Translational Equilibrium

Interesting Link (example problems):

Weight and Mass:

You probably already know this:

W = mg
Thus, to find the weight of an object, multiply its mass (in kg) by the gravitational acceleration (we'll use 9.80 m/s2). The resulting combination of units is called the newton (N). Naturally, if the object is not at sea level on the Earth's surface, or if it's on another planet, the gravitational acceleration (and hence the weight) is different.

Example 1: The weight of a 2 kg object (near the Earth's surface) is (2 kg)(9.8 m/s2) = 19.6 N.

Newton's First Law:

"A body at rest, or in uniform motion, will remain at rest or in uniform motion if no net force acts on the body."

In mathematical form the First Law is:

Remember that forces are vectors, so vector notation is essential here! It is often easier to work with the components of the forces, so that we can write (from this) the three scalar equations:

Please refer to this link for Example 2: Forces are Vectors!
And check out this link for Example 2a: Forces, Mass, Acceleration, and Velocity

Free Body Diagrams and Newton's Third Law:

Suppose a body weighing 15 N is at rest on a table. If there are no applied forces, the table exerts a force upward on the body equal to its weight. Since this force is perpendicular to the surface (the table), it is called the "normal" force (mathematicians use the word "normal" to mean "perpendicular".) Thus,

Figure 5.6b on page 115 shows this. The normal force and the weight are equal but oppositely directed. They act on the TV set. In Figure 5.6a two additional forces are shown that do not act on the TV set. n' is the force that the TV set exerts on the table (because of its weight), and w' is the force that the TV set exerts on the earth (at its center). The forces n and n' are an action-reaction pair; this is Newton's Third Law:

Because reactions do not act on the same body as the action forces, a free body (Fig. 5.6b) shows only the action forces. For examples of free body diagrams see Figure 5.7b on page 117 and Figure 5.10b & c on page 119. You should study Example 5.6 very carefully! (There are a number of other examples in Chapter 5 showing free body diagrams, but accelerations are involved and I want to avoid that topic for now.) Serway's "Problem-Solving Strategy" on page 118 is very useful; you should make sure that you follow every step, every time you do an equilibrium problem!

Examples:

Examples and problems are the best way to learn this, so let's take a look at a few!