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# Question about the Normal Reaction Force (M1) watch

1. What is the normal reaction force? When is it perpendicular and when it is angled, and how do I tell the difference? Also, if a rod is smoothly hinged to a vertical wall at one end and held in the horizontal position by a light string at the other end, which direction is the normal reaction and how do you know? Thanks
2. (Original post by akrapovic)
What is the normal reaction force? When is it perpendicular and when it is angled, and how do I tell the difference? Also, if a rod is smoothly hinged to a vertical wall at one end and held in the horizontal position by a light string at the other end, which direction is the normal reaction and how do you know? Thanks
The normal reaction force is always at 90 degrees to the surface because it's defined to be so. It's often confused with the contact force which is the resultant force of the normal reaction and friction which acts parallel the surface.

In your example of a hinged rod: There will only be a normal reaction force is a force is being exerted on the wall. Since the forces on the wall must be equal (since it won't accelerate F = ma) we say it's exerting an opposing force.

So if the string is not pulling the hinge to the side we'd not expect a normal reaction force but it will exert a force upwards, we just don't call it a normal reaction force as it's not normal to the wall.

TL;DR
Vertical force of the wall + vertical force of the string - weight = 0
Horizontal force of the wall (normal reaction, since this is normal to the wall) = horizontal force of the string
3. (Original post by eugaurie)
The normal reaction force is always at 90 degrees to the surface because it's defined to be so. It's often confused with the contact force which is the resultant force of the normal reaction and friction which acts parallel the surface.

In your example of a hinged rod: There will only be a normal reaction force is a force is being exerted on the wall. Since the forces on the wall must be equal (since it won't accelerate F = ma) we say it's exerting an opposing force.

So if the string is not pulling the hinge to the side we'd not expect a normal reaction force but it will exert a force upwards, we just don't call it a normal reaction force as it's not normal to the wall.

TL;DR
Vertical force of the wall + vertical force of the string - weight = 0
Horizontal force of the wall (normal reaction, since this is normal to the wall) = horizontal force of the string
So how do I know the angle of the normal reaction between the hinge and the wall? And why is it not perpendicular? because I can't seem to wrap my head around what direction it would act and why.
4. (Original post by akrapovic)
So how do I know the angle of the normal reaction between the hinge and the wall? And why is it not perpendicular? because I can't seem to wrap my head around what direction it would act and why.
Say the string is at some angle theta to the horizontal.

We need to forces to be balanced (because the acceleration of the rod is 0).
The contact force exerted from any surface has 2 components, that perpendicular to the surface (Normal reaction) and that parallel to it (friction).

You'll agree that the string exerts a horizontal force of T(tension)*cos theta, to cancel this the horizontal force of the wall must also equal Tcos(theta).

Now we need the vertical forces to cancel.
Total force up = Tsin(theta) + friction on the wall
Total force down = weight of the rod.
Tsin(theta) + friction = weight
-> Friction = Weight - Tsin(theta)

Now we have friction = Tsin(theta), and normal reaction = Tcos(theta)

The total force exerted by the wall (The contact force) = (T^2 sin^2(theta) + T^2 cos^2(theta))^0.5 = T

And we can draw a triangle and see it'll act at angle phi above the horizontal where: tan(phi) = Upwards component / Horizontal component = Friction/normal reaction = sin(theta)/cos(theta) = tan(theta)

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Updated: April 21, 2017
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