This latter point needs to be expanded on. In order to accurately determine the forces acting on an object we must know how the object is moving relative to an inertial reference frame. Equations of motion have been developed which relate the forces acting on an object to its motion (in particular, the acceleration), as measured from an inertial reference frame.

If the sum of the forces acting on an object is zero, then that object has zero acceleration relative to an inertial reference frame. Conversely, if the sum of the forces acting on an object is not zero, then that object is accelerating relative to an inertial reference frame.

The reverse is also true. If an object has zero acceleration relative to an inertial reference frame, the sum of the forces acting on that object is zero. Conversely, if an object is accelerating relative to an inertial reference frame, the sum of the forces acting on that object is not zero.

The fundamental nature of forces is broken down in Newton's Laws.

The force or forces acting on an object is always due to: (1) Contact with another object, and/or (2) A body force acting on it, such as gravity, or a magnetic field.

Forces are always depicted as vectors acting at some location on an object, as shown below (for example). The forces are given as:

However, representing forces as vectors is merely a mathematical convenience for solving problems using the equations of motion.

But, forces don’t actually exist as vectors in real-world problems. To understand the reason for this we must look back at points (1) and (2), listed above.

When an object touches another object there is contact, not at an infinitely small point, but over an area of finite size. Thus, it is more suitable to speak in terms of a pressure that acts on the objects over the contact area. This pressure in turn, when multiplied by the contact area, gives the resultant force acting on each object. So, the force acting on an object (due to contact with another object) is actually a resultant force (based on pressure times area), which is commonly represented as a vector in the equations of motion. This is done for mathematical convenience.

For example, let’s say we have a man sitting on the edge of a crate. We represent his weight by a resultant force vector

In addition, there is also a resultant contact force acting on the bottom of the crate (and pushing upwards) due to contact with the floor. As explained before, this resultant force is the result of a pressure that acts over the area in contact with the floor. The bottom of the crate is the contact area with the floor. Let's look more closely at this pressure distribution.

The pressure distribution acting on the bottom of the crate might look something like this:

We can replace this pressure distribution with an equivalent resultant force (

To illustrate by way of example, let’s assume that the pressure distribution on the bottom of the crate only varies in the

Assume that the width of the crate into the page is

The resultant force

The distance

The resultant force

If we were to apply the equations of motion to the crate, the force

Coming back to point (2) from before, if a body force such as gravity is acting on an object, the body force “pulls” equally on all the mass elements in it. For the sake of mathematical convenience, the total gravity force pulling on the entire body is also represented as a single resultant force vector acting at a certain location inside the object (and pointing in the direction of gravity). The location of this resultant gravity force (

The magnitude of the vector

Knowing the magnitude and direction of vector

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