Swinging String Attached to Mouse Cursor: Vectors Explored

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    String Vectors
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Discussion Overview

The discussion revolves around the mechanics of a program simulating a swinging string attached to a mouse cursor, focusing on the forces acting on the ball at the end of the string. Participants explore the relevant vectors, including gravity, tension, and potential effects of friction and drag, while considering both theoretical and practical aspects of the simulation.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant identifies gravity and the mouse cursor as two initial force vectors acting on the ball, seeking further guidance on additional vectors.
  • Another participant clarifies that the forces acting on the ball include tension and gravity, noting the directionality of these vectors.
  • There is a suggestion that if the string can stretch, it could be modeled as a spring, affecting the tension force based on elongation.
  • A participant questions how to model the swinging motion of the ball when the cursor is moved, emphasizing the role of gravity in this motion.
  • Another participant asserts that theoretically, the swinging should not stop, attributing real-life damping effects to friction and other forces.
  • One participant emphasizes that gravity is essential for the swinging motion, while friction and air drag are the primary factors that would cause the motion to cease.
  • A structured approach is proposed, suggesting to first model the forces without cursor movement, then introduce cursor acceleration, and finally account for drag and frictional forces.

Areas of Agreement / Disagreement

Participants express differing views on the effects of gravity and friction on the swinging motion, with some emphasizing the importance of friction and drag, while others focus on the theoretical aspects of swinging without these factors. The discussion remains unresolved regarding the best approach to model the system.

Contextual Notes

Participants have not reached consensus on the treatment of friction and drag in the simulation, and there are varying assumptions about the string's properties (e.g., whether it can stretch). The discussion also highlights the complexity of accurately modeling the forces involved.

phaelax
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I'm trying to write a program where a piece of string is attach to the mouse cursor, and the other end has a ball on it. I want to be able to swing it around freely, but I'm not sure how to figure all the vectors. So far, I have 2 force vectors, gravity and the mouse cursor. Any ideas where else I can start?
 
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The two forces that act on the ball is tension and gravity. The gravity force vector should always point from the ball downwards, and the tension force vector should always point from the ball towards the cursor (assuming the string is to remain straight at all times).

If you are allowing the string to stretch, you can treat it as a spring, in which case the magnitude of its force is proportional to the elongation of the string. If it's not allowed to stretch the magnitude of the force would vary depending on the position of the ball and its motion, with a maximum allowed tension so the string will be torn if the limit is exceeded.
 
So if I were to move the cursor to the left, pulling the string, the ball at the end would swing back and forth when I stop moving the cursor. How would I do that? Since gravity is always pulling down on it, I know its got to have something to do with gradually slowing the swinging.
 
Well, theoretically the swinging should not stop. In real life it does, due to friction... but are you going to account for that as well?
 
The ball will be swinging in the air. So the only thing that could affect it is wind or gravity, right?
 
phaelax said: "Since gravity is always pulling down on it, I know its got to have something to do with gradually slowing the swinging."

Gravity doesn't make the ball stop swinging back and forth, in fact without gravity, it wouldn't swing back and forth at all. The only thing that would make it stop swinging is friction at the point where the cursor is attached to the string, and as you said, wind, or the drag caused by the ball moving through the air. But trust me here, you don't want to mess with that yet! If I were you, I'd do this in 3 steps.

1) Don't let the cursor move, and just model two forces: gravity (constant and always down) and tension (magnitude T and always along the direction of the string). You can get help from people here on how to calculate T if you can't figure it out.

2) Now let the cursor accelerate

3) Now add the drag and frictional forces.

If you can make it through #1 you will have learned quite a bit of physics, and it will be pretty cool

If you can make it through #2, you will have learned A LOT of physics and it will be VERY cool! (And I'll want a copy!)

So let us know how it goes.
 
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