Question

Three identical springs each have the same spring constant k. if these three springs are attached end to end forming a spring three times the length of one of the original springs, what will be the spring constant of the combination?

Answer 1

The spring constant of the combination can be calculated using the formula: k_comb = (k1 + k2 + k3) / L, where k1, k2, and k3 are the spring constants of the individual springs, and L is the length of the combined spring.

Step-by-step explanation:

The spring constant of the combination can be calculated using the formula:

kcomb = (k1 + k2 + k3) / L

Where k1, k2, and k3 are the spring constants of the individual springs, and L is the length of the combined spring. In this case, since the combined spring is three times the length of one of the original springs, L = 3L1. Substituting this value into the formula gives:

kcomb = (k1 + k2 + k3) / 3L1

Answer 2

If the springs are connected together from end to end, they are arranged in series. For springs in series, the forces are additive.

Spring 1: F1 = k1(Δx1)
Spring 2: F2 = k2(Δx2)
Spring 1: F3 = k3(Δx3)

Total Force = k1(Δx1)+k2(Δx2)+k3(Δx3)
Total Force = (k1+k2+k3)(Δx,total)

The spring constants are added together and multiplied with the total length of elongation to find the total force acting on it.