Question

does the size and the diameter of a spring affect how much it will extend when I add a certain mass to it?

Ex:

Giving that the weight applied is the same

A thick spring will extend more that a thinner one? Or a longer spring will extend more that a short one?

Answer 1

how much it will extend when I add a certain mass to it depends on spring constant of the spring (k).

and Spring constant is inversely proportional to length and extension in spring is also inversely proportional to spring constant. which means extension in spring is directly proportional to the length of spring.

Longer the spring more will it extend.

In dealing with a coil spring the spring constant will depend on the stiffness of the spring material, the thickness of the wire from which the spring is wound and, diameter of the turns of the coil, the number of turns per unit length and the overall length of the spring.

So, Thick spring will extend less than thinner spring.

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The mass of the spring will depend on the density of the material, the thickness of the wire from which the spring is wound, the diameter of the turns of the coil, the number of turns per meter of spring length and the overall length of the spring.

Since the mass and the spring constant have some factors in common, they will in general not be independent of each other, but the spring constant may not vary in any simple way with the mass of a spring.

More exactly, the spring constant will probably change for springs of different mass, made out of the same material. If the change in mass is due only to a longer spring, the spring constant will decrease. Long springs tend to be softer than short ones. If the change in mass is due only to thicker wire, the spring constant will increase. Springs made of fat material are stiffer than those made of thin material. If the change in mass is due to some combination of changed wire and changed length, we may not be able to say. It might even be possible to construct two springs of different mass with the same spring constant.