The potential energy, P, in a spring is represented using the formula P = A equals StartFraction one-half EndFraction b h.kx2. Lupe uses an equivalent equation, which is solved for k, to determine the answers to her homework.

Question

Which equation should she use?

k = 2Px2
k = k equals StartFraction one-half EndFraction P x squared.Px2
k = k equals StartFraction 2 P Over x squared EndFraction.
k = k equals StartFraction P Over 2 x squared EndFraction.

Answer 1

The potential energy in a spring is given by the formula:

\[ P = \frac{1}{2} k x^2 \]

To solve for \( k \), we can rearrange the equation:

1. Start with the original equation: \[ P = \frac{1}{2} k x^2 \]

2. Multiply both sides by 2 to eliminate the fraction: \[ 2P = k x^2 \]

3. To isolate \( k \), divide both sides by \( x^2 \): \[ k = \frac{2P}{x^2} \]

So, the correct equation for \( k \) that Lupe should use is:

\[ k = \frac{2P}{x^2} \]

This corresponds to the option:

k = StartFraction 2 P Over x squared EndFraction.