Question

there are four springs, s1, s2, s3, and s4, with spring constants k1 = 50 n/m, k2 = 30 n/m, k3 = 75 n/m, and k4 = 25 n/m, respectively. if the same amount of force is applied on all four springs, which spring will have the highest displacement? s2 s1 s3 s4

Explanation:

Step1: Recall Hooke's Law

$F = kx$, where $F$ is force, $k$ is spring - constant and $x$ is displacement. Rearranging for displacement gives $x=\frac{F}{k}$.

Step2: Analyze the relationship

Since the force $F$ is the same for all springs, displacement $x$ is inversely proportional to the spring - constant $k$. The spring with the smallest spring - constant will have the highest displacement.

Step3: Compare spring - constants

We have $k_1 = 50\ N/m$, $k_2=30\ N/m$, $k_3 = 75\ N/m$, $k_4 = 25\ N/m$. The smallest spring - constant is $k_4 = 25\ N/m$.

Answer:

D. $S_4$