Equilibrium : normal reaction of a rotational center?

• Doomski
In summary, the problem involves a force of 90 N applied to a member supported by a frictionless pin and a cable passing over a pulley. The tension in the cable is 117 N and the reaction at D is 129.8 N. To solve for the reaction, assumptions must be made about the weight of the system and the L-shaped piece.
Doomski

Homework Statement

I'm trying to figure out the reaction at D,that's where the system can rotate.

Problem:
A force P of magnitude 90 N is applied to member ACDE, which is supported by a frictionless pin at D and by the cable ABE. Since the cable passes over a small pulley at B, the tension may be assumed to be the same in portions AB and BE of the cable. For the case when a=3m, determine:
a)the tension in the cable
b) the reaction at D

2. The attempt at a solution

I've calculated the tension in the cable through the sum of momentum=0, T= 117N. For the reaction, I used the sum of forces=0; We don't have the mass of the system, so I assumed there's three forces acting on D, a normal force and the weight of the system that cancel each other (probably wrong?) and the reaction. From that,I got R = 129.8N. Is that right?
Are there a difference between a normal reaction of a table, for example, and Rd ??

Thanks.

Edit: I had to paint the figure because the photo wasn't clear.

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Last edited:
Doomski said:
I've calculated the tension in the cable through the sum of momentum=0, T= 117N
To get that, I have to assume the horizontal part of the L piece is weightless. Doesn't your method assume that?
To find the reaction at D, you will need to assume the same for the vertical part. You have three unknown scalars, tension and the components of the reaction force, and only three available equations. Any more unknowns make it unsolvable.

Doomski
haruspex said:
To get that, I have to assume the horizontal part of the L piece is weightless. Doesn't your method assume that?
To find the reaction at D, you will need to assume the same for the vertical part. You have three unknown scalars, tension and the components of the reaction force, and only three available equations. Any more unknowns make it unsolvable.

Now that makes sense, thank you!

1. What is equilibrium in terms of rotational motion?

Equilibrium in rotational motion refers to the state in which an object's rotational center, also known as its center of mass, remains at a fixed position and does not experience any rotational acceleration or change in angular velocity.

2. How is the normal reaction of a rotational center defined?

The normal reaction of a rotational center is the force exerted on an object's rotational center by a supporting surface or pivot point, perpendicular to the surface or pivot. It is also known as the support force or pivot force.

3. What factors affect the normal reaction of a rotational center?

The normal reaction of a rotational center depends on the object's mass, the distance of its center of mass from the pivot point, and the acceleration due to gravity. It also depends on the type of support or pivot, such as a fixed point, hinge, or rolling contact.

4. How does the normal reaction of a rotational center relate to the object's stability?

The normal reaction of a rotational center is directly related to an object's stability. A larger normal reaction force means a greater resistance to tipping or toppling over, while a smaller normal reaction force indicates a lower stability and a higher risk of falling or rotating out of equilibrium.

5. Can the normal reaction of a rotational center be zero?

Yes, the normal reaction of a rotational center can be zero if the object's center of mass is directly above or below the pivot point, resulting in a balanced torque and no net force acting on the object's rotational center. This is known as a neutral equilibrium.

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