Pre-lecture: Constant vs. Non-constant Forces (Springs)
- The MP lets us predict the motion of any system subject to any interaction
- Sometimes we can do that with pencil and paper and other times, we can't
- We can always predict the motion of a system with pencil and paper when the net force is constant over the interval we care about
- Quickly derive velocity and position prediction equations – Show as integrals; suggest there's a different derivation in notes, that doesn't require calculus.
- But, when the force is non-constant, we typically can't predict the motion with pencil and paper
- For example, when a force changes with position or velocity, the equation we have to integrate might not have an anti-derivative (sometimes for special situations e.g., a time del force with integrable bits or a position/velocity depdent force in 1 dimension, we can)
- But in general we have to rely on predicting that motion in a step wise fashion
- Consider a spring force - Demonstrate - suggest computation to do the iteration.