Work kinetic energy theorem

In summary, the conversation discusses using energy considerations to calculate the average force exerted by a pile driver on a steel I-beam while the pile driver is brought to rest after falling 5 m and driving the beam 12 cm into the ground. The use of cos 0 and cos 180 is explained as the angle between the force and displacement, as per the definition of Work. The displacement is h+d for the force of gravity, while it is only d for the beam force, as the beam force only acts while in contact with the pile driver. The angle between the direction of displacement and gravity is 0 since they both point downwards.
  • #1
-EquinoX-
564
1

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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  • #2
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)
 
  • #3
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?
 
  • #4
-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).
 
  • #5
the direction of the displacement and the gravity are both down.. so is that why it's 0?
 
  • #6
-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.
 

What is the work kinetic energy theorem?

The work kinetic energy theorem is a fundamental principle in physics that states that the net work done on an object is equal to the change in its kinetic energy. In simpler terms, it explains how the energy of an object changes when a force is applied to it.

What is the equation for the work kinetic energy theorem?

The equation for the work kinetic energy theorem is W = ΔKE = KEf - KEi = ½ mvf2 - ½ mvi2, where W represents work, ΔKE represents the change in kinetic energy, KEf is the final kinetic energy, KEi is the initial kinetic energy, m is the mass of the object, and v is its velocity.

How does the work kinetic energy theorem apply to real-life situations?

The work kinetic energy theorem can be applied to various real-life situations, such as throwing a ball, riding a bike, or braking a car. In all of these cases, a force is applied to an object, causing its kinetic energy to change. This principle is also used in industries such as engineering and mechanics to calculate the work and energy involved in various processes.

What is the relationship between work and kinetic energy?

The work kinetic energy theorem states that work and kinetic energy are directly related. When work is done on an object, its kinetic energy changes. This means that the more work is done on an object, the greater its kinetic energy will be.

What are the limitations of the work kinetic energy theorem?

The work kinetic energy theorem only applies to objects in motion and does not take into account other forms of energy, such as potential energy. It also assumes that the force applied to an object is parallel to its displacement. In reality, there are often other forces at play, such as friction, which can affect the object's kinetic energy and limit the accuracy of this theorem.

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