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Note: Assume standard Newtonian mechanics for the first parts of this problem. Required data are provided at the foot of the problem.
On October 15, 1991 an ultra-high energy proton came to earth, near Utah, from space with an energy of $3.2\pm 0.9\times 10^{20}$ electron volts. This REALLY is a lot of energy for a proton to possess, so much so it was dubbed the 'Oh-my-god' particle! To see why, explore the energy it contains by comparing this figure with the kinetic energy for the motion of more every-day objects - find an
everyday situation which really gives an intuitive sense of the amount of energy of this ultra-high energy proton.
If you used the Newtonian expression $KE=\frac{1}{2}mv^2$ for the energy, how fast would the proton be travelling? How does this compare with the speed of light? What does this tell you?
Imagine that a small, hand-sized, ball of meteoric iron with the same kinetic energy per kilogram as this ultra-high energy proton struck earth. Analyse the possible effect this would have.
Extension: Clearly, the energies referred to in the question push the furthest reaches of Einstein's theory of special relativity. Use this situation to determine the actual velocity of the proton relative to Earth using the formula involving the rest mass $m_0$ of a stationary object and the speed of light $c$
$$E= \frac{m_0c}{\sqrt{1-\frac{v^2}{c^2}}}\;.$$
Data for the problem
1 electron volt $\left(\mathrm{eV}\right)$ = $1.602 176 46 \times 10^{-19}\textrm{ J}$
Rest mass of the proton is $9.3828\times 10^8\textrm{ eV}$
Mass of proton $1.672 621 58\times 10^{-27}\textrm{ kg}$
Speed of light $2.99 792 458\times 10^8\textrm{ ms}^{-1}$