# A broader view on contact forces

I am aware that all the contact forces we experience like tension, friction, normal reaction, et cetera are complex manifestations of the fundamental forces which are gravitational forces, electromagnetic forces, strong and weak nuclear forces.

Suppose now that a body is placed on a stationary table. We say that since it is observed that the body is also at rest in spite of gravitational force acting on it, there must be an equal and opposite force acting on the body to cancel it out and that force is named as the normal reaction.

Normal reaction is said to be fundamentally arising out of electromagnetic interactions between the atoms of surface and body.

I also read that these electromagnetic forces between the surfaces in contact is known as contact force, and there I found that normal reaction is defined as the vertical component of contact force and friction as the horizontal component.

Now, I've a few questions.

Firstly, what makes the normal force, which is just a force due to random interactions of atoms electrically, is equal in magnitude to the gravitational force. I could explain why the normal reaction is opposite in direction, which is the obvious conclusion from how it is defined, but how can all the electric interactions between the atoms be planned so as to result in force equal to the gravitational force. I could not see any connection between the gravitational and electric forces...

The second question that comes to my mind, which is quite silly, but still connected, is that if a very heavy body is kept on a table and the table breaks due to its weight, then is it that the maximum normal force table could exert was lower than the weight of the body and hence it broke.

Another of my question, which I think is wise to put it here as it is all connected, is that, if a body is kept on the floor of a lift and a slight force is acting on the body, such that it is not large enough to move the body(due to friction), and the lift starts accelerating downwards, with the force still acting on body, then normal reaction increases and the contact force remains the same (assumed this, because the surface is the same), then will the friction acting between the body and the floor of lift, will also change.

But, I feel again, that the contact force should also change in this case, but I'm unable to find a reason why it would change. I feel this because it is not possible that one component changes and the resultant does not. I'm not sure of what change in friction would be.

Please help me in all this. You may not answer all of my questions but just give me a direction on how to think on this The reason for these question, I think, is that contact forces and their connection with non contact forces is not discussed very clearly, almost everywhere I've read about it.

• Normal force isn't necessarily vertical. It's normal (perpendicular) to the surface. Friction is parallel to the surface. On an inclined plane those directions aren't horizontal and vertical. – JMac Aug 29 '17 at 13:24
• In the first sentence of your question you include centripetal force in a list with friction, tension and normal force. This makes it seem a given force is either a centripetal force or one of these others when in fact a centripetal force is just any force that acts towards the centre of rotation. It could be friction (like a car driving a round a level curve) or tension (like a kid on swing) or the normal force (like a salad spinner) or some combination of forces. – M. Enns Aug 29 '17 at 15:07
• Sorry to say, but I'm getting rather confused. This is so because I'm receiving varied replies and I'm in no position now to find the connection between all which I'm sure exists.On one hand it is said that the table gets deformed, which makes me think how the table gets deformed..is it because of electromagnetic interactions, then it comes that it is about minimizing conservation of energy and momentum, then I am thinking is the momentum linear or angular. The thing which I want to say is that I want to know a straight answer, which shows connection between all this. – Abhinav Dhawan Aug 31 '17 at 12:49

"Firstly, what makes the normal force, which is just a force due to random interactions of atoms electrically, is equal in magnitude to the gravitational force."

(1) The normal contact force (this is a better name than 'normal reaction') is equal to the weight of a body in equilibrium on a horizontal surface. It isn't equal to the body's weight if, for example, the body has just landed on the surface from a height. Nor if the surface gives way!

(2) But how does the surface 'know' how to provide a the normal contact force that equals the weight when there's equilibrium, whatever the body's weight? The surface is deformed by the body. It's like hanging a weight on a spring. If done gently, the spring stretches and the tension in it increases (because of interatomic forces when atoms are separated further than their equilibrium positions) until the tension equals the weight. So it is with the surface: it deforms (maybe not noticeably) until the normal contact force equals the weight of the body placed on it.

• Be careful, @PhilipWood. The normal force is not equal to weight if the object is on an incline, and static friction is involved (the object can be in equilibrium in this circumstance). – David White Aug 29 '17 at 22:24
• I assumed the surface to be horizontal. I should have said that. Mea culpa. – Philip Wood Aug 29 '17 at 22:53
• How and why this 'deformity' of surface increase(or decrease) when the complete system is accelerating (like in the case of lift accelerating)? – Abhinav Dhawan Aug 30 '17 at 16:38
• If the system is accelerating, the body isn't in equilibrium. The contact force is greater than the weight if the body is accelerating upwards, and less than the weight if the body is accelerating downwards. – Philip Wood Aug 30 '17 at 17:25
• @PhilipWood, I'm pointing out your hidden assumption in the hope that you will update your answer so others will not be confused. I wasn't looking for an apology. Why is this important to me? Because I see a LOT of first-time high school physics students making the assumption that normal force ALWAYS equals the weight of the object, and I am "sensitized" to an answer that reinforces this incorrect assumption. – David White Aug 31 '17 at 1:38

but how can all the electric interactions between the atoms be planned so as to result in force equal to the gravitational force.

