3D Equilibrium Statics Problems

[tamara1025]

I'm so stuck on this problem. I got it completely wrong on my test because I don't even know where to start. All i recall is that we mus use the vector approach? The problem states:
For the figure shown, calculate the reactions at point O due to the tensions in the two cables BA and BC. T(BA)=700 N, T(BC)=800 N. Assume that the tree is rigidly fixed to the ground.

 

[pongo38]

Vectors or not, there has to be a similarity between the geometrical triangle OBC and the force components on the cable BC. To get the force components in terms of ijk, you need to project OC onto the x-axis. Let's call it OC'. Then the geometric distances BO, OC', and C'C are in the same ratio as the force components of the 800 N force. There should be as many as 3 reaction components at O that are forces, and three that are moments, although My will be zero by inspection because the forces both seem to pass through it.

 

[Mene]

I can understand your frustration with 3D equilibrium statics problems. These types of problems can be challenging, but with the right approach, they can be solved effectively.

First, it is important to understand the concept of equilibrium in 3D space. In this case, the tree is considered a rigid body, meaning it will not deform under the applied forces. This allows us to use the vector approach, which involves breaking down the forces into their x, y, and z components.

Next, we can use the principle of static equilibrium, which states that the sum of all forces acting on a rigid body must equal zero, and the sum of all moments (torques) acting on the body must also equal zero. This means that the forces and moments acting on the tree at point O must be balanced.

To solve this problem, we can start by drawing a free body diagram of the tree at point O. This will help us visualize the forces acting on the tree and their directions. From the problem statement, we know that there are two cables, BA and BC, with tensions of 700 N and 800 N, respectively.

We can then use the vector approach to break down these forces into their x, y, and z components. This will give us three equations to solve for the reactions at point O. Remember to consider the direction of the forces and the direction of the coordinate axes in your calculations.

Once we have solved for the reactions at point O, we can check our solution by ensuring that the sum of the forces and moments acting on the tree at point O equal zero. If they do not, then there may be an error in our calculations.

I understand that this problem may seem daunting, but with practice and a solid understanding of the principles involved, you will be able to solve these types of problems effectively. Don't be discouraged by getting it wrong on your test, use it as a learning opportunity and keep practicing. Good luck!