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Problems

           Here are the assigned problems. The problem solving handout gives specific instructions on how to solve these problems (as well as others you may encounter in other coruses or later in life).  Dr. Jeff's solutions can be found by clicking on the document icons. (Remember, these are not necessarily the only solutions; other assumptions and model may produce in different results. Of course, not all models and assumptions are equally valid. Your solution must match the given information and general physical behavior of the world.)

Charges Unit
Due September 12(Solutions ):


         Follow the problem solving algorithm (as best as you can) when you write up your solution/ model. Each problem will require a slightly different solution; although, the basics will always be there.
         For these first problems I would like everybody to explicitly identify each of the four components or representations of the algorithm. Draw horizontal lines dividing your solution into four segments (they need not be equal segments). In the first put the pictorial representation, the second has the conceptual, third has mathematical and the final has your evaluation. Again, don’t feel like there is one and only one conceptual representation; everybody’s will be different. But, each will state clearly the physics principles at work, assumptions used, etc.
        Remember all of this is not because of any twisted desire to torture you. Rather, these steps are designed to help you work through complicated problems and be able to explain your reasoning to somebody else. The points on problems are usually distributed into five portions- pictorial, conceptual, mathematical, evaluation, and finally overall neatness & organization. Like with most of our assignments, feel free to work with others or ask for help from Dr. Jeff, but the work that you turn in must be your own.

       Last year during Winter Break, you and some friends went to the mountains to ski and celebrate your best friend’s birthday. After cleaning up and changing into your new wool sweater, Santa was nice to you last year, you and some of the others began to set everything up in the cabin. You had food, assorted beverages, and a few balloons to help “set the mood.” After blowing up the balloons, and nearly passing out, you filled up your arms with a bunch and went about scattering them around. When you got to the last two you decided to hang them above the table. You grabbed a piece of string that was about four feet long, and tied the two ends to the balloons and then tossed it over the ceiling light, so the balloons hung down on either side. The funny thing was that they did not hang straight down, instead the balloons were somehow pushed apart, so the two halves of the string made a 60° angle. At the time you didn’t quite understand why the balloons did this, you just had some vague notion about “static electricity.” And, honestly you were much more focused on the party than the balloons that night. But, now you know what was going on and can give a thorough explanation, with numerical estimates for the important quantities.

       For this next summer you have already landed an internship with LA Department of Water and Power. They have asked you to help design the air cleaners that will be used on a new coal burning power plant. This is a significant project as nearly half of all of the electricity they generate comes from burning coal. If the pollutants are not removed from the exhaust before being released into the air, the city would suffer from even worse pollution. Burning coal produces carbon dioxide (CO2), sulfur dioxide (SO2) and nitrogen oxides (NOx). These gases are vented from the boiler. Bottom ash, which is made of coarse fragments that fall to the bottom of the boiler, is removed. Fly ash, which is very light (typically between 1 x 10-3 g and 1 x 10-6 g) and small in diameter (typically between 1 mm and 0.1mm), exits the boiler along with the hot gases. It is this fly ash with which you are concerned. Current plants are using electrostatic precipitators to remove the fly ash. They wish to continue using this technology as it removes over 99% of these particles, but you must redesign the system to match the specifications of the new plant.
       An ash precipitator removes solid emissions from smokestacks by electrostatic means. As the gas, laden with fly ash, leaves the boiler it is sent through a system that first gives the particles a net negative charge. The average net charge is 10-10 C/ particle. The gas then proceeds to a vertical stack. There the small particles move upward with the gases at 2 –5 feet/ second. In the stack, two charged parallel, vertical plates are placed so that the smoke passes through them. (The plates have opposite charges.) The horizontal electric field between the plates deflects the ash and traps it on one of the plates. For your system you know that the space between the vertical plates will be 2 feet. The height of the stack (and therefore the region with an electric field) is 50 feet. The air that leaves the plates is now free from harmful particles. You want to know how powerful the electric field needs to be such that most of the particles deflect into the plates and never make it out of the stack.

Electricity Unit
Due October 7:


          You have a great summer job in a university research laboratory. Unfortunately, during the summer there is an accident in the lab, and you are suddenly transported back in time. You find yourself face to face with J. J. Thomson in 1905. He is one of the scientists who is proposing a model of the atom where the positive charge is spread throughout the volume and the negative charges, electrons, are scattered in the positive charge. Affectionately, this is known as the “plum pudding model” as the electrons look like small raisins scattered in the dough. (As far as you can tell, plum pudding doesn’t actually contain any plums; silly British. You figure that the most similar food from your past would be your Aunt’s Christmas fruitcake.) From your physics and chemistry classes you know that Thomson’s model isn’t correct. In 1911 Rutherford and his coworkers will learn that the positive charge is confined to a small spot in the center- the nucleus. You want to convince Thomson that his model is flawed. You start discussing your ideas. He agrees with you that for hydrogen, the radius of the atom is 1.5 x 10-10m. He also understands that hydrogen can emit red light, which has an oscillation frequency of 6.0 x 1014Hz. You hope to show him that if his model were true, the electron inside hydrogen would have an oscillation frequency that differs from what is observed.

