They can also undercut my affinity for symbolic algebra, but I think that we'll be able to press ahead ok symbolically, for the most part.
Here's a progression of whiteboard problems that they did on the second day of school; they read about both relativistic momentum and the momentum principle the night before. They were familiar (though not by name) with the momentum principle already, having done a lot with both Newton's 2nd and impulse last year.
- Projectile motion: given the initial velocity (speed and angle), use the momentum principle (not kinematic equations!) to find the velocity of the particle after some amount of time.
- Projectile motion: use the position update formula to determine the location of the projectile at that time (quickie review of average velocity, including vector form now - hey, we're actually using average v for something!). This is great - two dimensions, no waiting (and no toolkit equations)!
- Space shuttle: if it used its maneuvering thrusters to fly towards Proxima Centauri, what would the issues be? Fuel consumption's a huge one, but let's pretend that it's not, and that the shuttle's mass stays constant (removing this assumption would be a great place to start a capstone!), and that it can get away from Earth easily enough. Using some nominal mass value and the real thrust of the maneuvering thrusters, how fast would it be going after, say, 15 years (using the momentum principle)? It's going to take a while to get there, after all! Answer: more than the speed of light. That's a problem. Now we look at the model that we use, and how the p and v grow with time (use program referenced in earlier post). What really happens, though is this (use relativistic def'n with the program). The momentum principle's always true - it's that def'n of p that was wrong.
- OK: how fast will it be going, then after 15 years?
- How far will have gone? Oops - that's too far.
- Unfortunately, we can't solve analytically for how long it'll take, because of p's complex dependence on v. Time for a program! We sketched it out in pseudocode together, and they finished it in class or for HW.