# String tension

phaelax
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?

## Answers and Replies

Chen
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.

phaelax
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.

Chen
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?

phaelax
The ball will be swinging in the air. So the only thing that could affect it is wind or gravity, right?

jdavel
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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