Equilibrium

The word equilibrium in Latin meant to "hold in equal balance" .  In Physics we use the word to mean balanced forces. There are two types of equilibrium:

• Static

• Dynamic

Static Equilibrium

The science of Statics studies how to keep bodies from moving when forces are applied to them.  Generally, we use this science to design and build structures like roads, bridges, buildings, etc.... so that they are stable even under structural stress (such as loads, weights, winds, storms, earth tremors..).

Newton's First Law is the starting point to explain the concept of statics.

Objects at rest will stay at rest.  Object in motion at constant speed will continue to move at constant speed unless acted upon by an external unbalanced force.

Therefore, if the condition of static equilibrium exists, all forces on an object must be balanced.

There are two conditions that have to be satisfied in order for static equilibrium to exist.

1. The vector sum of all the forces acting of an object in the x direction must be Zero
2. The vector sum of all the forces acting of an object in the y direction must be Zero

Mathematically speaking the above two conditions can be written as:

Example 1:

Examine the system shown in the diagram below and calculate the tension in both cables.

Solution:

i) Find the angles 

ii) Apply conditions for static equilibrium:

iii) Consider the vertical direction: 

Note that in the horizontal direction T_1x =  T_{2x .}  This does not give us any additional information about this system and can therefore be disregarded.

Example 2

Problem – Static Equilibrium

A 0.500 kg cake was left overnight on a kitchen counter.  The counter's surface has a coefficient of friction of 0.60.   Aware of the presence of mice in the house little Johnny sets up a trap. Using his Physics’ knowledge,  he attaches a string from the cake to the refrigerator’s handle and places some sticky paper on the floor below (as shown in the diagram). In the middle of the night, Pepi (a 150 g mouse) climbs the string.  Will Pepi get to eat the cake or will he fall to the floor onto the sticky paper where he will be trapped?  See the diagram below:

Click here to see the Solution  but only after you have tried this problem on your own.

More Problems and Solutions  in your Textbook:
Physics Book Two, Concepts and Connections,  Brian Heimbecker et Al, Irwin Publishing.
 

1. Section 3.3 1-6 p133-134

2. Section 3.4 1-3 p138

3. Section 3.5 1-6 p133-134

4. Section 3.5 1-4 p147-148
   To See the Solutions to some of the above problems, click here

Other Links:

• Lab on Inertial Mass and Gravitational Mass

• The beam Balance (Center of Mass)

• Center of Gravity