Find TENSION in Two Uneven Strings Holding Up a Block | Statics For Physicists & Engineers

Static Equilibrium Problem Setup
📌 The problem involves solving for the tension in two uneven strings supporting a hanging block, a common scenario in physics and engineering.
⚖️ Equilibrium is achieved by applying Newton's Second Law to the system in both the x and y axes, where net force must equal zero ($\sum F_x = 0$ and $\sum F_y = 0$) since there is no acceleration.
📏 A complete free-body diagram is crucial, accounting for the two tension vectors ($T_1$ and $T_2$) and the force of gravity ($mg$) acting downward.
⬆️ The convention set is that up and to the right are positive directions for force components.

Force Component Resolution
🔍 Tension forces ($T_1$ and $T_2$) must be broken down into horizontal ($T_x$) and vertical ($T_y$) components using right-triangle trigonometry relating them back to $T_1$ and $T_2$.
⬅️ In the x-axis, the horizontal components must cancel out: $-T_{1x} + T_{2x} = 0$.
⬆️ In the y-axis, the upward components must balance the downward gravitational force: $T_{1y} + T_{2y} - mg = 0$.
🍎 The weight ($mg$) is specified as 9.8 Newtons in this example calculation.

Solving the System of Equations
🧮 Substituting the trigonometric expressions for the components results in two linear equations with two unknowns ($T_1$ and $T_2$).
➕ Once the two equations are derived from the x and y axis analysis, the physics problem is complete, leaving only the task of solving the system algebraically.
🧠 The mathematical outcome might show that one tension ($T_1$) is greater than the other ($T_2$), which is a direct consequence of satisfying the zero net force condition, not an intuitive guess.

Key Points & Insights
➡️ To solve for unknown tensions in a static system, resolve all forces into horizontal and vertical components.
➡️ The condition for static equilibrium requires that the sum of forces in both perpendicular axes must be zero.
➡️ Solving this type of problem culminates in a system of two equations and two unknowns derived from Newton's Second Law applied to the static state.

📸 Video summarized with SummaryTube.com on Jan 15, 2026, 16:38 UTC