Why shorter springs are stiffer than longer springs?

Answer 1

I assume you already know and understand that a spring has a spring constant and to calculate that we use the FORCE (F) exerted on the spring and the change in length (x) to find the proportionality constant (k).

I believe this concept is explained in detail before.

to understand WHY the spring is stiffer when it's shorter you have to considder the principles of elasticity where STRESS = ELASTICITY x STRAIN

although its not the same thing for a spring (in theory) lets use the PRINCIPLE to understand the behaviorof the spring

Stress is the force used to compress it, we won't considder this because the force exerted on the long and short springmay be the same and elasticity remain unchanged (the materials for the short and long springs are the same)

STRAIN is the relationship of the CHANGE in length and the original length

so lets take two springs of same material. one is 8m and one 4m long both are compressed to 2m, which will have greater strain.... hence require greater force to get it to 2m?

Strain is final LENGTH/original Lenth

2m/8m = 0.25

2m/4m = 0.5 THEREFOR the strain on the shorter spring is GREATER.