To find the normal force acting on an object, you need to consider the interaction between the object and its supporting surface. The normal force is the force exerted by a surface perpendicular to the surface. Here's how you can find the normal force:
Identify the object: Determine the object for which you want to find the normal force. For example, let's consider a book resting on a table.
Define the coordinate system: Establish a coordinate system that is convenient for your problem. Typically, you would choose one axis perpendicular to the surface, which is often the vertical axis, and another axis parallel to the surface.
Identify the forces: Identify all the forces acting on the object. In this case, the forces acting on the book are the force of gravity (mg) and the normal force (N) exerted by the table on the book.
Consider the equilibrium: If the object is at rest or in equilibrium, the sum of the forces acting on it must be zero. This applies to the components along each axis of your chosen coordinate system.
Determine the forces along each axis: Resolve the forces into their components along the chosen coordinate system. In the case of the book on the table, the weight (mg) has a downward component (mg) along the vertical axis, while the normal force (N) acts upward, perpendicular to the surface.
Apply Newton's second law: For equilibrium in the vertical direction, the sum of the forces in that direction must be zero. So, considering the vertical axis, you have:
ΣF_y = N - mg = 0
Solve this equation for N:
N = mg
Therefore, in this case, the magnitude of the normal force (N) is equal to the weight (mg) of the object.
Note: The normal force can vary in situations where the object is on an inclined plane or in the presence of other external forces. The above method is specific to finding the normal force when an object is resting on a horizontal surface.