Conceptual Question on the Force of a relaxed spring

[Kibbel]

Homework Statement

When running a moving cart into a relaxed spring, will the force of the spring be constant on the cart?

Homework Equations

$$\Delta$$P$$\rightarrow$$ =$$\rightarrow$$Fnet$$\Delta$$t

or F = 1/2kx^2?

The Attempt at a Solution

my guess is that the more you compress or strech a spring, the stronger the opposing force

 

[G01]

Your conceptual explanation is correct. That is essentially Hooke's Law. The force caused by an ideal spring increases linearly with it's compression (or expansion).

However, F does not equal 1/2kx^2. That is the potential energy. F=-kx