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Tension in Physics Problems

Sep 22, 2025

Overview

This lecture covers methods for solving tension problems in physics, focusing on objects being lifted or in equilibrium, and how to break down forces for calculations.

Solving Tension with Acceleration

  • The tension force in a rope lifting an object equals mass times (gravity plus acceleration): ( T = m(g + a) ).
  • For a 50 kg box accelerated upward at 2.3 m/s²: ( T = 50 \times (9.8 + 2.3) = 605 ) N.
  • The weight force (( W )) is ( m \times g = 50 \times 9.8 = 490 ) N.
  • When descending with downward acceleration (-0.75 m/s²): ( T = 50 \times (9.8 - 0.75) = 452.5 ) N.
  • Tension is greater than weight when accelerating upward; less when accelerating downward.

Tension in Ropes at Angles (Equilibrium)

  • For a box at rest, the sum of forces in both x and y directions is zero (equilibrium condition).
  • Break each rope's tension into x and y components using trigonometry: ( T_x = T \cos \theta ), ( T_y = T \sin \theta ).
  • Set up equations:
    • ( T_{1x} = T_{2x} ), ( T_1 \cos 60° = T_2 \cos 30° ) leading to ( T_1 = 1.732 T_2 ).
    • ( mg = T_1 \sin 60° + T_2 \sin 30° ).
  • For a 60 kg box, solving yields ( T_2 = 294 ) N, ( T_1 = 509.2 ) N.
  • Components check: sum of x and y forces equals zero, confirming equilibrium.

Simpler 2-Rope Equilibrium Problem

  • For a 100 kg mass with two ropes (one at 60°):
    • Y-direction: ( mg = T_1 \sin 60° ) gives ( T_1 = 1132 ) N.
    • X-direction: ( T_2 = T_1 \cos 60° = 566 ) N.
  • Component check validates that all forces cancel, keeping the object at rest.

Key Terms & Definitions

  • Tension — Force transmitted through a rope, cable, or string by a pulling action.
  • Equilibrium — State where all forces on an object sum to zero; object is at rest or moves at constant velocity.
  • Free Body Diagram — A diagram showing all forces acting on an object.
  • Weight Force (( W )) — The force due to gravity: ( W = mg ).

Action Items / Next Steps

  • Practice drawing free body diagrams for tension problems.
  • Solve additional equilibrium problems using component methods.
  • Review trigonometric calculations for force components.

Full transcript