Tension between two rigid bodies

• Rikudo
In summary, the conversation discusses the calculation of tension (T) between two rods, A and B, connected at a fulcrum point. The initial calculation of T using forces and Newton's 2nd law results in T = 3m + (2m/3). However, when considering torque equilibrium and the non-zero size of the connection, the value of T changes to T = mg/2. The conversation highlights the importance of considering both forces and torques when analyzing interactions between rigid bodies.
Rikudo
Homework Statement
A balance consists of a straight light rod A, a right-angled light rod B rigidly welded with rod A and a fixed fulcrum F. Four loads are suspended from the balance with the help of light threads. The rods have equidistant marks on them. Find the mass of the load C.
Relevant Equations
Torque and Newton's 2nd law

Ok. So, I already worked on this problem, and get ##m_c## = 2m/3, which is correct according to the book.
However, I also want to know the value of the tension (T) between rod A and B.

Note: Before we start working on my modified question, I want to point out that the force exerted by the fulcrum is F = 5m + 2m/3 (I get this by using Newton law)

If we only look at the forces which is working on rod A, then with using the Newton 2nd law, we will get:
$$F = mg + mg + T$$
$$T = 3m + \frac{2m} {3}$$

Strangely, I gained a different result when I tried using torque equation for rod A, with point F as the origin. (Here, L is the length between two marks)
$$0 = -3mgL + 4mgL-2TL$$
$$T = mg/2$$

Not only that, changing the location of the origin also changed the value of the tension. What is happening here?

Delta2
These are rods, not ropes. The force between the rods is not the only interaction. In order for B to be in equilibrium, it must quite clearly also be affected by a net torque from A.

Sorry, but I don't understand what you mean. Could you please elaborate?

Delta2
You have treated the interaction between the rods as if they were characterised by a single force between them. This is not accurate. In addition to the net force between the rods, there is also a net torque. You can see this easily by considering the torque equilibrium of rod B around the connection point. B will not be in equilibrium unless there is a torque acting on it from A.

Ah. For B to be equilibrium, rod A also must exert a force to B in the left direction. Is this what I overlooked?

Rikudo said:
Ah. For B to be equilibrium, rod A also must exert a force to B in the left direction. Is this what I overlooked?
No. Torque. Not an additional net force.

But,Torque is created by exerting force

Delta2
Rikudo said:
But,Torque is created by exerting force
Yes, but if you idealise the connection with a point, then a force cannot create a torque around that point so you must also idealise the forces acting within the connection with a single force and a torque. In reality, the connection has a non-zero size. The torque is created by the force not being uniform across the connection. It will be more up on the side B extends to and is likely even pointing down on the other side. Summing up the forces acting across the connection gives you the idealised single force. Summing up the torques gives you the idealised torque.

Given any rigid body, the effect of any forces acting on it may be summarised as a total force and a total torque. The torque will generally depend on the point unless the force is zero.

You can act upon a body with forces and torques separately. You can create a torque without adding a resultant force by adding two forces equal in magnitude and opposite in direction that are offset by a distance. In your case, this all happens in the weld, which in reality has some finite size.

Delta2 and Rikudo
Rikudo said:
But,Torque is created by exerting force
Considering the direction of gravity action, force T does not have any lever respect to the point at which the right-angled light rod B is rigidly welded with rod A.
Therefore, exerting force T can’t create any torque at that welded joint.

Nevertheless, the masses hanging from rod B enjoy two levers to load that welded joint with the summation of two clockwise torques: 3mL and (2/3)m5L.

Therefore, that welded joint is simultaneously loaded with a vertical downwards force and a clockwise net torque.

Rikudo

1. What is tension between two rigid bodies?

Tension between two rigid bodies is a force that acts along the length of a rigid object, pulling the two ends of the object in opposite directions. It is caused by the internal forces within the object, which resist any changes in the object's shape or position.

2. How is tension calculated?

Tension is calculated by multiplying the mass of the object by its acceleration. This is known as Newton's second law of motion, which states that force is equal to mass times acceleration (F=ma).

3. What factors affect the tension between two rigid bodies?

The tension between two rigid bodies is affected by the mass and acceleration of the objects, as well as the angle at which the force is applied. The type of material and its elasticity can also affect the tension.

4. How does tension affect the motion of a rigid body?

Tension can either accelerate or decelerate the motion of a rigid body, depending on the direction of the force. If the force is in the same direction as the motion, it will accelerate the object. If the force is in the opposite direction, it will decelerate the object.

5. Can tension cause a rigid body to break?

Yes, excessive tension can cause a rigid body to break. This is because the internal forces within the object are unable to resist the external force, causing the object to deform or break. It is important to consider the maximum tension a material can withstand when designing structures or objects.

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