How Do You Calculate Tension in Wires Supporting a Loaded Rod?

[jonny17]

I am having trouble getting to grips with moments and couples and i have got stuck on the following question:

"A uniform horizontal rod AB is 120cm long and weighs 250N. It is supported by two veritcal wires, one 10cm from A and the other 20cm from B. Loads of 100N and 350N hang from the rod at distances of 50cm and 100cm respectively from A. Calculate the tension in each wire"

I'm not quite sure what 'tension' means exactly but I am guessing that I have to use the formula (force x distance) to somehow work the problem out. Initially, can one can say that the tension from the weight of the rod in each wire is the (distance from centre of mass that wire is attached x 250N) which would mean that the tension in the first wire is equal to (0.5m x 250N) as the wire is attached 50cm from the centre of mass. Therefore the tension from the weight of the rod in the other wire is equal to (0.4m x 250N). However it is at this point that i get stuck! If any of the above is wrong please tell me and if anyone could give me an idea where to go, that would be great.

Jon

 

[Doc Al]

Equilibrium

Tension just means the force that each wire must exert to support the rod plus loads.

Start by identifying all the forces acting on the rod. I count 5 forces: the tensions in each wire, the two loads, the weight of the rod itself (which acts through the center of mass). Draw a diagram.

For equilbrium to hold:
(1) The sum of the forces must equal zero. (What does that tell you about T₁ + T₂?)
(2) The sum of the torques (about any axis) must equal zero. I recommend using the point where a wire attaches to the rod as an axis--find the sum of torques about that point.

 

[M98Ranger]

Hi Jon,

Thank you for reaching out for help with your understanding of moments and couples. It seems like you have a good understanding of the basic concepts, but just need some guidance on how to apply them to this specific question.

Firstly, tension is a force that is pulling or stretching an object in opposite directions. In this case, the wires are providing tension to support the rod and the loads hanging from it.

You are correct in using the formula force x distance to calculate the tension in each wire. However, there are a few more factors that you need to consider in order to solve this problem.

Firstly, you need to find the total weight of the rod and the loads hanging from it. This can be calculated by adding the weight of the rod (250N) to the weight of the two loads (100N + 350N = 450N).

Next, you need to find the total distance of the rod and the loads from the two wires. This can be calculated by adding the distances from the wires to the centre of mass of the rod (10cm + 50cm = 60cm for the first wire and 20cm + 100cm = 120cm for the second wire).

Now, you can use the formula (force x distance) to calculate the tension in each wire. For the first wire, it would be (450N x 60cm = 27,000Ncm). To convert this to Newtons (N), you need to divide by the distance from the wire to the centre of mass (60cm). So the tension in the first wire would be 27,000Ncm/60cm = 450N.

Similarly, for the second wire, the tension would be (450N x 120cm = 54,000Ncm) divided by the distance from the wire to the centre of mass (120cm), resulting in a tension of 54,000Ncm/120cm = 450N.

I hope this helps you understand how to approach this problem. Remember to always consider all the factors and use the appropriate units in your calculations. If you are still having trouble, don't hesitate to ask for further clarification or assistance. Good luck!