# 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?

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.)

• Normal forces are subject to Newton's 3rd law like any other force. If there is no force of gravity pushing the body into the ground, how can there be a normal force reacting that? Apr 24 at 14:40
• @RC_23 But the normal force and the force of gravity are not action-reaction pairs :/ Apr 24 at 16:07
• In a Free body diagram of the body in question: if the ground exerts a nonzero normal force "upward," what is counteracting that? If nothing is counteracting that, what will happen to the body? Apr 24 at 17:14
• @RC_23 If nothing is counteracting It, then it will have net acceleration upwards. I get that. What's your point? Apr 24 at 17:22
• Would not everything on the earth be sucked into space by the explosive decompression of the atmosphere? Apr 24 at 20:57

## 6 Answers

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.

• Can objects even really be said to be "touching" if there's no compression/force? I think the answer is "yes, but only mathematically, not physically". Apr 24 at 20:31
• Is that comment for me? Because I specifically wrote a physical mechanism (van der Waals interaction) which is the barest minimum quantum electrodynamical attraction between neutral-neutral objects. In reality we tend to have dipoles, increasing the attraction. Apr 24 at 20:35

"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.

• Do physicists or material-scientists actually measure the 'springiness' of materials like this? (the laser beam method) Apr 24 at 16:14
• @Hiraṇyajihva The normal force that the book and table exert on one another equals the downward force of gravity on the book, or $mg$ where $m$ is the mass of the book. That’s because the downward force of gravity on the book equals the upward normal force the table exerts on the book for a net force of zero as it does not accelerate. Then, per Newton’s 3rd law, upward normal force the table exerts on the book is equal and opposite to the downward normal force the book exerts on the table. Apr 24 at 17:12
• No, I mean the gravitational force between the two bodies, the book and the table.@BobD Apr 24 at 17:21
• This is essentially how atomic force microscopy works. Apr 24 at 21:13
• @Hiraṇyajihva The gravitational force between kilogram-scale masses is extremely hard to measure. Look at the history of the Cavendish experiment (which also used a mirror to measure small angular deflection). I have done the bending-table experiment as a classroom demonstration. As another commenter says, this method is very similar in principle to AFM.
– rob
Apr 24 at 23:40

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.

• Thanks! Is there a way to compare the normal force of the two bodies and the force of gravity between the two bodies (since they also have mass)? Apr 24 at 16:12
• The force of gravity acts on the book. The normal force exerted by the table on the book equals the gravitational force on the book for a net force of zero on the book. Per Newton's 3rd law the book exerts and equal and opposite normal force on the table. The book undergoes axial compression due to the force of gravity and the equal and opposite force Apr 24 at 18:16

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.

• Ah, thanks, contact force was always so mysterious to me. How would the gravitational attraction between the two bodies affect this? Apr 24 at 16:10
• You don't even need sci-fi artificial gravity for this. Thanks to the equivalence principle, a simple rocket engine on the ship works just as well. Apr 24 at 23:34
• … In fact, there are probably videos online showing this effect in some form, e.g. from flights to the ISS when the second stage rocket burn ends. While most things in space capsules tend to be tied down pretty tight during launch, there's a tradition of bringing a small plush toy along as a "zero g indicator": if the toy floats, the spacecraft is in freefall. Here's one video I found showing this, although in that case the toy is initially handing from a string rather than resting on a surface. Apr 24 at 23:36
• @IlmariKaronen, Double Plus Good link! Of course, the strings from which the toys were dangling probably stored significantly more energy than the golf ball/table system that I described would be able to do. Apr 24 at 23:45

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.

• Sorry, I don't seem to understand why the cow will be 'over' accelerated. Is it because the mass is small so the acceleration will have to be huge to match the force? Apr 24 at 16:11
• Because the spring is compressed so that $kx=(m+M)g$, but is suddenly pushing on $mg$, so I thought about suspending $M$ from a rope, which also has problems, because at the end of the day: you cannot separate gravity from acceleration.
– JEB
Apr 24 at 17:45

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.

• I don't think this is true. Every object on Earth in contact with the ground has the same tangential velocity as the Earth at that point. Inertia will keep it all moving together unless it's disturbed Apr 24 at 14:28
• That's a good point. Many forgot to factor in the force of gravity between the two bodies. Apr 24 at 16:08
• @RC_23 The earth does not have velocity tangential to its own rotation, so it depends on what the table is fixed to. If it's fixed to the earth, I assume it would remain so, and the body, not itself fixed, would thus move away from the table. The assumption of a fixed table is insufficiently defined in this problem. Apr 24 at 21:00