Mechanical principles using D'lamberts

• Grinter1
In summary, the problem involves a pile hammer of mass 150kg falling through a distance of 5m and striking a pile of mass 400kg, driving it 75mm into the ground. The hammer does not rebound and the average resistance of the ground needs to be determined. This can be solved using the principles of conservation of momentum and D'lamberts principle or by using conservation of energy. The latter approach may be more physically viable as it takes into account the force constant and the energy stored by the ground.
Grinter1
First time doing this and i dnt really know how to begin.

Homework Statement

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

Homework Equations

v=u+at
v2(squared)=u2(squared)+2as
S=ut+0.5at2(squared)

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:
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

well i don't 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

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

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

1. What is D'lambert's principle?

D'lambert's principle is a mechanical principle that states that the motion of a body is equivalent to the motion of its center of mass plus the motion of the body about its center of mass. It is often used in the analysis of complex mechanical systems.

2. What are the applications of D'lambert's principle?

D'lambert's principle has many applications in the field of mechanics and engineering. It is commonly used in the analysis of rigid bodies, as well as in the study of vibrations and oscillations in mechanical systems.

3. How is D'lambert's principle applied in real-world scenarios?

D'lambert's principle is often applied in real-world scenarios to calculate the forces and accelerations acting on a body. It is also used to analyze the stability and equilibrium of structures and machines.

4. What are the advantages of using D'lambert's principle?

One of the main advantages of using D'lambert's principle is that it simplifies the analysis of complex mechanical systems. It also allows for a more accurate calculation of forces and accelerations, making it a valuable tool for engineers and scientists.

5. Are there any limitations of D'lambert's principle?

While D'lambert's principle is a useful tool in many cases, it does have some limitations. It can only be applied to rigid bodies, and it assumes that the body is in a state of static equilibrium. It also does not take into account factors such as friction and air resistance.

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