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Unformatted text preview: Physics 194 Exam #1 practice problems solutions 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 of each other for them to fuse into helium, predict what speed they must be fired at to get that close. 15 1.3 10 m b. Describe any assumptions you made in making your prediction. Use energy principles with the system being the two deuterium nuclei. The initial state of the system will be the two nuclei very far apart. The final state of the system will be after the helium nucleus has formed. ( ) ( ) ( )( ( ) ) ( ) , , 2 2 , 2 2 , 2 9 2 1 9 2 , 27 27 15 6 , 1 2 2 8.99 10 1.602 10 1.673 10 1.675 10 1.3 10 7.28 10 i f i E i f E f D D D i f p n D i f w D i p n f D i E W E K U K U q m v k r e m m v k r N m C C ke v m m r kg kg m v m s + = + + = + + = + + = = = + + = In making this prediction I had to assume the two deuterium nuclei were far enough away that the electric potential energy between them was approximately zero. I also assumed the two nuclei were point-like. Lastly, I assumed the two nuclei were fired at each other exactly head on. 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 10.3 then how fast are the electrons traveling when they enter the capacitor? V + + + + + + Since these are electrons we are talking about I dont have to worry about the effects of gravity in this situation. The electric field inside the capacitor is approximately uniform and points down. This means the electric force on the electrons will point up and will cause the electrons to decelerate. If they are just barely turning around by the time they reach the negative plate then it means they have a velocity of zero at that time. Ill start by using kinematics. My origin will be at the hole in the positive plate and Ill use the standard coordinate system. My initial moment will be when the electron just enters the capacitor and my final moment will be when the electron is just turning around....
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- Spring '09