Rope Equilibrium with Horizontal Force
Interactive Simulation of Rope Bending Under Force
Mass (m):
6 kg
Rope Length (L):
2 m
Horizontal Force (F):
50 N
Left Angle (θ₁):
0.0°
Right Angle (θ₂):
0.0°
Physics Explanation
This simulation demonstrates how a rope bends when a horizontal force is applied at its midpoint while supporting a mass.
Given parameters:
- Mass (m) = 6 kg
- Weight (W) = m × g = 6 × 10 = 60 N
- Rope length = 2 m
- Horizontal force (F) = 50 N (adjustable)
At equilibrium, the vector sum of all forces must be zero. The forces involved are:
- Tension in the left segment of the rope (T₁)
- Tension in the right segment of the rope (T₂)
- Weight of the mass (W = 60 N downward)
- Applied horizontal force (F)
ΣFₓ = 0 ⇒ T₂ sinθ₂ - T₁ sinθ₁ = F
ΣFᵧ = 0 ⇒ T₂ cosθ₂ + T₁ cosθ₁ = W
ΣFᵧ = 0 ⇒ T₂ cosθ₂ + T₁ cosθ₁ = W
The rope will bend at the point where force is applied, creating different angles on each side.
