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

[-EquinoX-]

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?

 

[glennpagano44]

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)

 

[-EquinoX-]

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?

 

[Doc Al]

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).

 

[-EquinoX-]

the direction of the displacement and the gravity are both down.. so is that why it's 0?

 

[Doc Al]

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.