Equilibrium Physics Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

hard
A 50 N50 \text{ N} sign hangs from two cables, each making a 30°30° angle with the horizontal. What is the tension in each cable?

Solution

  1. 1
    By symmetry, both cables have the same tension TT.
  2. 2
    Vertical equilibrium: the vertical components of both tensions balance the weight: 2Tsin⁡30°=502T \sin 30° = 50
  3. 3
    Solve: 2T×0.5=50  ⟹  T=50 N2T \times 0.5 = 50 \implies T = 50 \text{ N}

Answer

T=50 NT = 50 \text{ N}
In equilibrium problems with angled supports, we resolve forces into components. Only the vertical components support the weight, while horizontal components cancel.

About Equilibrium

A state in which all forces acting on an object balance so that the net force equals zero and there is no acceleration.

Learn more about Equilibrium →

More Equilibrium Examples

Example 1 easy

A [formula] lamp hangs from a single vertical cord. What is the tension in the cord?

Example 3 medium

An object is in equilibrium under three forces: [formula] east, [formula] north. What is the magnitu

Example 4 easy

A [formula] sign is held at rest by two vertical supports. One support pulls upward with [formula].

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