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# Introduction to forces

Quantities can be categorised as either scalars or vectors. A scalar quantity is one that is described only by magnitude/size. A vector quantity is one that is described by both magnitude and direction. An example of this is distance, which is a scalar, and displacement, which is a vector. While distance gives the total ground covered regardless of direction, displacement is defined by the overall change in position from the original one. For example, if a car travels the route shown in the diagram, the distance it has covered is the sum of the values of the small sections it has travelled, whereas the displacement is the distance between the start and end position in the South direction. A force is a vector quantity; it is described in both magnitude and direction. Forces, and all other vector quantities, can be drawn as arrows, where the size of the arrow represents the magnitude of the vector and the direction the arrow is pointing in shows the direction of the vector.

A force is a push or pull acting on an object due to its interaction with another object. A force can be either a contact or a non-contact one, depending on whether the interacting objects are touching. It is a vector quantity and is measured in Newtons (N). Some examples of contact and non-contact forces can be found in the table.

A resultant force is the force obtained when two or more forces are acting on a body. To find the resultant force, the sum of forces acting along the same line can be taken, accounting for the direction. When forces are acting perpendicularly to each other, the Pythagoras' theorem can be used to find the resultant force. An object is balanced, ie. in equilibrium, when the resultant force acting on it is 0. A free-body force diagram is a diagram which shows the relative magnitude and direction of all the forces acting on an object. The object is drawn as a dot and all forces acting on it are drawn as arrows pointing away from it. Each force must be labelled with the name of the force.

Vectors, including forces, can be resolved into their horizontal and vertical components, usually given as Fₓ and Fᵧ, if their magnitude and direction are known using trigonometric functions. The resultant force between forces that are not acting on a straight line or at right angles can be found by resolving them into their horizontal and vertical components, and continuing as usual. To find the resultant force between two vectors, we can draw the two vectors one after the other, ie. the second starts where the first ends. The resultant force is the vector that joins the start and the finish points. Also, you can determine whether an object is in equilibrium, ie. stable, by drawing all the forces acting on it one after the other. If the last vector ends where the first started, then the object is in equilibrium.

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