5.1.3 Forces as Vectors

Combining Forces

When more than one force acts on an object, the resultant force (or net force) is the combined effect of all individual forces. Forces can be combined in the following ways:

• Same direction: Add the magnitudes of the forces.
  • Example: Two forces of 10 N and 5 N acting in the same direction give a resultant force of 15 N.
• Opposite direction: Subtract the smaller force from the larger force.
  • Example: A 10 N force and a 5 N force acting in opposite directions result in a 5 N resultant force, in the direction of the larger force.

Free-Body Diagrams

• A free-body diagram is a simple diagram used to show all the forces acting on an object. Each force is represented by an arrow pointing in the direction of the force. The length of each arrow corresponds to the force's magnitude.

Resolving Forces

• Resolving a force means splitting a force into two components that are perpendicular to each other (usually horizontal and vertical).
  • Example: A force of 100 N acts at 45°. It can be resolved into two components: one in the horizontal direction (100 cos 45°) and one in the vertical direction (100 sin 45°).

Equilibrium

An object is in equilibrium when:

• All the forces acting on it are balanced, and
• The resultant force is zero.
  • Example: If a book rests on a table, the force of gravity pulling the book down is balanced by the upward normal force from the table.

Parallelogram of Forces

• When two forces act at an angle to each other, their combined effect (the resultant force) can be found using the parallelogram of forces method.
  • The two forces are represented as adjacent sides of a parallelogram. The diagonal of the parallelogram gives the resultant force in both magnitude and direction.