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An intuitive definition of force —that is, a push or a pull—is a good place to start. We know that a push or a pull has both magnitude and direction (therefore, it is a vector quantity), so we can define force as the push or pull on an object with a specific magnitude and direction.
The total force is equal to the magnitude of that vector. As a simple example, if you have $10N$ at $0^o$ and $10N$ at $45^o$ you get a resulting vector $\vec{F}$ whose components are $F_x = 17.07N$ and $F_y = 7.07N$. The Force is then $|\vec{F}| = 18.48N$.
When multiple forces act on an object, the forces combine. Adding together all of the forces acting on an object gives the total force, or net force. An external force is a force that acts on an object within the system from outside the system.
The goal of a force analysis is to determine the net force and the corresponding acceleration. The net force is the vector sum of all the forces. That is, the net force is the resultant of all the forces; it is the result of adding all the forces together as vectors.
The net force concept is critical to understanding the connection between the forces an object experiences and the subsequent motion it displays. In this Lesson, The Physics Classroom describes what the net force is and illustrates its meaning through numerous examples.
Newton’s second law of motion gives a relationship among acceleration, force, and mass. It can help us make predictions. Each of those physical quantities can be defined independently, so the second law tells us something basic and universal about nature. The next section introduces the third and final law of motion.
Since force is a vector, we can write Newton's second law as a → = Σ F → m . This shows that the direction of the total acceleration vector points in the same direction as the net force vector. In other words, if the net force Σ F points right, the acceleration a must point right.