[A bit of background physics to help you. Whenever an object is subjected to a force which depends linearly on distance, the object will oscillate at a specific frequency. This is known as simple harmonic motion. Masses on the ends of springs do this. So do pendulums; as long as you stick with small oscillations. So, if the force is of the form F= -kx, where k is a constant that describes the spring (a big k is a stiff spring and a small k is a flimsy spring). The frequency of vibration will be , where m is the object’s mass. You can read more about these type of oscillations in chapter 15 of our text.] (Solution )

          While Thomson is looking over your calculations, trying to understand the implications (you’re right and he’s wrong), you chat with one of his assistants. Since you have already changed history by giving Thomson an idea that is not supposed to happen for several more years, you figure what the heck, you might as well go all the way. (Clearly you don’t remember the lessons you learned about time travel while watching Star Trek.) You discuss an idea to fire high-speed protons perpendicularly at a foil of gold (protons’ velocity is parallel to the foil’s normal vector). This is the essence of Rutherford’s experiment. This 3cm by 3cm square essentially serves as the target for the protons. You want to show Thomson’s assistant the implications of “your” model. For example, if a proton is fired with an initial speed of 8.00 x 106 m/s such that it heads toward a gold atom, you want to show that it never actually collides. Don’t forget the details of “your” model- that the positive & neutral charges reside in a dense nucleus and the electrons circle about almost as it they were planets circling the sun. The electrons are relatively far away from the nucleus, so much so that when you’re near the nucleus you can ignore them. (Analogous to being inside Mercury's orbit and not being concerned with Neptune.) (Solution )


Circuits Unit
Due Oct 26
(Solutions )
1. You and your lab partner were having so much fun in lab this week, you decided to keep collecting data on the light bulb. On the next page, you see all of your glorious data. Now that you’ve got it, what can you do with it? After glancing at section 27.4 of our text, you realize that you can use the data to calculate the temperature of the tungsten filament when the bulb is fully lit.


2. You and a friend are studying for a midterm and the session goes until the early morning. At about 4 am you decide to cook some breakfast. Despite being sleepy, things are going well— the waffles are cooking and the coffee is perking. Should you make some toast now? The 1000watt waffle iron and the 600watt coffee maker are plugged into kitchen wall electrical outlets. You will also use a kitchen wall outlet for the toaster. The kitchen wall outlets are all part of the same 110V circuit which has a 20A circuit breaker (with negligible resistance) to protect the wire carrying the largest current from getting too hot. You know that if you plug in too many appliances you will overload the circuit breaker. The toaster label says that its power output is 700 watts.

 

Magnetism Unit
Due Nov 16
(Solutions )
After watching The Hunt for Red October during a Sean Connery movie marathon you get an idea for a boat motor. You want to design a motor that is just like the one used in the movie- silent with no moving parts. (You figure that this might give you an advantage when you go fishing.) You know that the motor uses magnetic forces to thrust water backward, in other words a magnetohydrodynamic drive. Your preliminary idea has a permanent C-magnet much like the one shown below with the water flowing between the poles (in a channel which is 50cm wide and 50cm tall). The channel is 2m long, as is the magnet, which has a magnetic field of 1 tesla between the poles. (You got lucky and found a huge magnet that was lying around the physics department.) You want your motor to have a thrust force of 100N on the water that flows through the channel. You will connect two electrodes to the channel allowing you to pass current through the water. You need to decide what kind of battery or power supply to purchase (voltage and power ratings) and how to connect it to the channel. You look up seawater’s resistivity and find that it is approximately 25 Ω · m. While looking up this number you also remind yourself that the resistance of a uniform object is given by rl/A , where r is the resistivity, l the length of the object and A the cross sectional area.

You have landed a great summer job at UC-Irvine's medical school assisting in a research group investigating short lived radioactive isotopes which might be useful in fighting cancer.  Your group is working on a way of transporting alpha particles (helium nuclei) from where they are made to another room where they will collide with other material to form the isotopes.  Since the radioactive isotopes are not expected to live very long, it is important to know precisely how much time it will take to transport the alpha particles.  Your job is to design that part of the transport system which will deflect the beam of alpha particles (m = 6.64 x 10-27 kg, q = 3.2 x 10-19 C) through an angle of 90o by using a magnetic field.  The beam will be traveling horizontally in an evacuated tube.  At the place the tube is to make a 90o turn you decide to put a dipole magnet which provides a uniform vertical magnetic field of 0.030 T.  Your design has a tube of the appropriate shape between the poles of the magnet.  Before you submit your design for consideration, you must determine how long the alpha particles will spend in the uniform magnetic field in order to make the 90o-turn.