Question

the potential energy, \\(p\\), in a spring is represented using the formula \\(p = \frac{1}{2}kx^2\\). lupe uses an equivalent equation, which is solved for \\(k\\), to determine the answers to her homework.

which equation should she use?

\\(k = 2px^2\\)

\\(k = \frac{1}{2}px^2\\)

\\(k = \frac{2p}{x^2}\\)

\\(k = \frac{p}{2x^2}\\)

Explanation:

State the given formula and target variable

We are given the potential energy formula:

$$P = \frac{1}{2}kx^2$$

Our goal is to isolate the spring constant, \(k\), to find an equivalent equation solved for \(k\).

Isolate the variable k

Using the Linear Equation Solving knowledge point

$$
LATEXBLOCK0
$$

Match with the given options

Comparing our isolated equation \(k = \frac{2P}{x^2}\) with the choices:

• \(k = 2Px^2\) (Incorrect)
• \(k = \frac{1}{2}Px^2\) (Incorrect)
• \(k = \frac{2P}{x^2}\) (Correct)
• \(k = \frac{P}{2x^2}\) (Incorrect)

Answer:

• (A) \(k = 2Px^2\)
• (B) \(k = \frac{1}{2}Px^2\)
• (C) \(k = \frac{2P}{x^2}\) (Correct answer)
• (D) \(k = \frac{P}{2x^2}\)