Maths & Physics: Hookes Law

[Tekano]

alternatively known as the spring constant.



this was one of those rules that got me hooked with ICE and maths. it really cannot get any simpler to grasp from this - which was part of the attraction, I had always assumed that maths was hard and that the spring force would be a long complicated affair. this was the very first 'ahaah' moment when I could look at a wikipedia page and actually apply directly in ICE

In ICE it is essentially a force that subtracts the current position from a fixed original 'reset' position multiplied by a factor called 'k'

Capture_spring_force.JPG

here is a more elaborate demonstration video involving a little rig which modifies an original spring curve position and the ICE tree is placed on the visible spring curve.



hope this is enough to wet your appetite for the power of Maths and ICE. any questions fire away

[EricTRocks]

This is a great starter post. Thanks for posting. I was also impressed with how simple this force was to setup. In the grand scheme of things having to setup the whole simulation system is a bit complex but luckily ICE is there to save us from that.

[nautilus]

great post, because the force has hooked me, too. but these two things i never understood:

1. how can the position difference vector stay constant, when it changes over time?
what i mean: the difference vector changes (shortens) from frame to frame. how comes the speed stays same?

2. the vector changes direction when it "shoots over". how comes the force pulls back?

can someone explain?
thank you.
N

[dwigfor]

1. how can the position difference vector stay constant, when it changes over time?
what i mean: the difference vector changes (shortens) from frame to frame. how comes the speed stays same?

I think the speed remains the same, because there's nothing dampening it. Easiest ICE way to fix that is to add Drag Force.

2. the vector changes direction when it "shoots over". how comes the force pulls back?

N

I think it's because it is a negative force, traveling in the opposite direction. Further down the Wikipedia page, you see it represented as: F= -k X ("since the direction of the restoring force is opposite to that of the displacement.")

In the Ice Tree at top of page, Rob is subtracting the Point Position from the start position, so the force is always pointed inwards toward the original position.

[dwigfor]

One of the first ICE tutorials, by Todd Akita.



I thought it'd be relevant to include.

[Daniel Brassard]

KhanAcademy to the rescue.

https://www.khanacademy.org/science/phy ... ooke-s-law

[nautilus]

Hello Dwigfor,
thanks for the explanations.

1. how can the position difference vector stay constant, when it changes over time?
what i mean: the difference vector changes (shortens) from frame to frame. how comes the speed stays same?

I think the speed remains the same, because there's nothing dampening it. Easiest ICE way to fix that is to add Drag Force.
Alright, so that means, that once the force (pos diff vec) is set, it stays constant and is not changing any more from timestep to timestep, of course unless you change k, right?
(So that means it is different from setting the same pos diff vec as a velocity, and not as a force, since then it would get smaller and smaller as the object approaches the target - this was what always confused me).

2. the vector changes direction when it "shoots over". how comes the force pulls back?
N

I think it's because it is a negative force, traveling in the opposite direction. Further down the Wikipedia page, you see it represented as: F= -k X ("since the direction of the restoring force is opposite to that of the displacement.").

Now i get it, yes, wiki explains it, i never read it further down...thank you.
it is a kind of case-switch or if/else, right? If displacmeent is bigger than force, multiply force direction by -1. True?

Great post...