Modification of hooke with funky springs and evaluation

[springsvt]

I am having an argument with a co-worker about the solution to this.

There is a 4ft sq sheet of plywood with an 18" wide rubber band stretched across it. To measure the spring constant (stiffness) of the rubber band a 6" diameter circular metal plate is slipped under the center of the rubber band and pull out taking force readings at 1", 2", 3", 4" and so on from the face of the plywood.

An assumption is that the rubber band is fixed at the edges of the plywood and does not slip off the plate during the evaluation. Additionally, the rubber band is being evaluated within its linear range, before the yield stress (just go with it)

1) Does the spring constant change when (essentially) dividing the spring in half as described above? (i don’t think so because when you cut a metal spring in half the spring constant of the sides does not change)

2) In calculating the stiffness of the rubber band, does the angle of evaluation matter? i.e., does the measured force require a vector adjustment depending on the angle between the rubber band and the plywood? (i don’t think so) he says that:
where
F= force
S = stiffness
D= distance pulled
A= angle of evaluation
2 = number of springs
F=2*s*d*sin (a) meaning that the s changes depending on the distance pulled from the plywood
I say that
F=2*s*d meaning that the s is constant and does not change when the distance pulled from the plywood (good ole’ Hooke)

3) does the fact that the plate is round/does not cover the entire width of the rubber band have anything to do with the evaluated stiffness? (I don’t think it does, as long as the volume of material evaluated does not change during the test)

Your answers will help sway him but if I can get a text references I would really win, so references/key search words would be great.

 

[LightHero]

1) The spring constant of the rubber band does not change when the rubber band is divided in half. This is because the stiffness of a metal spring is independent of its length, and the same principle applies to rubber bands.2) The measured force does not require a vector adjustment depending on the angle between the rubber band and the plywood. Hooke's law states that the force is proportional to the distance the rubber band is stretched, regardless of the angle. Therefore, the stiffness of the rubber band is not affected by the angle of evaluation.3) The fact that the plate is round and does not cover the entire width of the rubber band does not affect the evaluated stiffness. As long as the volume of material evaluated does not change during the test, the stiffness should remain consistent.