Lecture Notes: Concept of Tension

Introduction to Tension

• Tension: Force within or applied by a string or wire.
  • Usually involves lifting or pulling.
  • Example: A weight suspended from a wire.

Fundamental Concepts

• Force of Gravity: Pulls the weight downwards (100 Newtons in example).
• Net Force: Must be zero if an object is stationary.
  • No acceleration means forces are balanced.

Understanding Tension in a Simple System

• Example: A weight hanging from a ceiling by a wire.
  • Downward force (gravity) is countered by the tension in the wire.
  • Tension in the wire equals the force of gravity.
  • This balance keeps the weight stationary.

Tension in a Guitar String

• Higher tension in strings results in higher pitched notes.
  • Tension is important for the functionality of strings in instruments.

Practical Applications

• Tension is critical in determining the strength required for wires or strings in constructions like bridges or swings.

More Complex Example: Two Strings

• Scenario: A weight is held by two strings attached at different points.
  • T1 and T2: Two tensions in the strings.
  • The weight is stationary, implying net forces in both x and y directions are zero.

Analyzing the System

• Forces Involved:
  • T2 (Second Wire): Pulls only horizontally (left), no vertical component.
  • T1 (First Wire): Has both vertical and horizontal components.

Solving for Tensions

• Vertical Forces:

  • Only T1 has a vertical component (T1_y), countering gravity.
  • T1_y = T1 * sin(30 degrees) = 100 Newtons (force of gravity).
  • Solving for T1: T1 = 200 Newtons.

• Horizontal Forces:

  • T2 (horizontal tension) balances the horizontal component of T1.
  • T2 = T1_x = T1 * cos(30 degrees).
  • T2 = 200 Newtons * √3/2 = 100√3 Newtons.

Conclusion

• Tension in strings can be broken into components to understand equilibrium in complex systems.
• Ensuring correct tension is crucial for stability and functionality in practical applications.

Reminder

• Use of trigonometry: Sine and cosine functions help in breaking forces into components.
• Angles: Understanding angles and reference geometry is essential for solving tension problems.