Question

Could someone help me with this from Six Idea That Shaped Physics, Unit E?

trons sepao E1M.2 Imagine that in some universe, the universal gravi tational constant G is large enough so that the force gravity exerts on two protons is as strong as the force an electro magnetic interaction between the same protons exert Estimate what your weight on the earth's surface wou be in such a universe (assuming the earth does not mass or size), compare vhy you would be reduced to a thin film. to your actual weight, and

Answer 1

The gravitational force between two protons $F_g=\frac{Gm^2}{r^2}$

The electrostatic force between two protons is $F_e=\frac{ke^2}{r^2}$

The two forces are equal, $\frac{Gm^2}{r^2}=\frac{ke^2}{r^2}$

$G=\frac{ke^2}{m^2}$

$G=\frac{8.99*10^9(1.6*10^{-19})^2}{(1.673*10^{-27})^2}=8.22*10^{25}\,N.m^2/kg^2$

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Mass of a person on earth $m=70\,kg$ , Weight of person on earth is $W=mg=70*9.81=686.7\,N$

Weight of person in universe with $G=8.22*10^{25}\,N.m^2/kg^2$ is $W'=\frac{GmM}{R^2}=\frac{8.22*10^{25}*70*5.972*10^{24}}{(6371*10^3)^2}=8.47*10^{38}\,N$

$\frac{W'}{W}=\frac{8.47*10^{38}}{686.7}=1.23*10^{36}$

Hence $W'>>W$

Weight of person in such a universe with $G=8.22*10^{25}\,N.m^2/kg^2$ is much larger than weight of a person on earth in a universe with $G=1.67*10^{-11}\,N.m^2/kg^2$

Due to this enormously large gravitational force, the muscles and bones will not be able to withstand the pressure and the person will be reduced to a thin film