Physics 281: Homework #2: due April 18

By the end of the week, there will be five problems (two from each lecture, plus a bonus).

1. Many of our options for renewable energy are intermittent in nature, yet our society wants to pump along without interruption. So in order to implement renewables on a large scale, we have to implement storage schemes. Imagine you want to store energy locally at your own home (will give you a sense of individual scale), and you want to explore alternatives to batteries. For scale, a rechargeable NiMH AA battery is typically rated at 2000 mA-hr at 1.5 V, and a golf-cart battery holds 150 A-h at 12 V. You contemplate three storage media, each occupying something like the volume of a room in a house:
   1. A flywheel: given reasonable constraints on your own personal flywheel, how many batteries (of each type) can you imagine supplanting?
   2. Pumped storage: you erect a tank to hold water at some height, storing gravitational potential energy. How much (in battery units) can you practically achieve?
   3. Compressed air: high pressure tanks into which you can pump air. Careful to realize that some heating in the compression means lost energy. How many batteries can you practically replace?
   
   Now put this in context: how long will each of these storage devices run your house's electricity demand, not counting your natural gas and gasoline energy requirements?
   
   
2. The media like to showcase funky energy schemes for the future, especially when the solution has been seemingly right under our noses the whole time. An example of this is the boast that reclaiming energy from human solid waste (i.e., extracting methane from sewar streams) is a brilliant solution that could have a major impact on energy and eliminate our dependence on foreign oil (actual quotes to this effect). Use your order-of-magnitude skills to estimate (or establish an upper bound on) the fraction of present energy demand (in the U.S. and in the world) that is possible by this means.
   
   
3. How fast might a person expect to go on a bicycle in the following scenarios?
   1. On a flat road, no wind, keeping up a steady (and not shabby) power output of 200 W.
   2. Coasting down a long hill. You make up a reasonable grade (think percent) for the problem.
   3. Climbing the same hill, again pumping out 200 W.
   
   
4. How long will it take a small round pebble to reach the bottom of the deep end of a swimming pool? Justify your assumptions. What size pebble (even a symmetric one) would rock back and forth as it fell? What is the largest size of a pebble that would fall in a viscous regime? Would we call this a pebble? Don't forget the 6π!
   
   
5. Invent a problem of your own in the spirit of this week's class topics. You do not need to provide a complete solution, though you might outline how it may go. The art is to strike a balance between trivial and hopelessly complex.
   

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