Question

The potential energy, P, in a spring is represented using the formula P= 1/2 kx². Lupe uses an equivalent equation, which is solved for k, to determine the answers to her homework

Which equation should she use?
a. k=2Px²
b. k= 1/2 Px²
c. k= 2P/x²
d. k= P/2x²

Answer 1

The correct equation Lupe should use to solve for the spring's force constant k in the potential energy formula P = 1/2 kx² is c. k = 2P/x². Option C is correct.

Step-by-step explanation:

The student's question is about solving the formula P = 1/2 kx² for the spring's force constant, k. The given formula represents the potential energy (P) stored in a spring, where x is the displacement from the spring's undeformed position. To solve for k, we rearrange the formula as follows:

P = 1/2 kx²
=> 2P = kx²
=> k = 2P/x²

Therefore, the correct equation that Lupe should use to determine the spring's force constant k is c. k = 2P/x².

The potential energy of a spring can be represented by the equation P= 1/2 kx², where P represents the potential energy, k is the spring's force constant, and x is the displacement from its undeformed position.

To solve for k, Lupe can rearrange the equation to k = 2P/x².

So, the correct equation for Lupe to use is k = 2P/x² (option c).