How can I determine the force at support B in a rigid bar system?

[coconut62]

Homework Statement

Please refer to the image.

Homework Equations

Sum of clockwise moment=sum of anticlockwise moment

The Attempt at a Solution

I had drawn out the force diagram and listed out the information required.

The question asks me to find force acting by the support B.

I troubled myself by taking moments about A and multiplying every forces with their respective distances from A.

However the answer was simple, they just added all other forces together, 33 + 4.4 + 129 = 166N.

I can't figure out where is the pivot. Or is there even a pivot? What's the theory behind this calculation?

 

[haruspex]

But how was the 129N figure obtained? You'd need to take moments to derive that.

 

[coconut62]

Haruspex, the 129N is obtained from another part of the question which is correct.

 

[haruspex]

Haruspex, the 129N is obtained from another part of the question which is correct.

Then it is indeed simple to determine the force at B in the way they use. For the system to be static, the sum of the vertical forces must be 0. You could also deduce it by taking moments about anywhere along the line except B.

 

[Nickie]

As a scientist, the force at support B in a rigid bar system can be determined by using the principle of moments. This principle states that the sum of clockwise moments is equal to the sum of anticlockwise moments in a system at equilibrium. In order to determine the force at support B, we need to find the point where the system is in equilibrium, or where the sum of moments is equal to zero.

To do this, we first need to identify all the forces acting on the system and their respective distances from the point of interest, which in this case is support B. In the given image, we can see that the forces acting on the system are 33N, 4.4N, and 129N. We also know that the distance between support B and the point where the 33N force is acting is 3m, the distance between support B and the point where the 4.4N force is acting is 1.5m, and the distance between support B and the point where the 129N force is acting is 2m.

Next, we can apply the principle of moments by setting up an equation where the sum of clockwise moments is equal to the sum of anticlockwise moments. This can be written as:

(33N x 3m) + (4.4N x 1.5m) + (129N x 2m) = 0

Solving for the unknown force at support B, we get:

(33N x 3m) + (4.4N x 1.5m) + (129N x 2m) = FB x 0

Therefore, FB = (33N x 3m) + (4.4N x 1.5m) + (129N x 2m) / 0

FB = 166N

This means that the force at support B is 166N, which is the sum of all the other forces acting on the system. This calculation is based on the principle of moments, which is a fundamental concept in mechanics and is used to solve problems involving forces and torques in a system at equilibrium.