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The potential energy, [tex]P[/tex], in a spring is represented using the formula [tex]P=\frac{1}{2} k x^2[/tex]. Lupe uses an equivalent equation, which is solved for [tex]k[/tex], to determine the answers to her homework.

Which equation should she use?

A. [tex]k=2 P x^2[/tex]
B. [tex]k=\frac{1}{2} P x^2[/tex]
C. [tex]k=\frac{2 P}{x^2}[/tex]
D. [tex]k=\frac{P}{2 x^2}[/tex]



Answer :

GinnyAnswer
To determine the correct equation for [tex]\( k \)[/tex] when given the potential energy formula [tex]\( P = \frac{1}{2} k x^2 \)[/tex], we need to solve for [tex]\( k \)[/tex].

Let's start with the given equation:
[tex]\[ P = \frac{1}{2} k x^2 \][/tex]

To isolate [tex]\( k \)[/tex], follow these steps:

1. Multiply both sides by 2 to eliminate the [tex]\(\frac{1}{2}\)[/tex] on the right side:
[tex]\[ 2P = k x^2 \][/tex]

2. Now, divide both sides by [tex]\( x^2 \)[/tex] to solve for [tex]\( k \)[/tex]:
[tex]\[ k = \frac{2P}{x^2} \][/tex]

This manipulation shows that the correct equation for [tex]\( k \)[/tex] is:
[tex]\[ k = \frac{2P}{x^2} \][/tex]

Thus, the correct option to use is:

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

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