You are asked to design spring bumpers for the walls of a parking garage. A freely rolling 1200-kg var moving at 0.65m/s is to compress the spring no more than 0.090m before stopping. What should be the force constant of the spring? Assume that the spring has neglible mass.
In trying to solve this question I learned that the derivative of energy with respect to speed = force.
If you derivative: (1/2)mv^2 = mv.
Now suddenly mv = F, and ma = F.
My plan is to derivate (1/2)mv^2, get the force of the car, and say that the spring pushes with an equal and opposite force, and put the force into this formula:
Force = Force constant of spring/displacement
Force/displacement = constant of force which is the answer.
I tried to solve it with the speed formulas but I got an answer that is roughly the same, 200N apart. The answer to the question above is 63000N/m so I doubt my first way of doing it is the correct way.