¿SABES HALLAR LA TENSIÓN DE LA CUERDA Y LA FUERZA? Estática

In this lesson, we'll solve an interesting statics problem step by step. A body weighing 40 N is in equilibrium, suspended by an inclined rope, while a horizontal force F acts on the point where it is attached. Our goal is to calculate the tension in the rope and the force required to keep the system completely motionless. The rope is 150 cm long, and the horizontal distance between the wall and the point where it is attached is 90 cm. These measurements form a right triangle, which will allow us to determine the angle of inclination of the rope using trigonometry. We'll begin by applying Newton's first law: since the system is in static equilibrium, the sum of all the forces must be equal to zero. To work clearly, we'll study what happens on the horizontal and vertical axes separately. Next, we will decompose the tension T into its two components: Horizontal component: Tx = T cos θ Vertical component: Ty = T sin θ From the geometry of the problem, we obtain: cos θ = 90/150 = 3/5 Therefore, the angle of inclination of the rope is approximately 53.1°. The condition of vertical equilibrium allows us to calculate the tension in the rope. Since the vertical component of the tension must balance the weight of 40 N, we obtain: T = 50 N Finally, we apply the condition of horizontal equilibrium. The force F must be equal to the magnitude of the horizontal component of the tension: F = 30 N RESULTS Tension in the rope: 50 N; Required horizontal force: 30 N This problem combines some of the most important concepts in statics: Newton's first law, equilibrium of forces, vector decomposition, horizontal and vertical components, trigonometry in right triangles, and inverse trigonometric functions. ▶️ Complete statics playlist:    • PRIMERA LEY DE NEWTON. Estática   At the end, you can check each step and use this same procedure to solve other equilibrium problems with ropes, weights, and horizontal forces. CHAPTERS 00:00 Statics Problem Statement 00:51 System Equilibrium Condition 01:02 Strategy: Separating the X and Y Axes 01:29 Force Diagram 02:08 Equilibrium of Forces on the Horizontal Axis 02:49 Equilibrium of Forces on the Vertical Axis 04:06 Decomposing Tension into Components 05:06 Right Triangle Geometry 05:21 Calculating the Angle Using the Cosine Law 06:03 Arccosine and Angle of the Chord 07:10 Horizontal and Vertical Components of Tension 08:04 Calculating the Tension in the Chord 08:22 Calculating the Horizontal Force F 09:01 Final Results: F and Tension #statics #mathematics #mathematicswithjuan