Question
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.
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.
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.
Answers
GPT-4o mini
To find the correct equation for \( k \) based on the potential energy formula given as:
\[
P = \frac{1}{2} k x^2,
\]
we need to rearrange this equation to solve for \( k \).
Starting with the original equation:
\[
P = \frac{1}{2} k x^2,
\]
we can multiply both sides by 2 to eliminate the fraction:
\[
2P = k x^2.
\]
Next, we solve for \( k \) by dividing both sides by \( x^2 \):
\[
k = \frac{2P}{x^2}.
\]
Thus, the correct equation that Lupe should use is:
\[
k = \frac{2P}{x^2}.
\]
This corresponds to the option:
\[ k = \frac{2P}{x^2}. \]
\[
P = \frac{1}{2} k x^2,
\]
we need to rearrange this equation to solve for \( k \).
Starting with the original equation:
\[
P = \frac{1}{2} k x^2,
\]
we can multiply both sides by 2 to eliminate the fraction:
\[
2P = k x^2.
\]
Next, we solve for \( k \) by dividing both sides by \( x^2 \):
\[
k = \frac{2P}{x^2}.
\]
Thus, the correct equation that Lupe should use is:
\[
k = \frac{2P}{x^2}.
\]
This corresponds to the option:
\[ k = \frac{2P}{x^2}. \]