First Law: Particles in Two-dimensional Equilibrium

An object is in two-dimensional equilibrium when forces acting on it in two directions are balanced.

Suppose a mass is suspended by two strings. The forces acting on the mass are its own weight acting downward, tension along the first string, and tension along the second string.

As the mass is in equilibrium, we consider magnitudes of horizontal and vertical components separately and add them to zero.

Now, consider two masses m₁ and m₂ at rest, connected by a light string going over a smooth, light pulley on an inclined surface.

Here, we consider both masses separately. The forces acting on m₁ are its weight, tension along the string, and the normal force due to the inclined surface. These force magnitudes should add up to zero and keep m₁ at rest.

The forces acting on m₂ are its weight acting downward and the string's tension acting upward. As m₂ is at rest, the net magnitude of force acting on it should be zero.