Eccentric rotation of a trebuchet arm

In summary, the conversation discusses the construction of a mathematical model for a trebuchet throw. The speaker has successfully built a simplified model, but is looking for equations to calculate the changes in potential gravitational energy and moment of inertia for a more accurate model where the pivot point is not included in the arm. They also mention using a sling, but ultimately decide not to include it in the model. The conversation ends with a request for a visual representation of the design.
  • #1
meisadam
2
0
If the word eccentric is not used correctly, please correct me.

Homework Statement


I am constructing a mathematical model of trebuchet throw. For the throwing part, I simply use the relation [tex] ΔE_p = E_k [/tex], so the change of potential gravitational energy goes into the rotational kinetic energy. I succesfully built the model, but it is oversimplified in at least one point, the arm does not rotate around a point that is "included" in it, but the pivot point is 8 cm above it. What equations can I use to calculate the changes in potential gravitational energy of such body and its moment of inertia?

Homework Equations


That's my question

The Attempt at a Solution


I have a complete model of the situation assuming the pivot point is included in the arm, but have no clue how to make it eccentric.
 
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  • #2
How hard would it be to sketch and scan what you are talking about, or to google image search and find something close to what you have. I'm not clear what you have and a picture is worth a thousand words. Is it built like the following?



or this,

http://www.youtube.com/watch?v=3hCyQIWmzS8&feature=related
 
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  • #4
Consider the equilibrium configuration of your design when you let it go, it will be significantly less then vertical. The arm will only move about 45 degrees, 90 degrees for the other design. The large mass moves less vertically so your projectile has less energy.
 
  • #5


I would first like to clarify the use of the word "eccentric" in this context. In physics, the term eccentric typically refers to a measure of how much an object's orbit deviates from a perfect circle. In the context of a trebuchet arm, I believe the term you are looking for is "off-center" or "non-symmetric" rotation.

To address your question, the equations you can use to calculate the changes in potential gravitational energy and moment of inertia for a trebuchet arm with off-center rotation will depend on the specific geometry and design of your trebuchet. However, in general, you can use the following equations:

1. Potential Gravitational Energy:
The potential gravitational energy of an object is given by the equation E_p = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object's center of mass above the ground. In the case of a trebuchet arm with off-center rotation, you will need to calculate the height of the arm's center of mass from the pivot point, rather than from the ground. This can be done using basic trigonometry and the known dimensions of your trebuchet arm.

2. Moment of Inertia:
The moment of inertia of an object is a measure of its resistance to rotational motion and is given by the equation I = ∑mr^2, where m is the mass of each component of the object and r is the distance of that component from the axis of rotation. In the case of a trebuchet arm with off-center rotation, you will need to take into account the non-symmetric distribution of mass along the arm and calculate the moment of inertia accordingly. This can also be done using basic trigonometry and the known dimensions of your trebuchet arm.

I hope this helps in your mathematical modeling of a trebuchet throw. As always, it is important to carefully consider all the variables and assumptions in your model to ensure its accuracy and relevance to real-world situations. Best of luck!
 

1. What is eccentric rotation?

Eccentric rotation is a type of rotational motion where the axis of rotation is not located at the center of the rotating object, but rather at a different point. This creates an off-center rotation, resulting in a non-uniform circular motion.

2. What is a trebuchet arm?

A trebuchet arm is the long, swinging beam or lever of a trebuchet, a medieval siege weapon used to launch projectiles. The arm is attached to a pivot point and is responsible for transferring the energy from the counterweight to the projectile, propelling it forward.

3. How does eccentric rotation affect the performance of a trebuchet arm?

Eccentric rotation can significantly impact the performance of a trebuchet arm. The off-center rotation creates an uneven distribution of force, causing the arm to move in a non-linear path. This can result in a less accurate or less powerful launch of the projectile.

4. Can eccentric rotation be beneficial for a trebuchet arm?

Yes, eccentric rotation can be beneficial for a trebuchet arm in some cases. By adjusting the position of the pivot point and the amount of off-center rotation, the trajectory of the projectile can be altered. This can be useful for targeting specific areas or for launching projectiles over obstacles.

5. How do scientists study the eccentric rotation of a trebuchet arm?

Scientists study the eccentric rotation of a trebuchet arm through a combination of theoretical calculations and experiments. They use mathematical models to predict how the arm will move and then compare these predictions to real-world data collected from physical experiments using trebuchet prototypes.

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