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# Chapter 1 : Introduction

1.1 Statics , what is it good for ?
1.2 Types of forces
1.3 Action and Re-action
1.4 Motion of a body due to forces
1.5 Graphical representation of forces

## 1.1 Statics , what is it good for ? NextSec

Let's say you as engineer are presented with all the design details of a certain structure and your task is to make sure that this structure
• does not break under influence of the design load ( that includes a certain safety factor ).
• no material is wasted
Here a structure can be just about anything of interest, the chair you are sitting on, a simple tower for a power line, a bridge over a river, or a climbing dome on a play ground.
Often a structure consists of many, sometimes thousands of members (parts) which are connected ( glued , welded, rivetted etc.) to each other. Each individual member is subject to break. So, how do you make sure that none does ?

Well, even if the design is already given to you this task can be difficult enough. It can be roughly broken down into two steps

• Determine the forces acting on each member (this is the EMch 11 stuff ).
• Determine whether the member under consideration can withstand the calculated forces with whatever safety margin is appropriate (this is EMch 213 stuff and things coming after that).
Here is a sample problem, take a peek. If this problem does not make much sense to you now you may want to read Chapter 1 in its entirety first and then come back to it.

## 1.2 Types of forces PrecSec   NextSec

A force is the action of one body onto another. We distinguish :
Contact or support forces
which occur whenever two bodies are in physical contact with each other. They always depend on the details of how the two bodies are connected to each other. You and the chair you are sitting on would be a nice example, your ear being attached to your head and not falling off would be another.
Field Forces
which may be due to gravity, electro-static,electro-magnetic or nuclear interactions. No physical contact between the involved bodies is necessary. Actually, the distance between two such bodies can be rather large in comparison to size of the bodies themselves (earth and moon for example).
Warning : Often there are forces of both types acting simultaneously between two bodies.
My example : Take a car sitting outside your house. The car is pulled towards the center of the earth by gravity (we call that force commonly "weight"). This force is constantly present even if the car drives over a hump at high speed and its wheels are not touching the ground momentarily. On the other hand (when the wheels are touching the ground) the earth's surface is pushing upwards onto the car at the points where the wheels touch the road surface. You can think of this force as a kind of resistance force the earth's surface is exerting onto the wheels, trying to prevent (resist) the wheels from penetrating the road surface. If the surface is made out of a soft material (like mud or sand) which has not much resistance the car's wheels will actually sink into the ground until enough resistance is encountered.

Discuss the problem of equating weight with the force of gravity in connection with the weightlessness of astronauts circling earth.

## 1.3 Action and Re-action PrecSec   NextSec

We just looked at what kind of forces are acting on a car sitting on the ground and argued that the earth exerts not only a gravitational pull onto the car but that the ground is pushing upwards against the wheels of the car.

But what does the car do to the earth ? Well, the contact force is easy, the car is pushing down onto the earth's surface and might even make a dent into it. Obviously, the force the car exerts onto the ground and the force from the ground onto the wheels are in opposite direction (one upwards one downwards in this example).

How about the gravitational force and with that all other field forces ? If I told you that the car is actually pulling the earth towards its own center of mass, you would probably ask me to prove that, wouldn't you ?

Well, let me ask YOU to make up a thought experiment which clearly shows that the gravitational forces between car and earth are oppositely directed. Here is my thought experiment. The fact that the gravitational force of earth onto moon and moon onto earth exist has some not so obvious but important consequences. One of them is that the center of masses of earth and moon actually revolve around and are always on exactly opposite sides of the combined center of mass. The result of that is that we observe two high tides per day at the sea shore.

ALL forces acting between any two bodies come in pairs and are exactly equal in value but exactly opposite in direction. This law is often called Newton's Third Law.

The interaction between different bodies is not always easy to see but is of utmost importance, so here is an example you definitely should have a look at.

## 1.4 Motion of a body due to forces PrecSec   NextSec

A force acting on a rigid body can in general cause the body to undergo two different types of motion.
• The body starts to accelerate
• The body will start to rotate
Whether the body actually moves/rotates depends on all the forces acting on the given body.
In statics we don't want any motion to happen and therefore :

#### Statics : Study of bodies in equilibrium

The demand that bodies neither translate ( = motion of its center of mass if you will) nor rotate ( = spinning around its center of mass ) will lead us to different types of equations relating the forces ( in magnitude and direction ) acting on a body to each other. Once we have enough equation we will solve for the unknown forces and we are done with the EMCH 211-step of a design process.

## 1.5 Graphical representation of forces PrecSec Figure 1.5a Graphical Representation of Forces

In Figure 1.5a we have three forces acting on the box-like body. Each force is represented by an arrow, pointing in the direction we think the force is acting and having a length proportional to the magnitude of the force.

Such a figure is called the Free Body Diagram (FBD) which will become the starting point for all our calculations.

There is a subtle but important difference between the value and the magnitude of a force. The magnitude (in Newtons or pounds) is always non-negative and identical to what you know from mathematics. The value ( in Newtons or pounds ) though can be negative as well as positive (and zero) . Why ? Well, in many case we know that a force is acting in vertical direction ( as an example ) but we don't know whether it is directed upwards or downwards until we actually have performed our calculations. But we can't perform our calculations until after we have drawn our FBD !!! The way out of this catch-22 situation is that we assume that it is acting upwards (for example) and draw our arrow correspondingly. If our calculations then give us a positive value for the force it is actually acting in the same direction as the drawn arrow, if its value comes out negative it is actually acting opposite to the drawn arrow.

Often the head or the tail of this arrow is placed at the point where the force is acting on the body. This point is then called the point of attachment.

Next to each arrow we have a symbol ( F1 etc. ) which we use later in equations or inside the text to indicate which of several forces we are talking about. The letters F and subscript 1,2 etc. are completely arbitrary although often used. Other letters which you find in textbooks to represent forces are P, Q, and R.

The arrow on top of each symbol is a reminder for us that a force is a quantity which has a value and direction. It is the same notation we use in vector algebra and vector calculus, because as we will shortly see, the physical quantity of a force is as far as mathematical properties are concerned equal to a vector.

NOTE : In Figure 1.5a we do not show the bodies which are exerting the shown forces F1 etc.

Well, maybe now you'd like to have another peek at the afore mentioned sample problem.

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Zig Herzog; hgnherzog@yahoo.com

Last revised: 09/14/13