First Law: Particles in One-dimensional Equilibrium

Newton's first law states that an object at rest remains at rest unless acted upon by a net external force. This means a stationary object will not move or change its state of motion without an external cause. The law establishes that equilibrium occurs when the sum of all forces acting on an object equals zero, resulting in no acceleration.

A free-body diagram represents an object as a particle and shows all forces acting on it using arrows. In one-dimensional equilibrium, forces act only in one direction, making algebraic analysis straightforward. For example, a hanging mass experiences tension upward and weight downward; equilibrium requires these forces to be equal in magnitude but opposite in direction.

According to Newton's first law, constant velocity motion requires zero net force. The car's engine force balances the frictional force between tires and road plus air drag. A net force of zero means the car is not accelerating, even though it is moving. This equilibrium state maintains constant velocity without external disturbance.

Friction opposes motion and acts as a balancing force in equilibrium. On a rough surface, an object slides briefly before friction brings it to rest. On a smoother surface with less friction, the object slides farther. On a frictionless surface, an object would slide indefinitely at constant velocity, demonstrating that friction is necessary to create equilibrium through force balance.

To solve one-dimensional equilibrium problems, sketch the situation with arrows representing all forces, then apply Newton's first law algebraically. Since all forces are parallel in one dimension, they can be added as scalars. Set the sum of forces equal to zero and solve for unknown quantities. This systematic approach ensures accurate analysis of mechanical equilibrium states.

Both a parked car and a car moving at constant velocity have zero net force, achieving equilibrium. A parked car has all forces balanced with no motion. A moving car at constant velocity maintains its motion because driving force equals resistance forces. In both cases, Newton's first law applies: zero net force means no acceleration, whether the object is stationary or moving uniformly.

One-dimensional equilibrium involves forces acting parallel in a single direction, allowing algebraic force analysis. Two-dimensional equilibrium requires forces acting in multiple directions, necessitating vector analysis. In one dimension, a hanging mass has tension and weight balanced vertically. More complex systems require analyzing forces in multiple directions using first law particles in two dimensional equilibrium principles.