Please Help!!! A spring force is given by the formula F=2x-15x^2, where F is in N and x is in m. What is the change in potential energy wen the spring is stretched 1m from it's equilibrium position.

Question

A spring force is given by the formula F=2x-15x², where F is in N and x is in m. What is the change in potential energy wen the spring is stretched 1m from it's equilibrium position.

Answer 1

U(x) is defined as -Integral of f(x)dx. Like most energies, there is an arbitrary constant. Since you want to know a difference in two states, the constant will cancel:

Find U(1)-U(0) = ΔU

Answer 2

Hi Katelyn, great problem! It always helps to break the problem down into its component parts:

1) What is the relationship between potential energy and force?

2) What does it mean for the spring to be in equilibrium? Or in other words, if the spring is in equilibrium, what does that say about the force on the spring?

3) Now given 1) and 2) how can you determine the change in potential energy, from when the spring is in equilibrium to when the spring is stretched 1 m from its equilibrium posiition?

I hope this helps!