I mean no offence, but planned implies motivation, which is not physics. The operating principle here is minimisation and conservation of energy and momentum, nothing more than that.

The second question that comes to my mind, which is quite silly, but still connected, is that if a very heavy body is kept on a table and the table breaks due to its weight, then is it that the maximum normal force table could exert was lower than the weight of the body and hence it broke.

Your question is not obvious to me, it is a balance of forces, that's all. A table may initially accept a weight but over time, the internal bonds of say, a wooden table, weaken due to damp, and the table fails. No mystery or causality issues arise. One event follows another.

Another of my question, which I think is wise to put it here as it is all connected, is that, if a body is kept on the floor of a lift and a slight force is acting on the body, such that it is not large enough to move the body(due to friction), and the lift starts accelerating downwards, with the force still acting on body, then normal reaction increases and the contact force remains the same (assumed this, because the surface is the same), then will the friction acting between the body and the floor of lift, will also change.

I don't fully follow this, my apologies, but a sudden downward fall of the lift floor, because of inertia, produces a brief period of reduced friction as the bodies involved will not be in contact.

• How the quest for minimizing the conservation of energy and momentum, yields normal force to be equal to the weight of body on a plane surface and how does changing the angle of plane changes this at atomic level? Sorry, for not being very clear, but that is what I want to ask basically and the other questions just follow up... – Abhinav Dhawan Aug 30 '17 at 6:25
• Well, my short (apologies) reply would be that when you get to the atomic level, classical normal forces don't apply. Most quantum level equations contain one or more variables that, when you give them high enough values, start to reproduce (as they must), effects we see ourselves, classical effects, in other words, such as normal forces. This is the correspondence principle en.wikipedia.org/wiki/Correspondence_principle – user167453 Aug 30 '17 at 8:52
• So, does by using quantum mechanics, we can reason why normal force is equal in magnitude to weight on a plane. I don't want to know what exactly we do (because I have not yet learn it) but I want to know that is it possible to provide the required reasoning – Abhinav Dhawan Aug 30 '17 at 16:31
• Also, in my last question (the lift one), the thing I want to ask is that if one component (normal force) of contact force changes, then shouldn't the contact force vector itself also change, and so do the friction which is the other component of contact force. If they do, have they been experimentally verified? – Abhinav Dhawan Aug 30 '17 at 16:34

Firstly, what makes the normal force, which is just a force due to random interactions of atoms electrically, is equal in magnitude to the gravitational force.

Let us consider the case of an object kept on a table. Firstly, you need to know that the table itself is in equilibrium. When you place a ball on it, in the presence of gravity, the ball exerts a force on the table. This would disturb the equilibrium of the table. Hence the table deforms slightly, to accommodate the new force and hence take a new equilibrium configuration. You can now see that the small deformation that the table undergoes is precisely because of an additional force of the ball. Hence you can get a picture of why there is a correlation between the magnitudes of the action and the reaction forces.

The second question that comes to my mind, which is quite silly, but still connected, is that if a very heavy body is kept on a table and the table breaks due to its weight, then is it that the maximum normal force table could exert was lower than the weight of the body and hence it broke.

This seems correct. Continuing with the previous explanation, this would mean that the new configuration that the table is trying to take, cannot be sustained by the internal mechanism that is holding the table together. These forces are electrostatic in nature.

Now, the frictional force is taken to be proportional to the normal reaction. This is sliding friction. To be more precise, the frictional force can have a magnitude between $[0,\mu N]$, where $mu$ is the coefficient of friction between the surfaces and $N$ is the normal reaction. The magnitude of this force is dependent on how other forces act on the body and friction only tries to balance it out, up to a limit. Hence, until you apply a force equal to $\mu N$, you will not be able to move the body.

Now for your last question, it would help to think about trying to pull a heavy table. You exert a force, say $F_0$, but are unable to move it. Now, you place 10 books on the table and try to move it with the same force $F_0$. Would the frictional force be same or different in both the cases? Clearly, the normal reaction for the table with books is greater that just a table. To answer this, you just have to answer whether the table is in equilibrium. Is it? Yes, because it is not accelerating, in spite of being acted upon by multiple forces. Now the only horizontal force you're applying is balanced by friction. Since you have not changed the magnitude of horizontal force, you can say that the frictional force is also the same!