Scalars, Vectors and Forces

Scalars and vectors — fill in the table

When adding vectors, direction matters — two 3 N forces can give 0 N (opposite) to 6 N (same direction). Free body diagrams show all forces acting on an object as arrows from the object: arrow length represents force magnitude, arrow direction shows force direction.

Resultant forces and equilibrium

• Resultant force: the single force that has the same effect as all forces acting together.
• Add forces in the same direction. Subtract opposing forces.
• If resultant = 0 → object in equilibrium (stationary or constant velocity).
• Scale drawing: draw forces tip-to-tail → resultant is the closing vector.
• Pythagoras: for two perpendicular forces. F_resultant = √(F1² + F2²).

Resolving forces (Higher)

• Any force can be split into horizontal and vertical components.
• Horizontal component: F_h = F cos θ.
• Vertical component: F_v = F sin θ.
• Useful for inclined planes: weight component along slope = mg sin θ.
• Weight component perpendicular to slope = mg cos θ.

Contact and non-contact forces — fill in the table

Forces always come in interaction pairs (Newton's 3rd law). Gravity is always attractive; electrostatic and magnetic forces can attract or repel.