Knowledge about the weakness of force

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The concept of force: People’s intuitive understanding of force originated from muscular activities such as pushing, pulling, lifting, and throwing. For example, when pushing a cart, the muscles in the arms become tense, giving a sense of effort; at the same time, it is possible to observe that the cart changes from rest to motion, its speed increases from slow to fast, or its direction of movement changes. Similarly, when pulling a spring with the hand, the muscles in the arm experience the same sensation, and one can also see the spring stretching and deforming. Further experimentation has shown that not only can humans exert such an effect on objects, but objects can also have this effect on one another. For example, hanging a weight on a spring will also cause the spring to stretch. By summarizing various examples of forces, it can be seen that the interaction between objects causes changes in their state of motion as well as deformation, with the degree of these effects depending on the strength of the interaction between the objects. To measure the effects produced by the interactions between such objects, people refer to these interactions as force. In essence: Force is manifested as the effect resulting from the interaction between objects. Therefore, cognitive ability, analytical ability, and research ability should all focus on the effects of force. Based on the effects of force, its effects can be divided into two types: the external effect of a force, which changes an object’s state of motion, and the internal effect of a force, which causes the object to deform. When a single force acts on an object, it causes both a change in the object’s state of motion and deformation of the object. When two or more forces act on the same object, it is possible that they do not change the object’s state of motion but only cause it to deform. When this occurs, we say that the object is in equilibrium, which indicates that the net effect of the several forces acting on it cancels each other out. When a force acts on an object, it always causes the object to deform. But under normal conditions, engineering components deform very little under the action of forces. Such minor deformation has a very small impact on the external effects of the force and can be ignored. In this way, when discussing the external effects of force, the actually deformed object can be regarded as a rigid body that does not deform. In this section, we focus on rigid bodies and discuss the external effects of forces. Two key points regarding the concept of force: 1. Force is an interaction between objects; without objects, force cannot exist. 2. Force is an interaction between objects, and it always appears in pairs between those objects. The way forces interact can be through direct contact, such as a person pushing a cart ； They can also attract or repel each other without direct contact, such as the Earth’s gravitational force on objects (i.e., gravity). Therefore, when analyzing forces, it is necessary to clarify which object is the subject of study, in order to analyze the effects of other objects on that object. The effect of a force on an object depends on three factors: (1) the magnitude of the force, (2) the direction of the force, and (3) the point where the force acts. If any one of these factors changes, the effect of the force will inevitably change as well. The magnitude of the force indicates the intensity of the mechanical interaction between objects. Forces can be divided into concentrated forces and distributed forces. According to the International System of Units, the unit of force is \"Newton\" (N) and \"kilonewton\" (kN) ； The unit of distributed force is \"newtons per square meter\" (N/m2), also known as pascals (Pa) and megapascals (MPa). MPa is equivalent to N/mm2. Representation of force: Force is a vector, which is indicated by bold letters or letters with a line above them, such as F or http://www.cngspw.com/Doc/data.WebNoteBooks/20060507140053/f.gif. In diagrams, forces are usually represented by arrowed lines. The length of the line segment indicates the magnitude of the force, while the direction indicated by the arrow shows the direction of the force. The starting or ending point of the line segment is placed at the point where the force acts. As shown in the figure below, there is the gravity P and the pulling force T acting on the cart. http://www.cngspw.com/Doc/data.WebNoteBooks/20060507140053/1-1.gif II. Basic properties of force The basic properties of force mainly include three: the law of action and reaction ； Law of two-force equilibrium ； Parallelogram law. 1. Law of Action and Reaction: The law of action and reaction reflects the objective laws governing the forces of interaction between two objects. The interaction between objects is mutual. Force is the mutual mechanical interaction between two objects. With respect to these two objects, the action force and the reaction force are always generated and disappear at the same time; once they arise, their magnitudes must be equal, their directions must be opposite, and their lines of action must be the same. This is the law of action and reaction. These two forces, which appear in pairs, act on two separate objects; therefore, their effects on each respective object cannot cancel each other out. As shown in the figure below, when lifting a heavy object, the force T exerted by the object on the steel wire rope and the reaction force T exerted by the rope on the object are generated simultaneously; they are equal in magnitude, opposite in direction, and act along the same straight line. 2. Law of equilibrium of two forces: The motion of any object is absolute, whereas rest is relative, temporary, and conditional. In mechanical analysis, a state in which an object is at rest or in uniform linear motion relative to the