There are two main ways in which force is explained. One is that force is any relations that causes a change in motion or deformation of a body/object. The other one is that force is a push or a pull. This two explanations actually agree.
Force is a vector quantity since it has both magnitude and direction. Whenever a force is to be calculated, its direction and magnitude have to be considered. That is the reason as to why sometimes you will get the force to be negative after doing your calculations. Negative simply means it is in the opposite direction. It is also possible to have two forces acting on the same object, but acting at different angels.
The S.I. unit of force is newton denoted by a capital N. The symbol that is used and internationally recognised for representing force is F.
In order to keep track of the forces that are acting on a given system, a free-body diagram can be used. The free body diagram shows all the forces acting on the body while taking into consideration the direction of the forces. With a free-body diagram, it is easy to add the forces graphically in determining the net force acting on the object.
Since forces are vector quantities, they can be resolved into independent components that are at orthogonal (at right angles) to each other. Forces are mainly resolved into X components and Y components.
The X component is the one that lies on the X axis, while the Y component lies on the Y axis. For example if you have a force acting on a body at an angle of 300, this force can be resolved into two components; one acting along the X axis while the other acts along the Y axis. If the two components are added up vectorially they should result to the original force. The resolution of forces method is one that is often used at the Junior College level, and so it is also the recommended method to solve problems during our Physics tuition classes.
Equilibrium is a situation that occurs when the resultant force (algebraic sum of all the forces) acting on a particle is zero (0). Therefore for equilibrium to be attained all the forces must cancel out. It mainly happens when there are opposite forces that are equal. For example if there is a total of sum of 50 N acting downwards on a body, for there to be an equilibrium, there have to be a total sum of 50 N acting upwards on the same body.
The equilibrium can be static or dynamic.
Static equilibrium: This is evident in objects that are at rest since they have zero net (resultant) force acting on them.
Dynamic equilibrium: This occurs when there is an equilibrium of forces on a body that is motion. When there is such an equilibrium, there is no net force acting on the moving object and hence the body continues with the same constant speed.