Undergrad To predict the nature of Normal Reaction in any mechanics set-up

[rahaverhma]

Is it true that in any mechanical set-up, it is possible to predict the nature of Normal Reaction ( magnitude, direction, etc. ) without solving through the dynamical equations of motion and constraints for the set-up as Normal Reaction is completely unknown? I mean is it true that we can explain NR intuitively beforehand?

 

[Dale]

No. Sometimes you need to actually do the math to get the magnitude and direction.

 

[kuruman]

No. Sometimes you need to actually do the math to get the magnitude and direction.

I think it is safe to say that, if a system is in contact with a surface providing an external normal force, the direction of that normal force exerted on the system is perpendicular to the surface and away from it. In short, you cannot pull but you can push with a surface.

 

[Dale]

the direction of that normal force exerted on the system is perpendicular to the surface and away from it

Yes, but there are mechanical setups where the direction of the surface is not known until after you solve the dynamical system. For example, consider two kids jumping on a trampoline.

 

[kuruman]

Yes, but there are mechanical setups where the direction of the surface is not known until after you solve the dynamical system. For example, consider two kids jumping on a trampoline.

I am not sure I understand what you are talking about. I can understand that a 2D surface has two normals which makes the direction undefined. However, the normal force is a contact force. When one asks about the direction of a contact force, it is tacitly assumed that there exists a system which is in contact with the surface. If there is no such system the normal force is zero. $N=0$ is the condition that we teach as meaning that contact is lost and when that happens the kids' feet are off the trampoline.

Thus, I am not convinced that the direction of the normal force is not always the perpendicular to the surface that points towards the system. After all, the electrons in the kids' feet are repelled by the electrons in the trampoline surface.

 

[Dale]

I am not convinced that the direction of the normal force is not always the perpendicular to the surface that points towards the system. After all, the electrons in the kids' feet are repelled by the electrons in the trampoline surface.

The normal force is always perpendicular to the surface. That is a matter of definition and has nothing to do with electrons. The normal force is defined as the perpendicular force.

But when you have two kids on a trampoline you don’t know which direction is perpendicular to the trampoline surface until you solve the dynamics of the whole system.

 

[hutchphd]

Normal Reaction

The normal reaction force is the locally perpendicular component of the contact force; the paralllel component is conventionally called the frictional force. These are names (definitions) which are helpful for clear description but not directly for specification of a particular system. No matter what they are called, one usually needs to solve the dynamics.

 

[A.T.]

Is it true that in any mechanical set-up, it is possible to predict the nature of Normal Reaction ( magnitude, direction, etc. ) without solving through the dynamical equations of motion and constraints for the set-up as Normal Reaction is completely unknown? I mean is it true that we can explain NR intuitively beforehand?

If you know the exact deformations and material properties, then you can predict the contact forces without knowing the dynamics.

 

[Dale]

If you know the exact deformations and material properties, then you can predict the contact forces without knowing the dynamics.

But there are many systems that you don’t know the deformations without knowing the dynamics. And further there are surfaces for which knowing the deformations is insufficient. Things like dense viscoelastic materials.

 

[wrobel]

It looks like a question about reactions of ideal constraints. If it is so then yes reactions of the ideal constraints are calculated explicitly as functions of time, generalized velocities, and generalized coordinates.

 

[Herman Trivilino]

However, the normal force is a contact force. When one asks about the direction of a contact force, it is tacitly assumed that there exists a system which is in contact with the surface.

I realize that this is probably tangential, but the so-called normal force is actually the perpendicular component of the contact force. Thus as @Dale points out it is by definition always perpendicular to the surface. (The parallel component is the so-called friction force.)

Also note that the word perpendicular refers to the intersection of two lines. The word normal refers to the intersection of a line and a plane. Thus the so-called normal force is normal to the surface.