Statics of Rigid Bodies - Why is the normal force not considered?

In summary, the normal force is often not explicitly considered in the analysis of rigid body statics because it typically acts perpendicular to the surface of contact and does not contribute to the net force or moment about the center of mass. Instead, the focus is on the sum of forces and moments that influence the overall equilibrium of the body. The normal force can be implicitly accounted for through the equilibrium equations, allowing for a simplified analysis while ensuring that all forces acting on the body are balanced.
  • #1
Nova_Chr0n0
16
3
Homework Statement
6–67. Determine the force that the smooth roller C exerts
on member AB. Also, what are the horizontal and vertical
components of reaction at pin A? Neglect the weight of the
frame and roller.
Relevant Equations
Equilibrium Equations
The problem is from Hibeller's book, Mechanics: Statics and attached below is the picture of the problem:

1700821107597.png


My question about this problem is about the FBD of the reactions. Here is how I drew it:

1700821364702.png


But when I tried checking the solution for the problem, they have this as their FBD:

1700821514445.png


My question is, why did they not include the Normal force created by the roller? Is it not considered as a reaction for the whole figure? I think I'm missing an important concept here and it confuses me. This topic is Frames and Machines.
 
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  • #3
Please, see:
https://en.m.wikipedia.org/wiki/Overdetermined_system

Resolving external forces with three available equations (summation of external forces and moments) is the first step.
With those values, you can calculate the internal forces and moments in any armature, frame, truss or mechanism.

For practical purpose, you could weld that roller to member AB, and both members at pin B, without modifying the shown conditions.
Its normal force can be considered an internal force of the whole mechanism.

Note that a Dy reactive force is needed to keep the static equilibrium.
You could simplify the "body" to a single member being wedged against the vertical surface by the applied clockwise moment (like shown below).
Dy is preventing the body from rotating about pivot A.

Dx will induce a moment on member BDC about pin B, which will translate into the roller normal force that you have mentioned (which will be a bending load on member AB).

As you can see, we need to calculate the chain reaction step by step, beginning with reaction forces at B and D.

4274BBF9-0A0A-4B68-A171-284D21BCC142.jpeg
 
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Sorry, I am really slow to catch up, so I need more clarification. My current understanding, based on the explanation, is that:

The normal force produced by the roller is considered an internal force and not an external force. Is it because the roller is part of the whole figure and therefore its normal force is not considered an external one? Here is what I'm thinking right now: Consider a box and a surface:
1700895154043.png


Here, the box is the figure and is experiencing a normal force. This normal force is exerted by the surface (which is a different figure that is not being examined) and not the box, so is it considered an external force?

In the figure I've shown, the red colors are an external object to the figure (highlighted as yellow) and are therefore considered an external force?

1700895393957.png
 
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  • #5
Nova_Chr0n0 said:
This normal force is exerted by the surface (which is a different figure that is not being examined) and not the box, so is it considered an external force?
Yes

Nova_Chr0n0 said:
In the figure I've shown, the red colors are an external object to the figure (highlighted as yellow) and are therefore considered an external force?
Yes
 
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FAQ: Statics of Rigid Bodies - Why is the normal force not considered?

Why is the normal force not considered in some statics problems?

The normal force is not considered in some statics problems because it may not be relevant to the specific conditions being analyzed. For example, if the problem focuses on forces parallel to the surface or only considers moments about a point where the normal force has no lever arm, it can be omitted for simplicity.

When can the normal force be neglected in statics problems?

The normal force can be neglected in statics problems when it does not contribute to the equilibrium equations being considered. This typically occurs in scenarios where the analysis is confined to the horizontal plane, or when the normal force acts through the point about which moments are being calculated, rendering its effect negligible.

How do you determine if the normal force should be included in a statics problem?

To determine if the normal force should be included, you need to analyze the forces and moments acting on the rigid body. If the normal force contributes to the vertical equilibrium or affects the moments about a point of interest, it must be included. Otherwise, it can be ignored if it does not influence the overall equilibrium.

What role does the normal force play in the equilibrium of rigid bodies?

The normal force plays a crucial role in maintaining the equilibrium of rigid bodies by counteracting other forces, such as gravitational forces, to prevent motion perpendicular to the contact surface. It ensures that the body remains stationary in the vertical direction and can affect the rotational equilibrium depending on its point of application.

Can the normal force be zero in a statics problem?

Yes, the normal force can be zero in a statics problem if there is no contact between the surfaces or if the body is in free fall. In such cases, the absence of a normal force does not affect the equilibrium analysis, as there are no perpendicular reactive forces to consider.

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