This preview shows page 1. Sign up to view the full content.
Unformatted text preview: Physics 204 summer 2008 Exam 1 practice problems 1. Nuclear fusion is a highly sought after alternate energy source because it is environmentally friendly and uses very abundant fuels. However, it is a technical challenge to get two atomic nuclei to fuse. One way to get two nuclei to fuse is to strip off their electrons then accelerate the nuclei to high speed and collide them together. Using this idea it is possible to fuse two deuterium nuclei into helium. Deuterium is an isotope of hydrogen, having one proton and one neutron in its nucleus. a. If the two deuterium nuclei need to get within 1.3 × 10 −15 m of each other for them to fuse into helium, predict what speed they must be fired at to get that close. b. Describe any assumptions you made in making your prediction. 2. A parallel plate capacitor might also be used to determine the speed of charged particles. Imagine that a beam of electrons is being fired into the parallel plate capacitor as shown. The power source has the ability to be adjusted so that the potential difference that it provides is just enough so that the electrons do not reach the negative plate. If this happens when the power source is set to 10.3V then how fast are the electrons traveling when they enter the capacitor? + + + + + + +
5.40cm − − − − − − 3. Have a look at the situation shown. A soda can is resting on a plastic stand. A piece of aluminum foil hangs vertically from a thread (the thread is an insulator) so it is touching the right side of the soda can. A glass sphere that has been rubbed with silk (so it becomes positive) is slowly moved closer to the left side of the can, eventually touching it briefly. It is then slowly moved away. Aluminum foil + +
+ + Soda can Plastic base
a. Describe what, if anything, happens to the glass sphere, the soda can, and the aluminum foil throughout this entire situation. Give any explanation for what happens (or why nothing happens). b. Repeat part a., except with the soda can replaced with a plastic bottle. 4. Two identical light bulbs are connected in series to a battery as shown. Your friend predicts that bulb #1 will be brighter than bulb #2 since it is closer to the positive terminal of the battery. You don’t think this sounds right… ε = 120V a. Give a detailed argument for why this is not a reasonable prediction. b. Predict numerically the power output of each bulb. R2 = 108Ω R1 = 108Ω 5. Two aluminum spheres hang by threads as shown. A glass rod that has been rubbed with silk (making the rod positively charged) is brought closer and closer as shown. a. Predict what you will see happen when the rod is brought close to (but not touching) the left sphere. Give an explanation for why you think this will happen. b. Predict what you will see happen when the rod is allowed to briefly touch the left sphere and then is moved far away. Give an explanation for why you think this will happen. + + + + + + + 6. A small aluminum sphere (1 centimeter in radius and mass 20.0g ) is placed on an electrically insulating tabletop. A plastic rod is rubbed with wool so the rod becomes negatively charged. The sphere is touched with the rod, adding electrons to it and giving the sphere an electric charge of −5.00 μ C . An electric field is then set up so the sphere accelerates upwards at 13.0 m s 2 over a distance of 1.00m . a. Draw a free body diagram for the sphere while it is in motion. b. Determine in detail (magnitude, direction, shape, etc.) the electric field required to make the sphere move in this particular way. 7. One simple model of a hydrogen atom is that it consists of a single proton as its nucleus and a single electron in a circular obit around the proton at a distance of 5.29 × 10−11 m . This electron is definitely not at rest and has a kinetic energy of 13.61eV . 1 An external force is applied to the electron which removes it from the atom and brings it to rest far away from the nucleus. Predict how much work (in eV ) would have to be done by this outside force. The result is called the ionization energy of hydrogen and is a measure of how strongly a hydrogen atom wants to “hang on” to its electron. 8. You are probably used to the idea of a moving object having nonzero kinetic energy, and that you can calculate the kinetic energy of that moving object using K = (1 2 ) mv . While this may seem innocent enough, consider the 2 following situation: You create an electron beam using a parallel plate device in the way we discussed in lecture, by drilling a hole in the middle of one of the plates, heating the surface of the other plate opposite the hole to eject electrons, and connecting both plates to a power source such as a battery. We discussed how we could determine the speed of the electrons as they exited the parallel plate device through the hole. a. Draw a diagram of this situation. Include the electric field inside the parallel plate device and a free body diagram for one of the electrons in the beam. b. Forgetting for the moment that this seems impossible. determine the potential difference the power source must provide to the parallel plate device for the electrons leaving the device to be traveling at twice the speed of light. 2 c. Describe any assumptions you made in answering parts a) and b). 1 eV or “electron volt” is a unit of energy that is convenient when dealing with atomic physics. It relates to Joules by the
conversion factor 1.00eV = 1.60 × 10 J .
