Neglect the effect of rotation of earth. Suppose the earth suddenly stops attracting objects placed near its surface

A person standing on the surface of the earth will

a) fly up

b) slip along the the surface

c) fly along the tangent to the earth's surface

d) remain standing

Now this is how i thought about it. When we stand on the ground, the Earth exerts gravitational force on us (Mg)

and

We exert a force on the ground and the ground exerts a force on us (normal reaction).

In the absence of Mg, shouldn't normal reaction still act which means we must fly up? However the answer is d)remain standing.

I still cant come to grips with the fact that no force will act on us in such a case. Wouldn't we still be pushing the ground (exerting a force) and the ground exerting (normal) force on us?? How would we still remain standing

• Why would you still be pushing on the ground? – JMac Jan 23 '18 at 17:00
• Look at videos of astronauts on the ISS. Your third and second last lines contradict each other. – user181180 Jan 23 '18 at 17:03
• Please can u explain why i wouldnt be pushing the ground. Whenever we stand, in addition to gravity acting on us, we exert a force on the ground and the ground exerts a force on us(action reaction pair and both equal in magnitude to mg). When gravity is absent why wont the action reaction pair be present can u please explain ?? – Hola Jan 23 '18 at 17:10
• @Heisenberg You just said, the action reaction pair is equal to $mg$. If we lose gravity, then $g = 0$; so the action-reaction pair is equal to $mg = m (0) = 0$. We only exert a force on the ground because if we didn't, we would be pulled down further. The ground keeps us from going further down; as gravity would want us to do. – JMac Jan 23 '18 at 17:18
• @JMac Oh my! Yes that makes complete sense. It was silly of me not to think of that! Thanks a lot for answering. I think im satisfied to say d) indeed is the right answer. Thanks a lot – Hola Jan 23 '18 at 17:31

Yes you are correct. The question is a bad one. It does not state that normal reaction disappears also. It would continue to act, if only for a short time (while contact continues), but without gravity it would propel the person away from the Earth. (The contact force would only disappear if the electrostatic force stopped, but that would be catastrophic because that is the force which holds atoms and molecules together, and also keeps them apart.)

If the person were balanced on a spring there is no question that the spring would continue to push him up when the force which holds him down (his weight) is removed. The same is true for wooden and even concrete floors. They also deform like very stiff springs. If the force which compresses them is removed (ie the person's weight) the force which they exert is unbalanced and pushes the person up.

I assume that gravity is switched off instantaneously. If it is switched off gradually then the forces on the person are balanced at every instant. This is a quasi-static process, and probably takes only a small (but finite) fraction of a second. The person does not gain any kinetic energy and does not fly up when the contact force becomes zero.

Adhesion forces (such as Van der Waals forces) would continue to act if the person remains in contact with the ground. These are usually much smaller than the weight of the person, and depend on contact area. They would not prevent him from being projected into space, but they might keep him from drifting away.

• Even their answer isn't logical for what they think would happen. If you got lucky for example, you might wind up in a position where you aren't sent skyrocketing into space; but then you absolutely wouldn't be standing. You would be floating near the surface. Also, that scenario would require you to be off the ground and without any velocity at the time this happened; so most likely you're going on a trip. – JMac Jan 23 '18 at 17:22
• @Heisenberg Books can be wrong. Especially those which are published locally. For the book to be correct the force from the floor would have to disappear at the same time as gravity. If the electrostatic force responsible for contact force disappeared the person's body and the Earth would fly apart! – sammy gerbil Jan 23 '18 at 17:35
• Alternatively you could assume that after gravity stops the person is placed in contact with the ground. Then the contact force would be very small or zero : it does not have to hold the person up. However, the question says the person is (already?) standing on the surface of the Earth. That suggests gravity was already present. Otherwise he would have been floating at the surface. – sammy gerbil Jan 23 '18 at 17:38
• @sammy its like this. The person is standing in the presence of gravity. Then suddenly the earths gravitational force fails which means g=0. When he was standing the normal was = mg. When the earths gravity fails . Wont the normal also become zero because g is zero meaning net force on him will become zero and hence he wont accelerate which will keep him standing still – Hola Jan 23 '18 at 17:44
• It seems to me that this problem is so very hypothetical that it might also be OK to imagine that the ground and the bottoms of our shoes (and our bodies) are rigid bodies. In that case, the "book answer" could apply. – Chet Miller Jan 23 '18 at 20:58

In absence of gravity and excluding other forces, we can write down \begin{equation} \vec{F}=M\vec{a}=\vec{0}, \end{equation} where $\vec F$ is the total force acting on your body, $\vec a$ is the acceleration of your body and $M$ is your mass.

Since $|\vec a|=0$, your body will just stand still in proximity of the ground, but it will not exert any force on the planet, so the normal reaction will simply be zero too.

The normal force will appear (i.e.: will be different from zero) only if you exert some force on the planet's surface. For example, you could push on the ground (maybe stretching out your legs) and then you would feel the normal force: this is, of course, what we call "jump".

normal force appear only when there is deformation in the surface by the object and in various cases this deformation is caused by the weight of the object and this weight is due to the attraction of the earth and according to your problem if we switch off gravity then their will be no attraction so no weight so as a result no deformation so no normal force.