Formula sheet for exam 3

Here is a draft formula sheet for exam 3. 

HW5

Homework 5 is now ready. We will go over many of them in class on Wednesday (at least the harder ones). Nominally it is due this coming Friday, before spring break, but I will not assess any late penalties until after spring break.

That means I'd like to have it by Friday, and you probably don't want to do homework over the break anyway, but turning it in Monday after the break is fine.

HW4 solutions

HW4 solutions are available. I probably got a bit carried away with number 5 (the baseball problem). Don't read too much in to that, I was just amused by it more than anything. You won't see anything remotely like it on an exam.

UPDATE: the server seems to be having trouble, and you will probably get a 'forbidden' error when trying to download the solutions. I'll get this resolved as quickly as I can.
Fixed. Past 2am and I'm using chmod from the command line on a Linux server to fix an access problem that didn't exist yesterday. Is it 1998 again?

In any case, your HW4 solutions are ready.  

The flow of wet and dry water

Friday we'll finish up our discussion of fluids. So far we've figured out quite a bit:

1. hydraulics (Pascal)
2. energy conservation in fluids without viscosity (Bernoulli)
3. variation of pressure with depth for an ideal fluid
4. work and forces to move fluids

We have a few things to sort out though.

• manometers: how to measure pressure? (simple application of 3 above)
• how do gasses differ? (density variations can't be neglected; 3 + ideal gas law)
• what about purely rotating fluids or smoothly flowing fluids? (energy balance)
• what about buoyancy? why does some stuff float? (3 & 4 for a foreign object in the fluid)
• what about drag forces/viscosity and terminal velocity? (subtle ...)
• what can we say about pressure vessels? (simple generalization of force & pressure)

I've tried for many hours, without success, to find a reasonable explanation of how viscous fluids move and the effects of turbulence without using tons of vector calculus. Fundamentally, I don't think one can do it quantitatively without some serious math, but I think I can give you a qualitative idea of what the issues are and how non-ideal fluids work.

If you are very comfortable with Cal III material, Feynman has a very nice discussion of wet & dry fluids (i.e., with and without drag/viscosity forces): Vol 2 Ch. 40 and Vol 2 Ch. 41. Fair warning, the math is difficult, and beyond what you are responsible for. But, if you're comfortable with the math and want a better idea of how fluids really works, I've not found a better description. Even if the math is too much, his discussions are worth a read - the qualitative descriptions and examples are very lucid.

Rocket launcher deliverable #2

Just like last week, you are basically free to do what you want during the lab work period, you just have to deliver to me the result I ask for by the end of the week. My impression so far is that you're all making very good progress, so this deliverable should be easy.

This week, I want you to tell me the following:

• Did you find that you need to use the same rocket and turret for reliable results, or did it not matter too much?
• Give an estimate of the variability in the launcher's range for at least 3 angles. For instance, if you do 5 launches at a given angle, what are the mean, maximum, and minimum ranges? 
• Given the variability you find, approximately what size target do you think you could hit reliably? Ballpark answer is fine.
• How does the actual range of the rocket compare to what you would predict without drag forces, evaluated for at least 2 angles?
• How much kinetic energy must be lost to drag forces for each of those angles (say, a % of the launch energy)?
• Using the example code I've given you (below), or code you've written, what drag coefficient makes your simulations match your measured data reasonably well?

HW 4, revised due date

The remaining HW4 problems were originally planned to be due on Friday 7 March. However, I think this week we spent (arguably) too much time on the rocket launchers and not enough time on problems. As a result, I suspect that the problems you have left may seem a bit too difficult to finish by Friday.

Therefore, I'll postpone the due date of the remaining (non-daily) problems until Monday 10 March, and I'll plan to go over the HW problems in Friday's class to get you started.

Also, as it turns out, XKCD has pointed you toward one of the solutions already. The author has a degree in physics, so this is the rare case where you can actually trust a webcomic to help you with your physics homework. (Seriously, read XKCD.com and what-if.xkcd.com, they are a valuable use of your time.)