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Statics is a branch of physics that deals with analyzing forces on objects at rest. When objects are in static equilibrium, the sum of forces and moments acting on them is zero. This means that nothing is moving. In the exercise, we deal with a rope keeping an object of weight 3160 N steady, illustrating static equilibrium.

In statics, we often work with diagrams to help visualize these forces and their effects. Free body diagrams are particularly useful. These diagrams show all the forces acting on an object, breaking them into their components.

For an object to remain at rest, the forces need to be balanced. In our problem, the tension in the rope balances the weight of the object. By calculating the tension, we ensure the rope can hold the object without collapsing.

Tension is the force conducted along a rope, string, or cable when it is pulled tight by forces acting from opposite ends. In our exercise, the tension in the rope is the force that counteracts the sag caused by the 3160 N weight.

To determine this tension, we consider both horizontal and vertical components of the force. The horizontal component, denoted as \( T_x \), equals half of the total tension in this symmetric setup, while the vertical component \( T_y \) deals with the weight's effect downwards.

Calculating tension involves understanding these components and their relationship with the forces acting on the rope. Trigonometry is often used to resolve these forces, as the tension force forms a diagonal in our right triangular setup.

Trigonometry helps us understand relationships within right-angled triangles, crucial in resolving forces in physics problems. In the exercise, trigonometry links the rope's tension with the geometry formed by the sag and horizontal distance.

We use trigonometric functions like sine, cosine, and tangent for this purpose. For instance, to find the angle \( \theta \) that the rope makes with the horizontal, the tangent function is used: \( \tan(\theta) = \frac{0.35}{1.72} \).\(\)
Once \( \theta \) is known, we can calculate the components of tension using \( T_x = T \cos(\theta) \) and \( T_y = T \sin(\theta) = 3160/2 \).

This understanding allows us to solve for the total tension considering both components, ensuring all forces are in equilibrium. Trigonometry not only bridges mathematical concepts to physics but also simplifies how these forces are analyzed.