# Module 4 -- Normal Force

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Contact forces are forces that we don't think much about because they seem so natural - if you bump into a wall, it will exert enough force on you to stop your motion toward the wall. This is because solid objects cannot pass through each other at normal speeds of encounter. Thus, each will modify the other's motion (yes, the wall will bend back a little). This fact implies that the objects interact. The resulting forces are called contact forces. The component of the contact force that prevents objects from passing through one another is called the normal force. The name normal force is meant to remind you that this component of the contact force is perpendicular (or normal) to the surface of contact. It is important to remember that both the objects in contact experience opposite normal forces as a result of Newton's Third Law.

#### Learning Goals

After completing this module, you should be able to:

• Describe the direction of the normal force acting on an object in contact with a surface.
• Use Newton's Second Law plus the constraint of equal accelerations perpendicular to the surface to solve for the normal force.
• Be able to draw normal forces on two touching objects that satisfy Newton's Third Law.

## Notation for Normal Forces

In this course, we will give normal forces a special symbol. Instead of writing F with two subscripts, we will generally write N with two subscripts. The subscripts will still indicate the target and the source of the force, respectively. We will discuss the reason for this special notation when we introduce the full form of the contact force.

## Normal Force as Constraint

The normal force is a constraint force, as is tension. It takes on whatever value is necessary to ensure that the objects in contact will not move into each other. This implies that the normal force constrains the motions of these objects so that they have the same velocity component perpendicular to the surface and will therefore remain in contact without getting closer or farther from each other. Thus when objects are in contact, the contact force will generate a force to cause the appropriate acceleration to change their velocities so they don't interpenetrate. Thus there is no "force law" for normal forces - the normal force must be found using Newton's second law and determining the acceleration of the objects from their (constrained) motion. To clarify this point, consider the following examples: