledriver hammer of mass 150kg falls freely through a distance of 5m to strike a pile of mass 400kg and drives 0.075m into the ground. the hammer does not rebound when driving the pile. Determine the average resistance of the ground.

The second question is linked to the first and is: Compare and contrast the use of D'Alembert's principle with the principle of conservation of energy when solving the problem given above.

so far i have used linear equations to work out the striking speed of the hammer. using:
s = 5m
a = 9.81m/s (gravity)
u = 0m/s (initial velocity)

i worked out v in the equation v(squared) = u(squared) + 2as. this came to 9.905m/s (striking speed)

i then put this value into v = u + at. and found t = 1second.

my next step was to find the resistance force when the hammer has struck the object and now they are moving together.

u = 9.905m/s (striking speed)
s = 0.075m (distance it goes into the ground)

i found a using v(squared) = u(squared) + 2as. this came to -654.06m/s

and t using v = u + at. this came to 0.015seconds.

i then used the resistance force equation F=ma. 550 x -654.06 = -349.733kN

this was quite straight forward after a few steps back to think about it, but im not sure if i have done the right process.

2. Relevant equations
v = u+at
V(squared) = U(squared) + 2as
F = ma
I = mv - mu
I = Ft

if this is correct, then the main problem for me is to work out the next stage of the question which is using the principle of conservation of energy. It has me really stumped because we dont have an example to follow that is similar, or anything even closely linked to it that we may use.

any help would be greatly appreciated, even just to clarify that my first question is correct.

2. Mar 15, 2012

### Staff: Mentor

Re: 2 Q's on average resistance of ground, d'alembert's principle and energy conserva

Hi Manners, Welcome to PF.

Okay, striking speed looks fine.
Okay, bit of a problem with that last part. When the pile driver slams into the pile, what you have in essence is a perfectly inelastic collision. The pile+driver is not going start with the same speed as the driver alone before the collision. What conservation law can you apply to find out what the initial speed of the pile+driver?

3. Mar 19, 2012

### Manners

Re: 2 Q's on average resistance of ground, d'alembert's principle and energy conserva

To be honest mate we havnt included a lot of other laws to the problem. It's only a Btec ND question so we are including those equations above.
The only other thing I can think of doing is using the linear equations again to work backwards through it and find the speed of the pile, as it starts from 0 and I already have the distance.

4. Mar 19, 2012

### Staff: Mentor

Re: 2 Q's on average resistance of ground, d'alembert's principle and energy conserva

That might be problematical since you aren't given the length of time that the pile is moving.

I suggest that you add conservation of momentum to the repertoire of equations