2 The Even though your answer may seem large it is quite possible to achieve potential differences of this magnitude with current
technology. So it’s possible to accelerate electrons beyond the speed of light? Actually it isn’t, and we’ll see which piece of physics
you’re using here isn’t reliable in this situation later in the course when we study Einstein. 9. Your friend is studying for his physics exam and while thinking about electric circuits he says to you “Take a look at this circuit.” He shows you the circuit shown in the diagram. “I predict that the 20 Ohm bulb will be brighter than the 10 Ohm bulb when they are in series, because it's the first bulb the current gets to. Then, if I switch the order of the bulbs the 10 Ohm bulb will be brighter for the same reason.” Do you agree with this? Explain your reasoning. If you don’t agree, give a prediction of your own and justify it. ε = 50.0V
R2 = 10.0Ω R1 = 20.0Ω 10. You and your friend are studying for your first physics exam when he says “Okay, I think I get it. If I have a circuit with a single battery and a single light bulb” (he draws the circuit shown) “and let’s say the power output of the resistor is 150W . If I add another identical light bulb in series then I predict that each one will have a power output of 75.0W so that energy is conserved.” Hmmm… You don’t think this sounds right… a. Give a detailed argument for why this is not a reasonable prediction. b. Predict numerically what you think the power output of each bulb will be once the second bulb is added to the circuit. ε = 120V P = 150W
1 11. The water molecule is naturally polarized, meaning that even if there is no external electric field there will still be a positive end and a negative end to the molecule. Even though the water molecule is somewhat complicated, this “natural electric dipole” can be approximated with the following model: • A single pointlike positive charge of magnitude q = 10e located at the point ( a, 0) where a = 3.9 × 10 −12 m . e is the elementary unit of electric charge, 1.60 × 10−19 C • A single pointlike negative charge of the same magnitude located at the point ( − a , 0) . a. Predict the value of the electric field at the point (5a , 0) . 3 b. Are there any locations in the vicinity of the dipole where the electric field is zero? Explain your reasoning in detail. Use pictures if you think they will help you. 12. You are trying to build a particle accelerator using a parallel plate capacitor setup. You take two 10.0cm × 10.0cm
aluminum plates, separate them by 10.0cm and connect them to a battery. You cut a hole in the positive plate and heat the spot on the negative plate opposite the hole with a blowtorch to release electrons. You then place the device in a vacuum chamber and remove the air. a. Predict what the charge on each plate would have to be in order to accelerate the electrons to 10% of the speed of light b. What assumptions did you make in making your prediction? Explain if you think any of them might not be completely appropriate. 13. Two identical hollow aluminum spheres (radius 2.00cm , mass 0.090kg ) are attached to the ends of insulating plastic stands. The spheres are put in contact with the opposite terminals of a strong power supply. This gives the two spheres opposite charges, each with a magnitude of 2.00 × 10 −8 C . One of the spheres is placed standing up on an electronic balance. The balance is then zeroed. The other sphere is brought nearby from directly above so that 3 Actually, this model will only give a very rough estimate of the electric field. The only situation when it’s very accurate is when
predicting the electric field at points much greater than a from the dipole. their centers are 8.00cm apart. The scale measures that the magnitude of the electric force between the two spheres is 6.13 × 10 −4 N , and you know the experiment is accurate enough that you know that the measured value is within 1.00% of the actual value. Is this result for the electric force between the spheres consistent with what you would expect? If it is, explain in detail why you think it is consistent. If the result is not consistent with what you would expect, then explain in detail why you think it is not consistent. Also come up with a detailed explanation for why the result differed from what you expected. 