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Introductory Physics Homework Help
Distance travelled in a Cyclotron
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[QUOTE="Uku, post: 3111995, member: 248965"] [h2]Homework Statement [/h2] Known data: [tex]v_{final}=3.99*10^{7}m/s[/tex] [tex]f_{osc}=12MHz[/tex] [tex]B=1.6T[/tex] [tex]R=0.53m[/tex] [tex]V_{acc}=80kV[/tex] [tex]q_{deut}=1.602*10^{-19}C[/tex] [tex]m_{deut}=3.344*10^{-27}kg[/tex] [b]answer according to Halliday and Resnick x=240m[/b] I got it all, and I have to find how much distance was traveled by the [b]deuteron[/b] in the cyclotron, from starting of acceleration to the end of it. [h2]The Attempt at a Solution[/h2] From the potential across the dees I get [tex]v_{gained_per_turn}=\sqrt{\frac{2E}{m_{deut}}}=2768586.602m/s[/tex] Since I know the final speed I can find the amount of turns the deuteron was in the cyclotron [tex]n=\frac{v_{final}}{v_{gained_per_turn}}=14.41turns[/tex] Since f is constant, so is T and I can find the amount of time spent in the cyclotron: [tex]t_{spent}=n*T=n*\frac{1}{f_{osc}}=1.2*10^{-6}s[/tex] The acceleration must be constant, the accelerating voltage is not changing [tex]a=\frac{v_{gained_per_turn}}{T}=3.32*10^{13}\frac{m}{s^{2}}[/tex] Now [tex]x=\frac{1}{2}a*t^{2}=23.92m[/tex] The answer in the book is 240m, which differs from mine ten times, smells like a power error? Or am I doing something wrong? [/QUOTE]
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Distance travelled in a Cyclotron
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