Forces

A force is a push or pull that can change motion. More precisely, the sum of all forces acting on an object determines its acceleration:

Newt the physics frog will help us build the idea from the ground up: first with no forces at all, then with spring-like forces and weight, and finally with the everyday contact forces that show up in free-body diagrams.

If vector arrows or component addition feel rusty, start with the Vectors page first. Free-body diagrams depend on adding force vectors, not just listing force names.

Force-Free Motion

If no force acts on an object, its velocity does not need to be zero. Zero acceleration simply means the velocity remains as it was. A short push can change Newt’s velocity, but otherwise Newt moves at constant velocity until the next force is applied.

Springs

Springs are a clean place to start because their force depends on displacement. In the ideal model, the force points back toward the relaxed position:

The constant $k$, called the spring constant, measures the stiffness. A larger displacement or a stiffer spring produces a larger restoring force.

This spring picture will become our microscopic model for contact forces. Atoms in a solid do not pass freely through one another. Push them a little too close and electric interactions push back; pull neighboring bits slightly apart and they tug back together. For small distortions, that push or pull often behaves like a tiny spring.

Gravity

Gravity does not require contact. Near Earth’s surface, we usually model it as a steady downward force:

The magnitude of this force $mg$ is known as the weight of the object. In the following diagrams, the force of gravity is then drawn as a weight arrow.

Normal Force

The normal force is the contact force perpendicular to a surface. A table does not decide to push upward as a separate magic rule. Newt compresses the surface very slightly, and the surface’s microscopic spring-like structure pushes back.

On a flat surface with no vertical acceleration, the normal force usually balances weight:

On a ramp or in an accelerating system, the normal force may be smaller or larger than $mg$. What stays true is the direction: the normal force is perpendicular to the contact surface.

Tension

Tension can also be modeled as a spring-like contact force, but now the microscopic pieces are stretched instead of compressed. A rope can pull because neighboring bits of rope are tugged slightly apart, and those internal bonds pull back toward their relaxed spacing.

Newt has an unusually useful rope: his tongue.

A slack rope, string, cable, or tongue does not apply a tension force. Once it becomes taut, it can pull only along its own length. That is why tension arrows in free-body diagrams point away from the object along the rope.