# Spring characteristics when loaded with a mass

• Jeviah
In summary, a coiled spring would have difficulty extending as far as a vertical spring, and could have adverse effects such as instability.
Jeviah

## Homework Statement

If a spring is loaded with a mass, the spring being completely vertical and the mass hanging below it there would be an extension in the spring relative to the mass applied/force applied according to hookes law. If the same spring was not vertical but coiled (similar to a garter spring but not connected to itself) I assume that the extension would still be the same as if it was vertical. My question is would having a tension spring coiled in this manner have any adverse effects such as instability in the spring, reducing the springs life span etc?

My reasoning behind this question is that coiling a spring in this manner will allow for the spring to extend as much as required while housing it in a much smaller area. I have read about constant force springs however as they do not obey hookes law and I have not/will not cover them in my studies I would prefer to avoid using them.

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## The Attempt at a Solution

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Jeviah said:
I assume that the extension would still be the same as if it was vertical
On this garter spring, where would you hang the mass you mention / apply the extending force ?
And: if not connected to itself, then: connected to what ?

Jeviah said:
was not vertical but coiled
Coiled around what, and how many times?
A rope coiled around a post experiences friction that grows exponentially with the arc length. I think you would quickly run into that problem with your coiled up spring.

Sorry that was a poor description on my part. So my plan is to coil a spring around an axle/wheel essentially, one end attached to the axle/wheel the other end attached to a load that can be removed. The load pulls on the spring and the spring extends, when the load is removed the spring would retract to its original position. The spring will have some flexible casing around it so it doesn't get tangled, also the materials used would be smooth with the hopes of reducing the friction. Friction between surfaces is undesirable but not a deal breaker as it would only slow down the extension/retraction of the spring. The best way I can describe it is that the design would be similar to a retractable tape measure, replacing the tape with a spring.

How many times it would be coiled around the axle I am unsure of at this point as I would need to research springs first and what maximum extension I need.

Jeviah said:
it would only slow down the extension/retraction of the spring.
No, it could stop it entirely.
Jeviah said:
similar to a retractable tape measure
The analogy doesn't quite work. The tape itself does not stretch. But at the centre of the holder there could be a coiled band, like a clockwork spring.
Clockwork springs can stick and need some lubrication, but they do have the advantage of being a flat strip of metal. I can't see the problem as being as easily solved with your flexible casing.

## What is the definition of "spring characteristics"?

Spring characteristics refer to the physical properties of a spring that affect its behavior when it is loaded with a mass. These include the spring constant, damping coefficient, and natural frequency.

## What is the spring constant?

The spring constant, also known as the stiffness coefficient, is a measure of how much force is required to stretch or compress a spring by a certain distance. It is typically represented by the symbol k and is measured in units of force per distance, such as Newtons per meter (N/m).

## How does the mass of an object affect the spring characteristics?

The mass of an object affects the spring characteristics by changing the amount of force required to stretch or compress the spring. The heavier the object, the more force is needed to achieve the same amount of displacement, resulting in a higher spring constant.

## What is damping coefficient?

The damping coefficient is a measure of how much a spring resists oscillation when it is loaded with a mass. A higher damping coefficient means the spring will return to its rest position more quickly after being displaced, resulting in less oscillation.

## What is natural frequency?

Natural frequency refers to the frequency at which a spring will oscillate when it is loaded with a mass. It is determined by the spring constant and the mass of the object, and can be calculated using the equation f0 = 1/(2π√(k/m)), where k is the spring constant and m is the mass of the object.

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