Mechanical Science | Get Help with Homework Assignment

[msingh12]

hi guys I am new here so I am not sure how this works but anyway I am having problem with the question below I am not sure how to go about answering it, as our class has had 7 teachers in the last two weeks and havnt even gone threw it but it has to be handed in next week please can some one give me some guidance on this. thank you.

Homework Statement

A pile driver, mass 200kg, is raised to a height of 5m above the pile, mass 1500kg,
before being released to fall freely so that the driver strikes the pile without
rebound and together drive the pile into the ground. The distance the pile is
driven into the ground is 225 mm. Using the principle of conservation of
momentum determining the ground resistance retarding the driver and the pile.

 

[berkeman]

hi guys I am new here so I am not sure how this works but anyway I am having problem with the question below I am not sure how to go about answering it, as our class has had 7 teachers in the last two weeks and havnt even gone threw it but it has to be handed in next week please can some one give me some guidance on this. thank you.

Homework Statement

A pile driver, mass 200kg, is raised to a height of 5m above the pile, mass 1500kg,
before being released to fall freely so that the driver strikes the pile without
rebound and together drive the pile into the ground. The distance the pile is
driven into the ground is 225 mm. Using the principle of conservation of
momentum determining the ground resistance retarding the driver and the pile.

I'm not sure how to try to answer it either. I've never heard of the term "ground resistance", but maybe it has some definition in your text or class notes?

How about starting by describing the concept and applicatoin of "conservation of momentum". What does it mean? When can you use it to help you solve problems? What is the momentum of the pile driver right before contact?

 

[Mene]

Hello,

First, let me start by saying that it's great that you are seeking help with your homework. it's important to ask for guidance when needed and to seek a deeper understanding of concepts and problems.

Now, let's break down the problem and see how we can use the principle of conservation of momentum to solve it.

The pile driver is initially raised to a height of 5m above the pile, which means it has potential energy due to its position. When it is released, this potential energy is converted into kinetic energy as it falls towards the pile.

At the moment of impact, the pile driver and the pile will have the same velocity and therefore the same momentum. This is because the principle of conservation of momentum states that the total momentum of a system remains constant, unless acted upon by an external force.

Now, let's use the equation for conservation of momentum to solve for the unknown ground resistance (R):

Initial momentum = Final momentum

Initial momentum = (mass of pile driver + mass of pile) x initial velocity of pile driver

Final momentum = (mass of pile driver + mass of pile) x final velocity of pile driver

Since the final velocity of the pile driver is zero (it stops after impact), the equation becomes:

(mass of pile driver + mass of pile) x initial velocity of pile driver = 0

Solving for initial velocity of pile driver:

Initial velocity of pile driver = (mass of pile x final velocity of pile) / (mass of pile driver + mass of pile)

Now, we know that the distance the pile is driven into the ground is 225 mm, or 0.225 m. We can use the equation for work to calculate the work done by the pile driver on the pile:

Work done = Force x distance

The force in this case is the ground resistance, R. Therefore, we can write the equation as:

Work done = R x 0.225m

But work done is also equal to the change in kinetic energy of the pile driver and the pile. So we can also write the equation as:

Change in kinetic energy = R x 0.225m

Now, we know that the initial kinetic energy of the pile driver and the pile is equal to the potential energy that the pile driver had when it was raised to a height of 5m.

Initial kinetic energy = Potential energy

(mass