Gravitational force and Electromagnetic force?

I think the part about electromagnetic force being exponentially stronger than gravitation got through to you!(An easy way to picture this is how static electricity can lift up things against the pull of the earth!) About the feather,the way you are able to support the feather against the gravitational pull of the earth is because of the electromagnetic forces exerted by your hand on the feather and vice versa. If these were much much weaker something as little as a feather would be able to crumple your hand, that is if it hadn't already been crumpled by gravity before that!

I've read in The Briefer History of Time (Stephen Hawking), that even very slight changes in the strength of the fundamental forces can cause great imbalance. If the electromagnetic force was stronger, atoms wouldn't be as stable as they are, and if it was weaker, atoms might not form at all, so the chances of life existing would be zero!

If there was a sudden change, hypothetically, this instant, the whole world could possibly crumble. But if that actually was the case we wouldn't even have been here.

The notion of "weak gravity" is "not even wrong"! It's comparing oranges to apples: it's meaningless to compare a dimension-full interaction (gravity) with a dimensionless interaction (standard model interactions such as the electromagnetic force), if no circumstance (e.g the specific charges and masses in comparison) is provided.

The Nobel laureate Frank Wilczek actually wrote a whole book ( The Lightness of Being) about what should be the right question: Given that the "charge" of the gravitational force is mass (energy tensor), the correct question is why are the masses of the elementary particles so small compared with the Planck scale?

This leads you to the nagging issue of natureness/hierarchy problem (the unnatural gap between the Planck mass and the weak scale/Higgs mass). As of yet, mortal physicists are still scratching their heads and fretting about this nasty "naturalness/hierarchy/fine-tuning problem". The world’s best minds are loosing sleeping on it (ask Lisa or Nima) and yet there is no answer.

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To give you some thought experiment of "strong" gravity:

• If the electron mass is increased to the mass of a flea egg ($10^{-8}$ kg, the plank mass), the gravitational attraction between electrons will be in balance with the repulsive electronic force. In technical jargon, the Schwarzschild radius and the Compton wavelength are of the same order for this case.

• If the electron mass is increased to the mass of a chicken egg, the
  gravitational force between electrons will trump the electronic force and electrons will be crushed into an electron black hole by gravity. Of course, true quantum gravity effects will be the dominant one in this case, the conventional semi-quantum black hole reasoning (a la Stephen Hawking) shall be taken with a grain of salt.

I agree with the answer of @MadMax. The question is quite prone to interpretation, so here another "point of view".

The electric and gravitational force laws are both inverse square laws, so if one computes the ratio of the forces between two bodies, the distances cancel.

Take two point particles with masses $m_1$, $m_2$ and charges $q_1$, $q_2$. You have the gravitational force

$$ F_G = G frac{m_1 m_2}{d^2} $$

and the electric Coulomb force (CGS units are used)

$$ F_C = frac{q_1 q_2}{d^2} $$

Clearly (depending on the actual values of $m_1$, $m_2$, $q_1$ ,$q_2$) you may have that $F_G > F_C$, or the other way round.

However, for (charged) elementary particles, you always have that $F_G ll F_C$. In particular, if you use two electrons ($m_1=m_2=m_e$, $q_1=q_2=q_e$), then you have

$$ F_G / F_C = frac{G m_e m_e}{q_e q_e} = G left(frac{m_e}{q_e} right)^2 sim 10^{-42} $$

where the quantity in the parentheses is the mass to charge ratio first measured by Thompson. As you see $F_G sim F_C/10^{42}$, independently on the distance $d$: the gravity attraction is really extremely weak.

In an Hydrogen atom you should compare the attraction between the electron and the proton (i.e. the Hydrogen nucleus). The proton is $sim 2000$ times more massive than the electron so $F_G$ is $2000$ times bigger than the electron-electron gravitational attraction considered before. In this case you should find $F_G/F_C sim 10^{-39}$. Still a super small number.

Clearly if you don't use fundamental particles but planets (that are almost neutral but have a huge mass), then $F_G$ wins.