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Tension Calculator

Enter the values to calculate the tension (force) in a rope, string, or similar object.

Object is Hanging:

Number of Objects:

Gravitational:

kg ▾

Object's Mass:

m/s² ▾

Weight α:

deg ▾

Weight β:

deg ▾

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Tension Calculator (Physics)

This calculator helps compute the tension (force) in a rope, cable, or string used to lift or pull objects. It supports calculations for:

Single or multiple ropes lifting objects
Ropes pulling objects across surfaces

What is Tension in Physics?

Tension is the pulling force transmitted along a rope, cable, or string. It acts opposite to compression and is experienced at both ends of the rope.

Finding Tension in Ropes Suspending an Object

1. Single Rope

For an object suspended by a single rope:

ΣF_y = 0 → T - W = 0 → T = W

W = Weight of the object
T = Tension in the rope

2. Two Ropes at Angles

When an object is suspended by two ropes at angles α and β:

Vertical components: T_1y = T₁·sin(α), T_2y = T₂·sin(β)
Horizontal components: T_1x = T_2x → T₁·cos(α) = T₂·cos(β)

Vertical equilibrium: W = T₁·sin(α) + T₂·sin(β)

Solving for T₂:

T₂ = W / [(cos(β)·sin(α)/cos(α)) + sin(β)]

Then, T₁ = T₂·cos(β)/cos(α)

Tension in Dynamic Equilibrium

When the object accelerates (a ≠ 0), tension varies:

Motion	Tension (T)
Moving upward with acceleration a	T = W + ma
Moving downward with acceleration a	T = W - ma
Stationary	T = W
Moving at uniform speed	T = W

Finding Tension While Pulling an Object

Determine acceleration using Newton’s 2nd Law: F = ma
Compute the net horizontal forces to find tension in the rope

Example Calculations

Example 1

A 10 kg mass is pulled along a frictionless surface at 35° angle. Find tension:

T = m·g·sin(θ) → T = 10 × 9.8 × sin(35°) ≈ 56.15 N

Example 2

A 30 kg tire is suspended by a string at rest:

W = m·g = 30 × 9.8 = 294 N

Since a = 0, T = W = 294 N

FAQ

Is tension a contact force?

Yes, tension arises from physical contact along the rope connecting the object and reference point.

Can tension be negative?

Tension is negative if it acts opposite to the motion’s direction.

Why is work done by tension zero?

Work: W = F × S. If displacement along the force is zero, W = 0.

How does gravity affect tension?

Gravity pulls downward; tension acts upward. If tension balances gravity, the object is stationary. Otherwise, it accelerates.

References

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