For the energy and springs question, I am having a difficult time understanding why the determination of the k for the spring requires the use of an energy approach. Why can't one simply just use the F=-kx equation and solve for the k, setting F equal to the weight of the block and x = to the 20 cm (this doesn't yield the same k value as that of kaplan, so I want to understand why). Is it incorrect to assume that the spring follows Hooke's law? If so, will all questions on the mcat indicate whether this is the case or not? Additionally, I was under the impression that when dealing with springs one did not have the freedom to choose the value of x = 0 to be at any point and that x=0 had to be set at the location at which the spring was neither stretched or compressed. So, why is Kaplan's method for determining the k valid?

For the energy and springs question, I am having a difficult time understanding why the determination of the k for the spring requires the use of an energy approach. Why can't one simply just use the F=-kx equation and solve for the k, setting F equal to the weight of the block and x = to the 20 cm (this doesn't yield the same k value as that of kaplan, so I want to understand why). Is it incorrect to assume that the spring follows Hooke's law? If so, will all questions on the mcat indicate whether this is the case or not? Additionally, I was under the impression that when dealing with springs one did not have the freedom to choose the value of x = 0 to be at any point and that x=0 had to be set at the location at which the spring was neither stretched or compressed. So, why is Kaplan's method for determining the k valid?

For the energy and springs question, I am having a difficult time understanding why the determination of the k for the spring requires the use of an energy approach. Why can't one simply just use the F=-kx equation and solve for the k, setting F equal to the weight of the block and x = to the 20 cm (this doesn't yield the same k value as that of kaplan, so I want to understand why). Is it incorrect to assume that the spring follows Hooke's law? If so, will all questions on the mcat indicate whether this is the case or not? Additionally, I was under the impression that when dealing with springs one did not have the freedom to choose the value of x = 0 to be at any point and that x=0 had to be set at the location at which the spring was neither stretched or compressed. So, why is Kaplan's method for determining the k valid?

If an object does not follow Hooke's law, it will be stated in the passage. Unless otherwise stated, it is ok to assume object follows Hooke's law. I don't have the book you are referring to look into the specific problem.

I don't have a book. But regarding the x-position: Gook law and energy formulation should talk about displacement (delta X) from the neutral state. That means that you can place your x-origin at any place, just use displacement in the formula.