Compute the kinetic energy of a proton (mass 1.67×10−27kg ) using both the nonrelativistic and relativistic expressions for speed of 9.00×10

Question

Compute the kinetic energy of a proton (mass 1.67×10−27kg ) using both the nonrelativistic and relativistic expressions for speed of 9.00×107m/s. Enter your answers numerically separated by a comma.

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Dâu 4 months 2021-09-05T06:28:46+00:00 1 Answers 3 views 0

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    2021-09-05T06:30:39+00:00

    Answer:

    The non-relativistic kinetic energy of a proton is 6.76\times10^{-12}\ J

    The relativistic kinetic energy of a proton is 7.25\times10^{-12}\ m/s

    Explanation:

    Given that,

    Mass of proton m=1.67\times10^{-27}\ kg

    Speed v= 9.00\times10^{7}\ m/s

    We need to calculate the kinetic energy for non relativistic

    Using formula of kinetic energy

    K.E=\dfrac{1}{2}mv^2

    Put the value into the formula

    K.E=\dfrac{1}{2}\times1.67\times10^{-27}\times(9.00\times10^{7})^2

    K.E=6.76\times10^{-12}\ J

    We need to calculate the kinetic energy for relativistic

    Using formula of kinetic energy

    K.E=mc^2(\sqrt{(\dfrac{1}{1-\dfrac{v^2}{c^2}})}-1)

    K.E=1.67\times10^{-27}\times(3\times10^{8})^{2}\cdot\left(\sqrt{\frac{1}{1-\frac{\left(9.00\times10^{7}\right)^{2}}{(3\times10^{8})^{2}}}}-1\right)

    K.E=7.25\times10^{-12}\ m/s

    Hence, The non-relativistic kinetic energy of a proton is 6.76\times10^{-12}\ J

    The relativistic kinetic energy of a proton is 7.25\times10^{-12}\ m/s

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