Equilibrium of forces describes situations where an object stays at rest or moves with constant velocity because all forces balance. This idea is central to bridges, cranes, hanging signs, ladders, and many other structures that must remain stable. In physics, a suspended crate or sign held by cables is a common model because the tension forces and weight can be shown clearly with vectors.
Learning equilibrium helps students connect free-body diagrams to real engineering decisions.
Translational equilibrium uses the first condition of equilibrium, which says the vector sum of all external forces must be zero. Forces are often resolved into horizontal and vertical components so that separate equations can be written for each direction. For a static hanging object, the upward components of cable tensions usually balance the weight, while the horizontal components cancel each other.
Solving these problems requires careful diagrams, consistent signs, and trigonometry.
Key Facts
- First condition of equilibrium: ΣF = 0
- For two-dimensional equilibrium: ΣFx = 0 and ΣFy = 0
- Weight near Earth: W = mg
- Force components: Fx = F cos θ and Fy = F sin θ when θ is measured from the horizontal
- Tension acts along a rope or cable and pulls away from the object it is attached to
- In static equilibrium, acceleration is zero, so Newton's second law becomes ΣF = ma = 0
Vocabulary
- Translational equilibrium
- A state in which an object's center of mass has no acceleration because the net external force is zero.
- Net force
- The vector sum of all forces acting on an object.
- Tension
- A pulling force transmitted through a rope, cable, string, or chain.
- Free-body diagram
- A simplified drawing that shows one object and all external forces acting on it.
- Force component
- The part of a force that acts along a chosen axis, such as the horizontal or vertical direction.
Common Mistakes to Avoid
- Drawing cable tension straight upward, which is wrong because tension acts along the cable direction, not automatically along a vertical axis.
- Forgetting that horizontal components must cancel, which leaves an impossible sideways net force for an object at rest.
- Using sine and cosine with the wrong angle, which gives swapped components and incorrect tensions.
- Treating equilibrium as meaning no forces act, which is wrong because equilibrium means the forces add to zero, not that they are absent.
Practice Questions
- 1 A 20 kg sign hangs from two identical cables that each make a 30 degree angle above the horizontal. Find the tension in each cable using g = 9.8 m/s^2.
- 2 A 50 N lamp is held by two cables. The left cable makes a 60 degree angle above the horizontal and the right cable makes a 30 degree angle above the horizontal. Find the tension in each cable.
- 3 A crate is at rest while suspended by two cables at unequal angles. Explain why the cable closer to horizontal usually has greater tension, using horizontal and vertical force components.