# Physics 104 Contextual Problems

## Problem #1 #!%?@! Fuses!

It is the dead of winter and you, a war correspondent for a great metropolitan newspaper, find yourself hunkered down with several other journalists in the basement of a bombed out building, while shelling is going on outside.

Miraculously, there is a 220 V power line still in operation in the basement, plus an entire crate of electric heaters. When you first arrived, there was also a box of fuses, but the supply is rapidly dwindling. Your companions have discovered that when they plug in one heater, rated at 1500 Watts, everything functions just fine, but it is still unbearably cold. When they plug in a second heater, the fuse blows. Unfortunately, the rating on the fuses is illegible.

You are the only one of the correspondents who ever learned any physics, and as the next-to-last fuse is blown by yet another desperate scribe plugging in a second heater, you realize it is time to take some responsibility in the matter. Starting with the assumption that even here fuses are supplied only in 5, 10, 15 etc. Ampere ratings, you set about to figure out how to get the maximum heat into the shelter without destroying the last fuse.

Your first thought is to short out the fuse, since the building has already been destroyed anyway, and then plug in several heaters. But several people balk at this idea. They don't want the building to burn down while they still need it.

Your next act is to curse these confounded heaters for their lack of a control knob; if they had controls, you could plug in more than one and not turn them all the way on. But, knobs there aren't.

It turns out that there is also a phone in the basement; the dial pad has been crushed and it is impossible to make any calls, but at this moment it rings. Perhaps it is "the authorities" letting you know that help is on the way. But alas! It turns out to be someone trying to get you to switch your long distance carrier. You hang up in dismay and set about your self-appointed task.

So, what do you do?

## Problem #2 #!%?@! 60-Cycle Hum!

It is Easter week and the sole engineer of the small company you have taken your first real job with is incommunicado, diving on Saba Island in the Caribbean. The company has one product, and so far no sales. It manufactures a seemingly wonderful and comparatively cheap heart monitor, but the one-woman sales staff is just back from another fruitless trip. She is grumbling to you in the coffee room that the speaker that is there to make the cute little cheeps every time the heart goes kerthump, and to make a piercing whistle to signal for the defribulator when the heart stops kerthumping, this traitor little speaker in the machines made by your company suffers from the ever dreaded "60-cycle hum". It does the cheeping and whistling just like it should, but it has an annoying 60-Hz buzz all the time. Bummer. Somehow the 60-Hz line current is being picked up and amplified by the electronics. And it drives people nuts. The saleswoman is certain it is the only reason your machines are not going like hot cakes.

She is off to Chicago Hope on the next day, trying once again, but knows it is pointless unless the hum can be eliminated. If only someone around there knew enough electronics to figure out how to keep the 60-Hz signal from getting to the speaker, while letting the higher pitched cheeps and whistle through, maybe, just maybe she could start making sales and turn the comany's fortunes around.

The company president, a CPA, is also in the coffee room, and at first looks very dejected, but then gets an idea! He offers a paid vacation to the destination of choice to anyone in the company who can cure this problem by the next day. (Having studied no physics, it is the best he can do, poor ineffectual guy.) In order to dramatize his offer, the president unscrews the speaker cover from the front of the machine and pulls the speaker out from the box. It remains connected to the innards by two green wires. On the back of the speaker it says "8 ohms". The president points to the green wires, and mutters, "All we need is some sort of traffic cop here to let the whistles through and stop the hum. There must be something in that assortment of electronics parts the engineer keeps laying around that will do the trick."

It turns out that there is also a phone in the coffee room, under a pile of magazines. No one even knew before that it was there, but at this moment it rings. Perhaps it is the engineer, checking in to see how things are going. But alas! It turns out to be someone trying to get you to switch your long distance carrier. You hang up in dismay and wonder whether you should admit that you had learned a smidgeon of electronics in a physics class.

So, what do you do?

## Problem #3 Beware of Greeks Bearing Shields!

You find yourself, due to obscure family connections, hired as a special assistant to a film crew, your duties not having been made entirely clear. To your great pleasure, the first assignment of the crew is on a small Greek island. They are planning a documentary on a legend about ancient Greek warriors having set enemy ships in the harbor ablaze. For the documentary, it is hoped that the conditions of the siege and subsequent torching can be recreated, in at least a quaint village pageantry sort of way. (The fleet of warships, for example, will be represented by the spruced up and decorated collection of village fishing boats.)

Your first assignment, before leaving home, has two parts. The first is to see what you can find out about the historical origins of this legend. The film proposal suggests that some famous Greek scientist may have been involved, and that the ships may have been Persian, possibly led by Darius or Xerxes. The second part is to assess the physical mechanism said to be responsible for the ignition of the boats' sails: The legend is that Greek soldiers on the seashore were equipped with highly reflective shields, and that with these shields they focused enough sunlight onto the sails to set them on fire.

The film crew believes that they could equip about 40 villagers with shields, coated with aluminum foil, and that the ships might typically be about 100 feet from shore. Your project involves deciding what shape the shields should have in order to focus the light, and then providing a clear analysis of whether or not the 40 shields could focus enough light to ignite the sails--without further "assistance" from the special effects team. (The crew is committed to 3 goals: showing the focused light on the sails, having the sails burst into flame--by hook or crook, and then being able to show by way of a simplified model why it works or doesn't work.)

The kicker is that they want your results before they buy your ticket to Greece. What's more, you notice that they seem to be having hushed conversations with several other people, handing each they same set of background materials they gave you. You suspect that the others have the same charge, and that only one of you will make it to the sun drenched Aegean.

As you return to your apartment to begin thinking about your situation, the phone rings. It is one of your old college friends from physics days suggesting that some of you get together for some laughs, to talk about weird TAs, weirder professors, and all that stuff they used to drag you through. "Ahah!" you think, "just maybe I'll get to Greece after all."

The report to the film crew is due Monday May 6.

## Rules

1. Choose two other people to work with on it. Discuss it with them and attempt to work out a reasonable response. Get their e-mail addresses in case you run into uncertainties later when you try to write it up.

2. Individually write up your approach and solution, including any assumptions you made.

3. The writeup need not be lengthy, but it should be clear--anyone else having been through Physics 104 should be able to understand your plan, and your reasons for it.

4. Put your own name and TA/section at the top; add the names of the others you worked with at the bottom--they should writeup their own independent solutions and your name should appear at the bottom of their work.

5. Turn this masterpiece in with your homework on Monday April 1.

6. The papers will be graded by the TAs, on a 3-point scale. These points will be added directly to the points totals for your exam grades, after the grading curve is made (so, yes, they are extra credit) separately from other homework and lab scores. With 4 such problems, if we get that many written, the total points will be equivalent to 1/8th of an exam. (This seems about right for a meaningful experiment, no?)

7. Like life, you could spend an inordinate amount of time on a problem of this kind. You have to decide when to stop. You will not get more points for going overboard. Just be sure to give good clear reasons for the things you say, showing their relationships to the situation at hand.

8. As with the first problem, there is no unique solution.

9. If you can't find people in the class to work with, find someone else, and tell who they are.

10. If there are no people whatsoever in your life that you can talk with about this problem, you need some new friends. Take a geek to lunch. We can be real nice folks when you get to know us.