Question

The potential energy, P, in a spring is represented using the formula P = 1/2kx2. 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 = 1/2Px2
k = 2p/x^2
k = p/2x^2

Answer 1

We need to find a way to get k by itself so lets get it by itself.
For convenience I will switch the equal sign.
1/2kx^2 = p
Multiply both sides by 2
kx^2 = 2p
divide by x^2
k = 2p/x^2

Answer 2

`k=(2P)/(x^2)`

Explanation:

The formula is
`P=(1)/(2)kx^2`

We need to solve for
`k`, so we can perform the steps shown below:

`P=(1)/(2)kx^2\\P=(kx^2)/(2)\\2P=kx^2\\(2P)/(x^2)=k`

Hence, the third answer choice is correct.