Question

the formula for elastic potential energy, p, of a spring is p = 1/2 kx², where k is the spring constant and x is the length it stretches. a spring has a spring constant of 0.81. which approximate formula can be used to determine the length it stretches, given p? a x = √1.02p b x = √2.47p

Explanation:

Step1: Solve the formula for \(x\)

Given \(P=\frac{1}{2}kx^{2}\), multiply both sides by \(2\) to get \(2P = kx^{2}\). Then divide both sides by \(k\): \(x^{2}=\frac{2P}{k}\).

Step2: Take the square root

Take the square root of both sides. Since \(x\) represents length (a non - negative quantity in this context), \(x=\sqrt{\frac{2P}{k}}\). Substitute \(k = 0.81\) into the formula: \(x=\sqrt{\frac{2P}{0.81}}=\sqrt{2.47P}\)

Answer:

\(x=\sqrt{2.47P}\) (Option B)