If there is no gravitational force on the earth (i.e. acceleration due to gravity is 0m/s^2), will bodies in contact still experience a normal force?

Question

My question arises from this post by Ashish Arora, where he asks: "If $g$ becomes zero suddenly, a body at rest on a fixed table will start moving away from it."

In the above question $g$ is the acceleration due to gravity.

Some in the comment section have stated that the body will fly away due to the loss in the centripetal acceleration provided by the earth's acceleration due to gravity.

Others have mentioned that Normal force is 'self-adjusting' and that if the acceleration due to gravity is zero, then the force experienced by the body towards the earth's centre is zero and there won't be any normal force.

I've been taught that if any two bodies are in contact, no matter what, they will experience 'some' contact force, due to the electromagnetic forces between the two surfaces in contact. So I would say that it does in fact leave the table (even the distance might be absolutely minuscule.)

So, who is correct. Was I taught wrong? (I guess it's more complex than a right or wrong answer though.)

Answer 1

The answer actually depends upon whether g is set to zero suddenly or slowly, because your question linked to a question that asked the suddenly case.

If there is a sudden loss of gravity, then it will fly. Because the existing normal reaction force is due to a little bit of bending just to prop up anything. If the gravity is suddenly lost, the electromagnetic and quantum forces that dealt the force resisting the bending, will suddenly be unopposed, and so the objects will fly off the table.

If there is a slow removal of gravity, then there will not be such a sudden rebound. The objects will not fly off the table because there would be weak van der Waals interection still keeping stuff together.

Answer 2

"Normal" is a direction, not a phenomenon. It is a shorter word for "perpendicular."

When two objects interact at a surface, there is a three-dimensional vector associated with the interaction force. The force parallel to the surface can be made smaller with lubrication, so we refer to it by its mechanism: we call it friction. The component that's perpendicular to the surface is just known by its direction: it's the force that's normal to the surface. I don't know the history behind that division, but it makes the pedagogy confusing.

At some level, all normal forces are a function of the springiness of material. With a stiff material like wood or glass, you can actually measure this springiness. A nice way to do it is to set a mirror on a table, and reflect a laser pointer from a fixed stand (mounted on the floor) off the mirror onto the wall. Then, start stacking bricks or steel weights on the table. You'll notice the reflection of the laser on the wall will move as the mirror rotates with the bending of the table. You can measure quite small angles this way: a milliradian, which is some small fraction of a degree of angle, corresponds to a millimeter of laser spot motion per meter of distance from the mirror.

For materials which crush locally, like Styrofoam, the mirror on the table won't work. But there is some length scale over which the weight applied to the table is opposed by the table squashing in response to it.

Because objects which are in contact with non-zero Force component normal to their surfaces are experiencing some springy interaction, if you were to remove the gravitational force holding them together, they will push apart. Somewhere in my posting history is an answer which discusses this for an amusement park drop ride. I'll look for that later and link it in here, unless someone else beats me to it, or unless I forget.

Answer 3

The normal force stems from electromagnetic interactions. You can think of the molecules of the object and the table in the region of contact as being interconnected by springs that are compressed due to the force of gravity. If that gravitational force is removed, the repulsive forces between the molecules will cause the objects to push apart.

Hope this helps.

Answer 4

It's not the contact force per se, it's the strain. Imagine a sci-fi space ship with artificial gravity, and a golf ball resting on a table in the ship. Both the ball and the table have elasticity. Both are slightly strained by the weight of the ball. If somebody flips the gravity switch to "Off," then that strain will relax, and it will give the ball a tiny impulse normal to, and away from the surface of the table.

Answer 5

You don't need to go totally hypothetical with this...at least not in the disappearing gravity way.

Materials and dimensions and non-linearities are complications, so consider a spherical cow of mass $m$ supported by a linear spring ($k$). The cow holds a point mass $M\gg m$, so gravity is counteracted by a spring compression such that $kx = (m+M)g$

Now instead of turning off gravity, just have the spherical cow drop the point mass: what happens?

Of course, the mass disappearing means the cow will be over accelerated (since $m\ll M$), but that's no worse than turning of gravity, since one could argue there'd be no inertia too, in which case the spherical cow scenario exactly models your question. That's the problem with non-physical hypotheticals, which I was trying to avoid.

Answer 6

The answer will depend on whether the gravitational force between all other objects is also be be considered zero. If the gravitational force between all the objects is to be considered zero, then the box will start moving in tangential direction with tangential velocity due to rotation of the earth.In this case there will not be any normal force between the table and box as there is no gravitational force between them due to their own masses.

If just the gravitational pull of earth is to be ignored, then the motion of the box will depend on the net gravitational force experienced by the box due to all other surrounding objects.

When two bodies are in contact, they will experience normal force because they will be attracted to each other due to gravitational force between them. This normal force will balance the gravitational force if the objects are moving with constant velocity. So if there is no gravitational force between the table and the box as a system (ignoring gravitational force between all the objects), there will be no normal force between them, but if there is gravitational force between them (only ignoring gravity of the earth) there may be normal force between them as it will also depend on the gravitational pull from other nearby objects.