How Far Does the Pile Move with Each Blow of the Hammer?

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Homework Help Overview

The problem involves a pile driver mechanism where a heavy hammer is dropped onto a pile to drive it into the ground. The mass of the hammer and the force required to drive the pile are provided, along with energy equations relevant to the situation.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to calculate the distance the pile moves using energy equations, but questions arise regarding the inclusion of potential energy changes as the pile moves. Some participants question the reference point for potential energy calculations.

Discussion Status

Participants are actively discussing the calculations and assumptions made regarding potential energy and work done on the pile. There is a recognition of the need to adjust the reference point for potential energy as the pile moves, indicating a productive exploration of the problem.

Contextual Notes

There is a discrepancy between the calculated distance and the expected answer, prompting further examination of the assumptions made in the energy calculations. The discussion highlights the importance of correctly referencing potential energy changes in relation to the pile's movement.

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Homework Statement



A pile driver has a hammer head of mass 4000 kg which is repeatedly raised 3.0 m above a pile and dropped onto it. The force required to drive the pile downwards into the ground is 500 000 N. When the hammerhead is dropped, all the energy foes into moving the pile. How far does the pile go with each blow?

Homework Equations



W= Fd
Et= Eg + Ek
Et= mgh + .5mv^2

The Attempt at a Solution



I found the total energy when the hammer is fully raised.

Et= mgh + .5mv^2
Et= (4000)(9.8)(3) + .5(4000((0)?2
Et= 117 600 J

then i did d= W divided by force to get distance

by slash isn't working for some reason so
117600 divided by 500 000=
=.2352 m
= 23.52 cm

The answer is supposed to be 25.5 cm though. I don't know what to do...
 
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What about the hammer weight? It has potential energy at the start of the pile motion.
 
I included it in the calculation. Please show me what you mean.
 
Your initial calculation had h = 3 m. Using PE = mgh where h =3, gives the PE above the pile top as the reference point. That's fine for calculating the total energy just before the hammer hits the pile.. But when it hits it, the pile moves to a depth 'x', and thus the PE change must be referenced to the depth x below the pile top. So using the instant the hammer hits the pile as the initial point, its energy is 117 600 plus mgx[/color], and the work done on the pile from the ground is 500 000(x).
 

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