How Is the Average Force Calculated When a Pile Driver Hits a Beam?

AI Thread Summary
The discussion focuses on calculating the average force exerted by a beam on a pile driver using energy considerations. A 2100 kg pile driver falls 5 m before impacting the beam and drives it an additional 12 cm into the ground. Participants clarify the use of angles in the work equation, specifically why cos 0 and cos 180 are relevant, as they relate to the direction of force and displacement. The angle is zero when the force and displacement are in the same direction, and the displacement for the beam force is only over the distance it acts, while gravity affects the pile driver during its entire fall. Understanding these concepts is crucial for accurately calculating the average force.
-EquinoX-
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Homework Statement


A 2100 kg pile driver is used to drive a steel I-beam into the ground. The pile driver falls 5 m before coming into contact with the top of the beam. Then it driver the beam 12 cm farther into the ground as it comes to rest. Using energy considerations, calculate the average force the beam exerts on the pile driver while the pile driver is brought to rest.


Homework Equations





The Attempt at a Solution



http://img238.imageshack.us/img238/7935/beamdi0.jpg
http://g.imageshack.us/img238/beamdi0.jpg/1/

I don't understand why they use cos 0 and cos 180 here? Can someone please explain it to me?
 
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You use the cos of 0 and 180 because that is the angle between the Force and displacment. This is the definition of Work. W=Fdcos(angle). This would make the work either negative or positive. If one moves an object against a force(gravity) then there would be a negative Wnet. If one moves an object with a force(gravity) the positive work is being done. Again, This is all due to the definition of work W=fdcos(angle)
 
okay, I get all that, however I can't see that that angle between the force and displacement is 0 and 180, can you please show me that? also why is it on the Wgravity the displacement is h+d and on the beam it's only d?
 
-EquinoX- said:
okay, I get all that, however I can't see that that angle between the force and displacement is 0 and 180, can you please show me that?
Compare the direction of the displacement (down) with the direction of gravity and the direction of the force from the beam.
also why is it on the Wgravity the displacement is h+d and on the beam it's only d?
The beam force only acts while in contact with the pile driver, which is over the distance d. Gravity acts on the pile driver during its fall as well (thus h+d).
 
the direction of the displacement and the gravity are both down.. so is that why it's 0?
 
-EquinoX- said:
the direction of the displacement and the gravity are both down.. so is that why it's 0?
Yes. They are two vectors that point in the same direction, so the angle between them is 0.
 
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