# Why is normal force in the direction of vector normal?

1. May 13, 2013

### hihiip201

This might be a bit philosophical, but is this just from experiment? that for a really really smooth surface, people found that the net force on an incline surface is found to be approximately in the direction normal to the incline plane? (approximately because there's no perfectly smooth surface, unless you use a magnetic plate i guess).

But are there any other reason, maybe just convention? that normal force is in the direction of normal to an incline plane?

2. May 13, 2013

### vanhees71

Of course, the total force is not normal but tangential to the surface of the (idealized) inclined plane. The reason is that the component of the gravitational force normal to the inclined plane is compensated by the contact forces exerted by the plane to the body on the plane.

3. May 13, 2013

### arildno

" that normal force is in the direction of normal to an incline plane? "
Correct.
In addition, the surface will usually exert a force tangential to itself, we Call that typically the force of friction.

4. May 13, 2013

### hihiip201

I'm aware of the force analysis of an object on an incline plane, my question is, how do we know that the force exerted on an object by an incline plane must be normal

5. May 13, 2013

### hihiip201

Maybe I should clarify what I'm asking.

My question is, why, or how do we know that the normal exerted on an object by an incline plane must be normal to the plane itself. Experiment? or convention?

6. May 13, 2013

### tiny-tim

hi hihiip201!
(you mean the reaction force exerted )

we don't know …

if the reaction force is normal, we say the plane is frictionless

if the reaction force isn't, we don't​

7. May 13, 2013

### 256bits

The normal force is perpendicular to the surface. It does not matter if the surface is smooth or rough. It is used to set up your FBD ( free body diagram ) so you can solve the problem at hand.

Other forces such as gravity or friction may make the resultant force offset at an angle to the perpendicular to the surface. Do not confuse the normal force with the resultant force.

See:
http://en.wikipedia.org/wiki/Surface_normal
for the definition of a normal vecrtor

8. May 13, 2013

### chingel

If the surface is smooth and frictionless then it doesn't resist sliding on the surface, i.e. there is no force tangential to the surface. However, since the surface is solid and you can't go through it, it will resist any normal force, since a net normal force would make the object move through the plane and the plane just resists that.

9. May 13, 2013

### Staff: Mentor

As others have alluded to, the force exerted by the inclined plane on a body in contact with the plane is not necessarily normal to the plane. The force can always be resolved into two components, one tangent to the plane, and the other normal to the plane. The component normal to the plane is typically referred to as the "normal force."

10. May 14, 2013

### hihiip201

I'm sorry, Maybe I should ask my question again with more precision.

Why is the reaction force of an incline, frictionless surface, necessarily in the normal direction of the plane.

how do we know, that for a smooth surface, the reaction force necessarily exert a force that is only normal to its plane. Did they physicists back then used that as a model to solve problems, and find that it generally works?

11. May 14, 2013

### hihiip201

so I guess the logic here is :

the direction of which motion is restricted = the direction of force?

12. May 14, 2013

### tiny-tim

i repeat …
if the reaction force is normal, we say the plane is frictionless

if the reaction force isn't, we don't​

13. May 14, 2013

### hihiip201

ok, I have the reasoning backward then.

thanks

14. May 14, 2013

### chingel

But you should understand it backwards also if you happen to have such a question. It can be taken as a definition, that if the force is normal, the plane is frictionless, but asking it the other way around, if the plane is frictionless (having some concept of friction beforehand, i.e. the plane is slippery, doesn't brake sliding etc), why is the force normal, is a perfectly acceptable question and you should keep on asking it until you feel that you can understand it.

First it is important to understand that the force normal to the plane has to be balanced, since the object cannot go through the plane. If there is an unbalanced force in a certain direction on an object, the object will start accelerating in that direction.

Then it is important to understand that if the plane is slippery, there is no resistance in moving across the plane, that means that there is no force from the plane against the direction of motion. Since there is no component of force parallel to the plane, it means that the total force from the plane is normal.

15. May 14, 2013

### Staff: Mentor

If you resolve the contact force between the inclined plane and the body into components normal and tangential to the plane, and I tell you that the tangential component (commonly referred to as the frictional force) is equal to zero, that leaves only the normal component (which then is equal to the resultant contact force). In general, the reaction force is not normal to the plane, even for a smooth surface. But the tangential component cannot be greater than the normal component times the coefficient of static friction. If the coefficient of static friction is very low, as it is for many materials (e.g., ice), then the tangential component is very small. In the limit of zero coefficient of static friction, the tangential component (frictional force) is equal to zero.