HW6 solutions

Here you go. Final exam details and Exam 4 solutions coming shortly.

Oscillations of coupled masses

This is relevant to your interests.

HW6 is out

Here is HW6, it is mostly about vibrations, with a little bit on waves and gravitation thrown in. They are fairly challenging, but we'll be going over quite a few of them in class as usual. This will be your second to last homework set - planning on one more short one before dead week.

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.  

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.)

HW4

Homework 4 is out. We may go through a few of these on Friday already.

HW 3 solutions / Exam

HW 3 solutions are out. Reading them carefully would be a good way to study ...

As a reminder for tomorrow's exam, you are allowed 1 sheet of standard paper (front and back) with notes. You'll also be given a formula sheet that should have everything you need, a draft of which is here.

Homework 3, number 7

This is a very tough one, and I planned on going over it in class on Wednesday. I'll sketch out the approach below.

If power is constant (which we're basically told it is for the default car), then the work done is W=P*T where T is the time over which the power is being supplied. This work done must be equal to the car's change in kinetic energy. If the car starts from rest, the work just equals the final kinetic energy, 

W =PT = (1/2)mv^2

This relates P, T, and velocity, but we don't know velocity. We do know the track length though. What we want to do is solve that for v, and integrate it to get x. Since the length of the track (x) is fixed, that will let us relate power and time by themselves.

v = sqrt(2PT/m) 

x = (integral) v dt = sqrt(4PT^3 / 3m)

The question now is what happens if we vary P by some little amount dP, what happens with T? By how much does it decrease dT? The distance x is a function of the variables P and T. It is fixed, so any change in P will have to be accompanied by a change in T to keep it constant. 

The question we're really asking then is for the function x(P,T) to remain constant, what must the rates of change in P and T be? We'd need to know the slope along the "P axis" (so dx/dP) and multiply by the tiny change in P (let's call that change DP instead of dp to keep the change straight from the derivative). We'd also need to know the same along the "T axis". Basically, the change in any function is slope times displacement for each axis, all added together. This is the same way we propagate experimental uncertainties, by the way, something I hope we will cover soon.

If the function were f(x,y), we'd approximate a small change in f due to small changes DX and DY in x and y as

Df = f(x+dx) - f(x) = (df/dx)*DX + (df/dy)*DY

In the simpler case, if you just have y(x), all this says is DY = (dy/dx)*DX. Back to the problem at hand, if we have x(P,T), 

Dx = (dx/dP)*DP + (dx/dT)*DT

Since the track length is fixed, we know Dx = 0. Thus,

(dx/dP)*DP = - (dx/dT)*DT

or   DT = -DP*(dx/dP)/(dx/dT)

Given the function above, take the derivatives with respect to P and T, divide them, and that times the change in power gives you the corresponding change in time.

I'll plan on going over this on Wednesday too.

Homework typo

I just realized that there is a typo in the due dates. Problems 3 & 4 are due today, but problems 5-10 are not due until Wednesday, 19 Feb (not today). 

New HW is out.

Here you go. First daily problems due this coming Friday, a couple more next Monday, and the whole thing due next Wednesday.

Homework 2 solutions

Here you go. I didn't get a solution finished for #8 yet, but since that required a trick that we'll not really cover in class until next week, it isn't something that would show up on the exam anyway.

HW2 problem 5

On problem 5, I failed to specify the coefficient of friction between block b and the flat surface. Take it to be 0.20.

Also note that the ramp can be treated as frictionless, only worry about friction for the flat surface.

Homework 2

Homework 2 is out. You do have one daily problem due Friday, but it (should be) relatively quick. Some of the problems are more involved than last week, so don't put off the rest of the problems ... we will do at least a few of them in class on Mon & Wed next week.

[Hint on the first daily problem: it is easy to write down the equation of motion for either car. The tricky part is making sure that their time coordinates agree. You might call t=0 the moment when the cop starts moving, and say the other car passed it at t=-2 seconds (time can be negative, that's fine). You could also call t=0 the moment the car passes the cop, and write the cop's position in such a way that it is 0 after 2 seconds, and following accelerated motion after that. Either way describes the same situation and the same physics, the math is slightly easier for one of the choices.]

Homework 1 solutions

HW1 solutions are available. Let me know if you notice any errors.

Next HW

Owing to the long weekend, I'm delaying putting out the second HW until Wednesday. Seems more realistic. I should have HW1 solutions out at that time as well. 

Submitting homework

The first homework submission went very well I thought. I've been accepting email homework quite a while now, and this was probably the easiest first homework submission I've had.

That being said, here are a couple of suggestions that will make the process easier for me:

Solutions for quiz 1, 15 Jan daily problem

Quiz 1 and solution.
15 Jan daily problem and solution.

Solution to Monday's daily problems

Here you go. Let me know if you see any mistakes.

Homework 1

Here is your first homework set. Note that there are multiple due dates - you have two problems due at the start of class 13 Jan, one due at the start of class on 15 Jan, and the rest are due by the end of the day on 17 Jan. Also note that I would like you to use the problem template format when turning in homework.