Jul 30 Doc 1

1] W=ΔK\nK=mc²(\\frac{1}{\\sqrt{1-\\frac{v²}{c²}}}-1)\n=mc²(\\frac{1}{\\sqrt{1-\\frac{v²}{c²}}}-1)\n=9.35×10^{-7}J=582eV=0.582MeV\n\\gamma=\\frac{1}{\\sqrt{1-\\frac{v²}{c²}}}\n\\beta=\\frac{v}{c}\n\\gamma=\\frac{1}{\\sqrt{1-\\beta²}}\n2) Em S=(x_{1},y_{1},z_{1},t_{1})\n(x_{1},y_{1},z_{1},t_{2})\n\\text{onde } t_{1},t_{2}\nEm \\text{s }(x_{1},y_{1},z_{1},t_{1})\n(x_{1},y_{1},z_{1},t_{2})\n\\text{então } \\Delta t=t_{2}-t_{1}\n\\Delta x=\\frac{v (x_{2}-x_{1})}{\\sqrt{1-\\frac{v²}{c²}}}\n3) V' = V-u\nV'_{s}=\\frac{u_{s}-u}{1-\\frac{u}{c}}\nV'_{m}=\\frac{u_{m}-u +u_{s}}{1-\\frac{u_{m}}{c}}\n=−u(1-\\sqrt{1-\\frac{v}{c}})\n\\text{onde } u=\\text{dado }\n4) V^{'}_{s}=\\frac{v_{x}}{\\sqrt{1-v_{y}²/c²}}\n\\\\text{e } dV = \\left[ u_{x}(1-\\frac{v_{x}V}{c²})-\\frac{u_{y}V}{c²}\\right] (1-\\frac{V_{x}V_{y}}{c²})\n2y=\\frac{(1-\\frac{v_{x}^{2}}{c²})dV}{1-\\frac{v_{y}}{c}}\n dV_{x}=\\left(\\frac{1-v^{2}/c^{2}}{(1-v_{x}V/c)}\\right)dZ\nd^{2}t=\\left(dt-\\frac{v}{c}dx\\right)\n=\\frac{(1-v^{2}V/c^{2})}{(1-\\beta V/c)^{2}}\n\\frac{dV_{y}}{dt}\n\\frac{dV_{y}}{dt}=\\frac{(1-\\frac{v}{c})dZ +\\beta V/dZ}{(1-V^{2}/c^{2})^{2}}\n\\text{e }\nV_{t}^{'}=\\left[ \\frac{(1-v_{y}^{2}/c²)}{(1-V^{2}/c²)}dZ\\right]\\left[dY -\\frac{v}{c}dX\\right]\n\\text{onde } V_{y} = \\gamma(1-\\frac{V_{x}^{2}V_{y}}{c²})\n\\frac{(1-\\frac{V_{x}V}{c})}{(1-\\frac{V_{x}^{2}}{c²})^{3}}\n