Question

spring a has a constant of 2 n/m, while spring b has a constant of 10 n/m. which of the following statements is true? (1 point) the same force will displace either spring the same distance in opposite direction. more force is required to displace spring a from its equilibrium position. the same force will displace either spring the same distance in the same direction. more force is required to displace spring b from its equilibrium position. check answer remaining attempts : 3

Explanation:

Step1: Recall Hooke's Law

Hooke's Law is $F = kx$, where $F$ is the force applied, $k$ is the spring - constant, and $x$ is the displacement from the equilibrium position. We can rewrite it as $x=\frac{F}{k}$.

Step2: Analyze the relationship between force, spring - constant and displacement

For a given force $F$, if $k_A = 2\ N/m$ and $k_B=10\ N/m$, and $x_A=\frac{F}{k_A}$, $x_B=\frac{F}{k_B}$. Since $k_B>k_A$, for the same $F$, $x_A > x_B$. Also, a larger spring - constant $k$ means more force is required to produce the same displacement. Spring B has a larger spring - constant ($k = 10\ N/m$) compared to spring A ($k = 2\ N/m$), so more force is required to displace spring B from its equilibrium position.

Answer:

More force is required to displace spring B from its equilibrium position.