Today, I'm going to start reviewing the basic principles of knowledge Area 6 Statics. Here is the outline of the material covered in the reference handbook. But my outline will be slightly simpler and a little bit shorter. I'll cover all of these topics, but with the outline as shown here. So in this segment we'll start looking at some basic concepts, in particular the concepts listed here. And in this segment, we'll look at Newton's laws, and then forces, units and some ideas of vector quantities. Now statics is a physical science that deals with the effects of forces on objects. And in particular, here we'll look at static equilibrium. In other words, situations or systems where the forces and, and moments on the object or body are in balance. And in addition, there's no deformation of the object. We assume that they're all rigid bodies. The basic laws, of course, are Newton's Laws of Motion, of motion which I'll just summarize as for a particle in the absence of external forces, a particle has constant velocity. In other words, it remains at rest or travels in a straight line at constant speed. If a force acts on a particle, it accelerates in the direction of travel with an acceleration given by the well known equation, force is equal to mass times acceleration. And finally, and actually the only one that we'll be using in this class, action and reaction are equal and opposite. Now, a force can be thought of as the action of one body on another. And of course, force is a vector quantity so that it has magnitude and direction. And I'll talk a little but, bit more about that in a minute. A little bit about units. There are three main systems of units which derive from the equation F equals ma, but which we generalize by force is equal to some constant times mass times acceleration. And the different systems of units have a different value of that constant k. In metric units or SI units, k is equal to 1 and we define the unit of force as the Newton, which gives an acceleration of 1 meter per second squared to a mass of 1 kilogram. The second one, the US customary system, which is the one. Which is used in the, Fe exam, we set k equal to one over gc, where gc is the universal gravitational constant, which has the magnitude and units as shown there. So, in this system, we define the unit of force as the pound force. As that force, which gives an acceleration of 32.2 feet per second squared to a mass of 1 pound mass. Then finally, there's a third system, sometimes called the British Gravitational system, where k is also equal to 1. And here the unit of mass is the slug, and the unit of force is a pound. Is the force that gives an acceleration of one foot per second squared to a mass of 1 slug. So, the basic units and the three different systems are shown here. In SI units the unit of mass is kilogram and force is Newton. And USCS the unit of mass is the pound mass. And the unit of force is the pound force. The different systems tend to be used by different disciplines. Mechanical engineers, chemical engineers tend to use pounds mass and pound force. Whereas civil engineers and aerospace engineers tend to use the slug and pound system when working in British units. And the conversion is quite simple. We can just think of a slug as being approximately 32 pounds mass and a Newton is approximately a quarter of a pound. So, in terms of statics and forces and objects, the Newton and, and a pound are fairly small forces. So, typically we'll see the kiloNewton, which is thousand Newton, or kips, which stands for a thousand pounds, or a kilo pound, kilo pounds, or a thousand pounds, we'll see fairly often. Now, forces are vectors. In other words, they have magnitude and direction. Or, to be more specific about it. Vectors are characterized by the point of application which is a single point where a force is applied, which is an assumption. And that can be illustrated by this simple diagram here of a bracket attached with a, a pin to a cable. And it's also characterized by its magnitude. And it's line of action and direction. So, the line of action is a line in space which passes through the application of the, of the force and is in the same direction as the force. So, in this example, the point a here. Where the force passes through the pin is the point of application and the line of application of the force is a line which is parallel to that force in that direction. Vectors can be either free in other words, you can place them anywhere on the diagram, and we'll see that occur later when we talk about couples or it can be sliding. In other words the vector can slide along this line at different locations or it can be fixed. For example passing through the point a in this example. Now forces are, are can be either contact forces or body forces. A contact force, is where we have direct physical contact. And, we can also illustrate that by means of this sphere, sitting on, on a horizontal bed or on the ground. So the forces which are acting here, we have an upward reaction force here which I'll denote by r. And that force is a contact force. It arises as as a direct contact with the surface of the object. On the other hand, the body force acts through the whole volume here. And the most obvious example of a body force is gravity. Which acts throughout the, the whole volume. So the body force due to gravity is the weight of the object and usually we replace that by the weight of the object acting straight downwards through the center of gravity. Now forces in turn can be either concentrated or distributed. A concentrated force acts as a point and a distributed force is distributed over either a line, area, or volume. And this can be most easily illustrated in this way for example If I have a tire here sitting on the ground, the contact force we usually approximate as a single result in force R. But, in reality of force, of course, the bottom of the ti, the tire is squished out slightly. So in reality, the force is distributed over a small area at the bottom here. But, we approximate that as though it acts at a point. And this is true even for a rel, relatively rigid materials, for example, a stainless steel ball bearing sitting on top of a rigid surface. Even in that case, if we look at the area of contact there in greater detail, we'll see that the area is squished down slightly so that the force is distributed over a finite area, but usually we approximate this as though it's a concentrated force. Sometimes we do have a true distributed forces, for example, case a here, a force distributed over a line, such as a hanging cable, whose weight is distributed over the length of that cable. Or the second case here, case b, the force is distributed over an area. For example, the pressure force due to the hydrostatic pressure distribution of water being held back by a dam. Or finally, the last case where the force is distributed over a volume. For example, gravity force in the case of the sphere. For this cantilever device here. The other concepts which are very important in static is the idea of a rigid body. And a rigid body means that there's no change in relative distance between any two points in the body as we apply forces to it. In other words it doesn't deform it's truly rigid and the second concept which is very important is the idea of the a particle which is an approximation of a body as having mass but negligible dimensions, in other words shrunk to a point. Now, very often in statics we need to calculate the resultant force. And the resultant force is simply the sum of the forces which are acting on an object. For example, in this case here, where we have two forces which are acting F1 and F2. And in that case the result in false is simply the vector. Some of those two forces, F1 and F2, which is as shown here. Or we can get this result in false by adding the, the falses vectorially from head to tail we get the same result. The resulting force is the final force which closes the force polygon after we've added them all together. So the section, the relevant section from the reference manual is shown over on the right here. Some other concepts which will be important are the idea of concurrent forces. Concurrent forces just means that the lines of actions of all of the forces pass through a single point. And finally two force bodies two force bodies in static equilibrium have two applied forces. Which are equal in magnitude, opposite in direction, and colinear. In other words, they pass through a single line. And we'll encounter those later on when we start looking at trusses. So, this finishes some of the basic concepts of statics.
