a stretched spring has 5184 j of elastic potential energy and a spring constant of 16,200 n/m. what is the…

Explanation:

Step1: Recall elastic - potential - energy formula

The formula for elastic potential energy is $U = \frac{1}{2}kx^{2}$, where $U$ is the elastic potential energy, $k$ is the spring constant, and $x$ is the displacement. We need to solve for $x$.

Step2: Rearrange the formula for $x$

Starting from $U=\frac{1}{2}kx^{2}$, we can first multiply both sides by 2 to get $2U = kx^{2}$. Then, divide both sides by $k$: $x^{2}=\frac{2U}{k}$. Taking the square - root of both sides gives $x=\sqrt{\frac{2U}{k}}$.

Step3: Substitute the given values

We are given that $U = 5184\ J$ and $k = 16200\ N/m$. Substituting these values into the formula $x=\sqrt{\frac{2U}{k}}$, we have $x=\sqrt{\frac{2\times5184}{16200}}$. First, calculate the value inside the square - root: $\frac{2\times5184}{16200}=\frac{10368}{16200}=0.64$. Then, $\sqrt{0.64}=0.80\ m$.

Answer:

$0.80\ m$