14. Give detailed explanation for why the following happens. Draw diagrams to illustrate your explanations. a. A metal spoon is placed on a Styrofoam plate. Several tiny bits of aluminum foil are placed into the bowl of the spoon. A glass rod is rubbed with silk (to make the rod positive). The rod is touched to the end of the handle of the spoon. At the instant this happens, the aluminum foil bits fly out of the spoon. b. Another metal spoon is placed on another Styrofoam plate. Several new bits of aluminum foil are placed into the bowl of this second spoon. The glass rod is rubbed with silk again (to insure the rod is still positive). This time, the rod is brought near the aluminum foil bits from directly above. Once the rod gets to within a centimeter of the foil bits, the bits jump up, touch the rod, then fall back into the bowl of the spoon. 15. A pair of light bulbs is connected to a pair of batteries as shown. ε1 = 1.50V ε 2 = 1.50V R2 = 10.0Ω R1 = 5.00Ω a. Predict the power output of each light bulb. b. Light bulb 2 is removed from the circuit and replaced with an ordinary length of wire. Your friend says “Light bulb number 1 will remain just as bright because P = ΔV 2 R and the potential difference hasn’t changed since its still 3 volts total, and the resistance of the bulb hasn’t changed.” You’re not so sure about this… Explain the problems with your friend’s reasoning, then make a numerical prediction for what the power output of bulb 1 will become. 16. A pair of light bulbs is connected to a pair of batteries as shown. a. Predict the power output of each light bulb. b. Light bulb 2 is removed from the circuit. Your friend says “Light bulb number 1 will get brighter because the power provided by the batteries isn’t being shared between two light bulbs any more.” You’re not so sure about this… Explain the problems with your friend’s reasoning, then make a numerical prediction for what the power output of bulb 1 will become once bulb 2 is removed. ε1 = 1.50V ε 2 = 1.50V R2 = 10.0Ω R1 = 5.00Ω 17. You take your fleece jacket and your wool sweater and rub them together. You bring the fleece jacket close to your friend’s hair. Their hair begins reaching out to the fleece jacket, seemingly attracted to it for some reason. You move the fleece jacket away and your friend’s hair returns to hanging down normally. You then repeat these steps with the wool sweater and exactly the same thing happens. Explain what is happening starting with when you rub the jacket and sweater together. Illustrate your explanation with appropriate diagrams. 18. You and your friend are studying together and your friend has some leftover pizza heating up in the microwave in the kitchen. Since your friend is into conserving energy the two ceiling lights in the kitchen are turned off. You go into the kitchen to get some snacks and turn the lights on while you are there. When you leave the kitchen you turn the lights off. But, your friend says “You know, since you turned the lights on in the kitchen I’ll have to leave the pizza in the microwave longer.” “Really? Are you sure?” you ask. “Definitely!” your friend replies. “Here’s why…” Your friend takes out a piece of paper and draws the circuit shown. “When you turned on the lights you closed the switch in the circuit. Since the power supply to the kitchen only puts out 120V, the microwave isn’t getting all of it while the lights are on. Since the power output of a device is P = I ΔV the power output of the microwave is lower when the lights are on. So, the pizza will have to stay in the microwave longer.” a. You’re pretty sure you’ve never noticed having to heat something longer in the microwave if the lights were on. Explain the problem with your friend’s reasoning and decide if you really should have to heat the pizza longer if the lights are on. Explain the reasoning behind your decision. Power supply
to kitchen ΔV = 120V Microwave R = 9.6Ω Light
R = 192Ω Light
R = 192Ω b. Assuming your friend’s circuit is a reasonable representation of the wiring in the kitchen, predict the power output of the microwave and the two light bulbs. ...
View Full Document
This note was uploaded on 10/04/2009 for the course PHYSICS 750:204 taught by Professor Croft during the Summer '08 term at Rutgers.
- Summer '08