Maximizing Projectile Distance with Torsion Spring Catapult

In summary: Ok, so do you understand how to compute the total energy from that chart (combined with knowledge of the length of the arm)?
  • #1
Berwin
3
0

Homework Statement



Determine maximum distance an one ounce projectile can be launched with a torsion spring catapult.
6vtWp.png


Homework Equations


E = F * d = 1/2 * m * v02Note: Theta is the measurement of how far the lever arm is being pulled back.

Am I missing something?
 
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  • #2
There does not appear to be enough information, in two ways.
There's no basis for figuring the distance through which the force acts. It doesn't say what the force is for smaller angles. It could be linear down to about 10 degrees, or it might suddenly drop to zero somewhere below 140.
But your equation E = F * d is only valid for constant forces, which this clearly is not. The more general form requires you to integrate F over the distance. If the force is a linear function of distance over the range of integration (which it looks to be from the table) then the result will be quadratic.
 
  • #3
If it helps at all, the torsion spring in this case is one you find in a mousetrap. We've attached a plastic spoon to the lever arm of the mousetrap, which together reach 0.17145 meters. Does this make a difference?
 
  • #4
Berwin said:
We've attached a plastic spoon to the lever arm of the mousetrap, which together reach 0.17145 meters.
That's useful info. So as the arm moves through angle dθ, the force advances rdθ, where r = 0.17145 m. That allows you to calculate the energy imparted as the angle changes.
However, just realized I should have checked something. The F values in the table really are the force at the end of the arm, yes? They're not torque (Nm)?
That leaves the question of whether the table is complete. I.e., as the angle falls below 140o, does the force suddenly vanish or does it continue to decline linearly?
 
  • #5
Yes, it's just the force at the end of the arm. The force suddenly vanishes. We only wanted to test the angles given above in the chart.
 
  • #6
Berwin said:
Yes, it's just the force at the end of the arm. The force suddenly vanishes. We only wanted to test the angles given above in the chart.
Ok, so do you understand how to compute the total energy from that chart (combined with knowledge of the length of the arm)?
 

1. What is a torsion spring catapult?

A torsion spring catapult is a type of catapult that uses the energy stored in a twisted spring to launch a projectile. It works by twisting the spring, which stores potential energy, and then releasing it to transfer the energy to the projectile and launch it forward.

2. How does a torsion spring catapult work?

A torsion spring catapult works by using the energy stored in a twisted spring to launch a projectile. The spring is twisted by winding it tightly using a lever or other mechanism. When the trigger is released, the spring unwinds rapidly, transferring the stored energy to the projectile and launching it forward.

3. What are the advantages of using a torsion spring catapult?

One of the main advantages of using a torsion spring catapult is its efficiency. The energy stored in the twisted spring is released quickly and efficiently, resulting in a powerful launch. Torsion spring catapults are also relatively easy to build and can be made with simple materials.

4. What are the limitations of a torsion spring catapult?

One limitation of a torsion spring catapult is its lack of accuracy. The release of the spring can be difficult to control, resulting in varying launch distances and angles. Additionally, torsion spring catapults are not as powerful as other types of catapults, such as trebuchets.

5. What are some potential applications of a torsion spring catapult?

Torsion spring catapults have been used historically as weapons of war, but they also have other applications. They can be used in science experiments to demonstrate principles of energy and motion, or as a fun STEM project for students. Torsion spring catapults can also be used in recreational activities, such as launching objects for distance or accuracy competitions.

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