Why does ##Sigma T. x=0## hold for tension

Thread starter Kashmir
Start date Jun 15, 2023
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Equilibrium Physics Tension

In summary, Sigma T. x=0 represents the net force in the x-direction on an object in tension, ensuring that the object is in a state of equilibrium. It applies to real-life situations, such as when a rope is used to pull a heavy object, and can also hold for other types of forces. If Sigma T. x=0 is not satisfied, the object may move or accelerate in the x-direction. This equation is related to Newton's First Law, as it indicates that there is no net force acting on the object in the x-direction, allowing it to remain in equilibrium.

Jun 15, 2023

Kashmir

Homework Statement: Found it on internet, couldn't understand why it works

Relevant Equations: $Sigma T. x=0$

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Jun 15, 2023

haruspex

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Consider the work done on the (ideal) pulleys.

1. Why is ##Sigma T. x=0## true for tension?

The equation ##Sigma T. x=0## is a result of Newton's Third Law of Motion, which states that for every action, there is an equal and opposite reaction. In the case of tension, the force applied by one object (such as a rope or string) is countered by an equal and opposite force applied by the other object it is attached to. This results in a net force of 0 in the x-direction, hence the equation ##Sigma T. x=0##.

2. Can ##Sigma T. x=0## also apply to other types of forces?

Yes, the principle of ##Sigma T. x=0## can be applied to any type of force that acts in opposite directions. For example, if two objects are pushing against each other with equal force, the net force in the x-direction would also be 0.

3. How does the angle of the tension force affect ##Sigma T. x=0##?

The angle of the tension force has no effect on the equation ##Sigma T. x=0##. As long as the forces acting in the x-direction are equal and opposite, the net force will always be 0.

4. Is ##Sigma T. x=0## always true for tension?

In ideal situations, where there is no friction or external forces acting on the objects, then yes, ##Sigma T. x=0## will always hold for tension. However, in real-world scenarios, there may be other factors that can affect the net force in the x-direction.

5. How is ##Sigma T. x=0## related to the conservation of energy?

The equation ##Sigma T. x=0## is a manifestation of the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred or transformed. In the case of tension, the energy applied by one object is transferred to the other object, resulting in a net force of 0 in the x-direction.