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re a foe VBR . # ’ 27 «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 ta fuse two deuterium nuclei into helium. Deuterium is an isotope of hydrogen, having one proton and one neutron in its nucleus. a. Ifthe two deuterium nuclei need to get within 1.3x 10m 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. ‘ Use energy principles with the system being the two deuterium nuclei. The initial state of the system willbe the twa . 0 + , nuclei very far apart. The final state of the system will be after the helium nucleus has formed. uO E,+W=E, => K,+U,,+0=K,+U,, : QO © % TL 2KlO mn, =A mov, [40 ork nfF ? =(m, +m,)vp, =A : k+ P10 2a *% _ ke _ | (8.99x10" N-m?/c*)(1.602x10°° cy Mos = (m, +7, Jr, \(1.673x107 kg +1.675x 10 kg}(1.3x10" m) ial @¥lC C 2 "=> Vpy = 7.28% 106 m/s . in making this prediction | had to assume the two deuterium nuclei were far enough away that the electric potential energy between them was approximately zero. | also assumed the two nuclet were point-like. Lastly, | assumed the two. nuclei were fired at each other exactly head on. 2. 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 wilt happen. b. Predict what you will see happen when the rod is allowed te briefly touch the left sphere and then is moved far away. Give an explanation for why yau think this will happen. . ——— When the red is close electrons from both spheres {because they are in contact} will be drawn toward the rod. The left sphere will have a net negative charge and the right sphere will have a net positive charge. The left sphere will be attracted to the rod, and the right sphere will be attracted to the left sphere. So, the two spheres remain in contact but will swing slightly to the left toward the rod. When the rod touches the left sphere, some electrons will transfer from the.sphere to the rod. Not too many will transfer since the rod is an insutator, so the spheres will still be attracted to each other. Once the rod is moved away the charges on the spheres will equalize. Since some electrons were transferred to the rod, both spheres will have a net positive charge so they will repel one another and there will be a small gap between them. 
