Can Physics Principles Clarify Ground Resistance in a Piledriver Problem?

[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.

Homework Statement

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)
v = 0m/s (stops dead)
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 I am not sure if i have done the right process.

Homework 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 don't 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.

thankyou all in advance

 

[gneill]

Hi Manners, Welcome to PF.

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.

Homework Statement

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)

Okay, striking speed looks fine.

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)
v = 0m/s (stops dead)
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

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?

 

[Manners]

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.

 

[gneill]

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.

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

 

[DeeNos]

Dear student,

Thank you for reaching out for help with your physics problem. It seems like you have made some good progress so far in solving the first question. Your use of equations and calculations seem to be correct, and it is always a good idea to take a step back and think about the problem before moving forward.

As for the second question, it is important to understand the difference between D'Alembert's principle and the principle of conservation of energy. D'Alembert's principle states that the sum of the external forces acting on a system is equal to the mass of the system multiplied by its acceleration. This principle can be used to analyze the forces acting on the hammer and pile system as it falls and strikes the ground.

On the other hand, the principle of conservation of energy states that energy cannot be created or destroyed, only transferred or transformed. In this problem, you can use this principle to analyze the energy of the hammer and pile system before and after the collision. This can help you determine the average resistance of the ground.

I would suggest starting by calculating the total energy of the system before the collision (potential energy due to gravity) and after the collision (kinetic energy of the hammer and pile as they move together). Then, using the principle of conservation of energy, you can equate these two values to determine the average resistance of the ground.

I hope this helps and good luck with your problem. Remember to always think critically and take your time when solving difficult physics problems.