\(\def \u#1{\,\mathrm{#1}}\) \(\def \abs#1{\left|#1\right|}\) \(\def \ast{*}\) \(\def \deg{^{\circ}}\) \(\def \ten#1{\times 10^{#1}}\) \(\def \redcancel#1{{\color{red}\cancel{#1}}}\) \(\def \BLUE#1{{\color{blue} #1}}\) \(\def \RED#1{{\color{red} #1}}\) \(\def \PURPLE#1{{\color{purple} #1}}\) \(\def \th#1,#2{#1,\!#2}\) \(\def \lshift#1#2{\underset{\Leftarrow\atop{#2}}#1}}\) \(\def \rshift#1#2{\underset{\Rightarrow\atop{#2}}#1}}\) \(\def \dotspot{{\color{lightgray}{\circ}}}\)
Chapter 1: Equilibrium
9.

Adjustable vs Fixed Forces

Weight
\(W\)
N
The other special thing about gravity is that it is a fixed force: that is, the weight of an object does not change in order to balance the other forces acting on the object. Fixed forces typically have formulas which you can use to calculate them. For example, the weight of an object is given by
$W=mg$, where $g=9.8\u{N/kg}$

where \(m\) is the mass of the object (in kilograms) and \(g\) is a special constant which we'll talk more about later. Thus, a 1kg object has a weight of 9.8N, while a 100kg person weigns 980 newtons.

A bathroom scale
Bathroom scales don't actually measure weight directly; instead they measure normal force. As you push down on the scale, the scale provides a corresponding normal force upward to cancel out your push, and the display registers the size of that normal force.

The normal, tension, and static friction forces, on the other hand, are examples of adjustable forces. They do not have a specific formula; rather, they take whatever values they need to take in order to keep the system in equilibrium, if possible.

When you place an object on a table, for instance, the table exerts just enough normal force on the object to counteract that object's weight and keep it stationary. If you push down on the object, the table's normal force increases. If you lift upward on the object, the normal force decreases.