# Modification of hooke with funky springs and evaluation

• springsvt
In summary: Text references and keywords to support these arguments can be found under Hooke's law and the linear range of rubber bands. In summary, the spring constant of a rubber band remains constant when divided in half and is not affected by the angle of evaluation or the shape of the plate used in testing.
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.

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.

## 1. How does the modification of Hooke with funky springs work?

The modification of Hooke with funky springs involves replacing the traditional springs used in Hooke's law with more complex and unpredictable springs. These funky springs can have varying stiffness and non-linear properties, resulting in a more dynamic and versatile system for evaluating forces.

## 2. What are the benefits of using funky springs in Hooke's law?

The use of funky springs in Hooke's law allows for a more accurate and realistic representation of forces in complex systems. The nonlinear properties of these springs can account for factors such as friction, elasticity, and deformation, making it a more precise tool for evaluating forces.

## 3. How do you evaluate the results of the modification of Hooke with funky springs?

Evaluating the results of the modification of Hooke with funky springs involves comparing the measured forces to the predicted forces using Hooke's law. The difference between the two values can provide insights into the characteristics of the funky springs and the system being studied.

## 4. Can the modification of Hooke with funky springs be applied to all systems?

While the modification of Hooke with funky springs can be applied to many systems, it may not be suitable for all situations. It is important to understand the properties and behaviors of the system being studied to determine if this modification is appropriate.

## 5. How does the modification of Hooke with funky springs impact the accuracy of the results?

The use of funky springs in Hooke's law may improve the accuracy of the results in some cases, as it accounts for additional factors that traditional springs cannot. However, the accuracy also depends on the quality and calibration of the funky springs being used. Proper testing and validation are important in ensuring accurate results.

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