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…

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

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

Answer

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. $S_4$