2.4 Net Force

The exertion of a force does not always result in a change in motion. Take, for example, the case of a man pushing on a 2000 kg box. Although the man exerts a force on the box, it does not accelerate. Does this mean Newton’s second law is false? It does not. Thus far, we have dealt only with unbalanced forces, or forces which are not opposed by other forces. However, objects are often subjected to many forces. The previously mentioned box is experiencing the force of gravity, the normal force (to be discussed later), the man’s force, and the frictional force exerted by the surface on which it rests. Any acceleration that occurs will be the result of the combination of these four forces, not just the one exerted by the man.

Before we proceed, the normal force must be defined. In this case, normal means perpendicular. The normal force is a contact force that acts perpendicular to the surface of contact. Imagine a book resting on a table. Gravity exerts a downward force on the book, yet the book does not fall to the earth. Therefore, the gravitational force must be balanced by another force: the normal force exerted by the table.

Recognition of this normal force is generally not intuitive. The table seems to be a passive object, how can it exert a force? The force is a result of the table’s desire to keep its shape. As the book pushes down on the table, it acts against the bonds holding the table together. The table’s matter exerts a force that opposes the book’s gravitational force: a normal force, equal in magnitude to the gravitational force and in an upward direction.

Predicting the result of numerous forces is done by adding the forces together using vector addition and then calculating the acceleration that results from the net force, using the equation F = ma [Newton’s Second Law]. This method is illustrated by the following example:

A boy exerts a force of 7.0 N west on a 2.0 kg box that rests on the floor. The force is exerted parallel to the floor. The friction force opposing that exerted by the boy is 5.0 N. What is the resulting acceleration of the box?

Since the box is resting on the floor (i.e. not accelerating either upward or downward) the normal force exerted by the floor must balance the weight of the box. To first find the weight, we’ll use Equation 2.1:

Since the normal force balances the gravitational force, it must have the same magnitude, but an opposite direction. Thus, if the gravitational force is 20 N, the normal force is -20 N.

The net vertical force is 0 N

Thus the resultant (net) force is 2.0 N west. To find the acceleration of the box, we use equation 2.1: