1. Spinning bucket of water problem. Imagine a bucket of water (mass m) spun in a vertical circle with constant speed (v), if that were possible. What is the minimum speed such the water does NOT fall out of the bucket?
2. Consider a 'loop the loop' (radius r) Roller Coaster. What is the minimum speed for you to travel in a car so that you don't fall out of the roller coaster? Is this the same problem as above?
3. Now consider a roller coaster again - this time, imagine that you are going to the bottom of a curve (with constant radius, r). How does your 'apparent weight' (as measured by a scale that you are conveniently sitting on) vary with the speed of the roller coaster?
4. Consider a car rounding a curve (radius r) with coefficient of friction (u) between wheels and road. What is the relationship between v and u?
I'm having a lot of trouble applying the things we learned in class to these problems. Can we set aside time to go over all of these in class, along with the backlog of problems we've accumulated?
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