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PE and KE
The Pile Driver
Purpose:
To obtain a clearer understanding of the relationships existing between potential and kinetic energy.
Apparatus:
Pile Driver; meter stick; nails, wooden blocks.
Procedure:
This experiment will be performed by the class as a whole because of the nature of the equipment
involved.
Theory:
Work is required to raise an object. The quantity of work is equal to the force required to lift the object
(equal to the object's weight) multiplied by the vertical distance through which the object is moved. In the
case of the pile driver, the force required to lift the hammer of mass m is F = m g and the work done in
lifting it a distance "h" is
Work to raise the hammer = F . h = m g h
Due to its position the hammer now has potential energy equal to the work done in raising it.
Work done in raising the hammer = F . h = m g h = P E
When the hammer is released, its potential energy is converted into kinetic energy.
since work done to raise hammer = F . h = m g h = PE = K E = 1/2 m v 2
Upon striking the nail, the kinetic energy is used in doing work, that is in driving the nail a distance "d" into
the block against an average resisting force "Fr " and therefore, if one assumes that all the KE is used to
drive the nail, the work performed in moving the nail is equal to the work done in lifting the hammer in the
pile driver.
thus work done to raise object = m g h = PE = KE = 1/2 mv2 = work done to drive nail = Fr . D
therefore
where
m g h = Fr . D
m = mass of hammer
g = acceleration due to gravity
h = distance of fall of the hammer from dropping point to final resting
point after dropping on nail
Fr = Force by which the wood resists penetration by the nail
D = Distance nail is moved into wood
Part 1: The Effect of the Height of the Hammer Upon the Penetration on the Nail
Start a nail in each of three blocks of the same kind of wood. The head of each nail should be the same
distance above the block. Record all data in TABLE I. Place one block in position, raise the hammer to the
maximum height and measure and record the height of the hammer above the top of the nail. Allow the
hammer to fall and again measure the height of the nail head above the block. Record and from the two
values determine the penetration.
Repeat with the other two blocks, but use a different height of fall in each case. Compute the resisting
force in newtons. NOTE: The penetration of the nail should be proportional to the height of the hammer
fall, all other conditions being the same.
PART 2: The Effect of Depth of Penetration Upon the Resisting Force.
Start a nail in a block of wood and in TABLE II record the distance of the head of the nail above the
block. Place the block in the proper position on the base of the pile driver and raise the hammer to the
maximum height. Measure and record the distance of the hammer above the nail. Allow the hammer to
fall. Measure and record distance of the nail's head above block. Compute penetration of nail due to this
blow. Repeat as many times as necessary until nail is completely driven into the block. The distance the
hammer falls increases for each succeeding blow. Record all data and calculations in TABLE II.
WRITE UP:
Do the calculations necessary to fill in the blank areas in both data tables (report only the properly
rounded answers and their labels).
For Part 1:
Plot, by computer, the relationship of Total Height of Fall of the Hammer on the ordinate vs. Nail
Penetration on the abscissa. Title the graph appropriately. Provide an equation as well as a written
statement describing the relationship of the graphed parameters. Put this information on the graph. Staple
your graph to the data table sheet.
For Part 2:
Plot, by computer, the effect of total penetration on resisting force. Plot total penetration of nail data as
abscissas and resisting force calculations as ordinates. Title the graph appropriately. Provide an equation as
well as a written statement describing the relationship of total penetration vs. resisting force. Put this
information on the graph.
Staple your graph to the data table sheet. The data table sheet should be first with the data tables on top.
Hammer Mass = 4.000 Kg
TABLE I
BLOCK RELEASE HEIGHT
# OF HAMMER ABOVE
NAIL HEAD (m)
DISTANCE O F NAIL HEAD
ABOVE BLOCK
INITIAL (m)
FINAL (m)
PENETRATION
OF NAIL (m)
TOTAL HEIGHT
OF HAMMER
FALL (m)
RESISTING
FORCE
IN NEWTONS
1
2
3
4
5
6
TABLE II
DROP RELEASE HEIGHT
# OF HAMMER ABOVE
NAIL HEAD (m)
1
2
3
4
5
6
7
DISTANCE O F NAIL HEAD
ABOVE
BLOCK
INITIAL (m)
FINAL (m)
PENETRATION OF
NAIL FOR DROP
(m)
TOTAL NAIL
PENETRATION
(m)
TOTAL HEIGHT
OF HAMMER
FALL (m)
RESISTING
FORCE
IN NEWTONS
Answer these questions:
1. Using your equation from Part 1, determine the average resisting force of the nail as it was driven
into the wood. Explain your logic.
2.
Compare the value you determined in question 1 with the individual Resisting Forces calculation
shown in Table 1. How and why are they different?
3. How much potential energy does the hammer have if it is lifted to a height of 98.74 cm?
4.
What is the kinetic energy of
the hammer just before hitting
the nail if it fell from a height
of 98.74 cm above the nail's head
(show in area to right)?
5.
What is the velocity of the hammer described in question 4 above just before it hits the nail head?
6.
From your graph from Table 2, describe the relationship of Fr and total depth of penetration of the
nail. How could you account for this relationship (describe its causal mechanism)?
7. Explain why the nail was not driven in as far when the hammer was not lifted as far. Support your
answer with data from this graph and use PE, KE, work to raise the hammer, and work to drive the
nail in your explanation.