Earth’s surface is referred to as an equilibrium state. When an object is in equilibrium with only two external forces acting on it, these two forces must be equal in magnitude, opposite in direction, and act along the same line. This is the law of two-force equilibrium. Taking lifting a heavy object as an example again, the object A is subject to two forces: the downward gravitational force P and the upward pulling force T. These forces are in opposite directions but act along the same line, as shown in the figure on the left below. When an object comes to rest in mid-air or moves in a straight line at a constant speed, it is in equilibrium, that is, T = P. Note: When analyzing the forces acting on an object, it is important to correctly distinguish between two-force equilibrium and action-reaction forces. The former refers to the action of two forces on the same object ； The latter are two forces acting on two separate objects, and their effects cannot cancel each other out. 3. The parallelogram law of forces: The parallelogram law of forces is the fundamental rule that describes the combination and decomposition of forces acting on the same object. Therefore, we will discuss it in two parts: the combination of forces and the decomposition of forces. The combination of forces – Two forces acting on the same object can be combined into a resultant force. The magnitude and direction of this resultant force are determined by the diagonal of the parallelogram formed by using the magnitudes of these two forces as its sides; the line of action of the resultant force passes through the point of intersection. This rule is known as the parallelogram law of forces. A schematic diagram of the parallelogram rule for forces shows that the resultant force R of the two forces F1 and F2 acting on point A of an object is equal to their vector sum. The method of combining forces using the parallelogram rule is called vector addition, denoted as: R = F1 + F2 (1-1). It can be seen from the parallelogram rule for forces that, in general, the magnitude of the resultant force is not equal to the algebraic sum of the magnitudes of the two component forces. It can be greater than the component forces, or it can be less than them; sometimes the resultant force can also be zero. Watch the animated diagram. Several forces acting on the same object are called a force system. A force system in which the lines of action of all forces converge at a single point is called a concurrent force system. For finding the resultant force of a system of concurrent forces, the parallelogram rule still applies; by combining the forces in pairs sequentially, the final resultant force R can be determined. Now, assume that there are three forces, F1, F2, and F3, acting at point A of a certain object. First, the resultant force R1 of F1 and F2 can be determined, and then R1 can be combined with F3 to obtain the resultant force R, as shown in the figure on the right. 　　 For the combination of multiple forces, it is not very convenient to use vector addition and graphical methods to solve it. By applying the resolution method, that is, by using the projections of forces on the rectangular coordinate axes to convert vector operations into algebraic operations, it is possible to determine the resultant more conveniently. The following will provide an introduction with the help of diagrams. The right diagram shows that point A on the object is subjected to a force F, with oxy being an arbitrarily chosen rectangular coordinate system. Let the angle between the force F and the positive direction of the x-axis be a. As can be seen from the graph, the projections of the force F on the x-axis and y-axis are respectively http://www.cngspw.com/Doc/data.WebNoteBooks/20060507140053/1-7.gif and http://www.cngspw.com/Doc/data.WebNoteBooks/20060507140053/1-2.gif. (1-2) The projection of a force on a coordinate axis equals the magnitude of the force multiplied by the cosine of the acute angle between the force and that axis; if the direction of the projection is the same as the positive direction of the coordinate axis, the projection is positive ； The opposite is negative. The projection of a force is a scalar quantity. Obviously, when a=0° or 180°, the force F is parallel to the x-axis; therefore, the projection of force F on the x-axis, Fx, is equal to F or -F ； When a=90°, the force F is perpendicular to the x-axis, so Fx = 0. Let a point A on an object be subjected to two forces, F1 and F2, as shown in the figure below. To find its resultant force, one can first determine the projections of each individual force on a particular coordinate axis, and then add them algebraically; this will give the projection of the resultant force on that coordinate axis: http://www.cngspw.com/Doc/data.WebNoteBooks/20060507140053/1-3.gif 　　　　(1-3) http://www.cngspw.com/Doc/data.WebNoteBooks/20060507140053/1-8.gif Projection theorem for resultant forces: The projection of the resultant force on a particular coordinate axis is equal to the algebraic sum of the projections of all individual forces on that same coordinate axis. This still applies to the combination of multiple forces; with the projections of the resultant force on the coordinate axes, it is not difficult to determine the magnitude and direction of the resultant force. http://www.cngspw.com/Doc/data.WebNoteBooks/20060507140053/1-4.gif (1-4) Decomposition of force — Depending on the requirements of a given problem, a force can also be broken down into two component forces. The method of decomposition is still the application of the parallelogram rule of forces. For example, in the object placed on an inclined plane as shown in the figure below, its weight P can be broken down into a downward force Px that is parallel to the inclined plane, and a normal force Py that is perpendicular to the inclined plane. It is this downward force Px that causes the object to tend to slide downward.