The method of considering the object of study as an isolated object and analyzing the characteristics of the external forces on it.External forces include initiative and restraint.It is also called drawing isolation diagram or drawing diagram, which is the basis of mechanical calculation.
Chinese name
force analysis
Foreign name
force analysis
Discipline
Mechanics and its branches
Properties
An Important Method for Analyzing the Motion State or Deformation State of Objects in Physics
(3) Electrostatic field force and Lorentz force[1]
Common constraint types
(1) Shelve constraints,binding forceAlong the normal of the contact surface
(2) Hinged base,binding forcePerpendicular to the axis of rotation, but the direction is undetermined, usually two mutuallyverticalThe component force that is perpendicular to the axis of rotation
(3) Spherical hinge seat, binding force across the spherical center, but the direction is uncertain, usually expressed by three mutually perpendicular components
(4) Roller base,binding forceThe contact surface perpendicular to the roller base
(5) For journal bearing and thrust bearing, the constraint force at the journal bearing is perpendicular to the shaft, but its direction is unknown, so it is represented by two components that are perpendicular to the shaft and perpendicular to each other. Thrust bearing is equal to journal bearing plus the constraint force. Three components can be drawn, one component along the shaft direction, and the other two components are perpendicular to each other and perpendicular to the shaft. For mechanical calculation of complex structures,Sometimes it is necessary to separate each component from the connection and draw the force diagram of each component separately. At this time, it must be noted that the force diagram must indicate the binding force at the connectionLaw of action and reaction.
brief introduction
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Force analysis is a method that regards the research object as an isolated object and analyzes the characteristics of the external forces it receives.External forces include main force and binding force (see constraints).The analysis of force characteristics is mainly to determine the action point and direction of these external forces.For example, gravity is the gravity of the earth on the object, which belongs to the external main force. The point of action is the center of gravity of the object, and the direction is plumb downward.The size of the restraint force is generally unknown (unless the force is measured by using the force reducer as the restraint body).The binding direction of some constraints can be determined.For example, the binding force of the rope is always pulling force, and the direction is along the rope when tensioning;The constraint force of the smooth surface is always pushing force, and the direction is along the normal of the surface.The restraint force along the rough contact surface is the friction force (see Friction).When the object will start to move, the friction reaches the maximum value.If the friction coefficient μ is known, the maximum static friction force FmThe numerical relationship with normal reaction N is Fm=μN。In the case of balance, the friction force F can be from 0 to FmThe magnitude of any value between shall be calculated according to the balance condition of the force.In addition, the binding force direction can also be determined by the structure of the hinge.For example, the constraint force of a cylindrical hinge can be represented by two forces on the plane perpendicular to the cylindrical axis;Another example is that the binding force direction of the movable support can be represented by a force N perpendicular to the bearing surface.
According to Newton's law of motion, whether an object is balanced is determined by external forces, and the acceleration of an object when it is unbalanced is also determined by external forces, both of which are independent of the internal forces interacting inside the object.Therefore, when solving mechanical problems, we often consciously select a part as the research object, treat it as an object, cut it from the constraints of the surrounding environment, and apply the corresponding external force.The object after the constraint is released is called the isolator.The drawing of the isolation body and all external forces it is subjected to is called the stress diagram.For example, the ladder AB with weight G is placed between the smooth vertical wall and the rough horizontal ground (Figure 1), the friction force between the ground and the ladder is F, and the horizontal rope is used to tighten the point D of the ladder and the point E of the wall.If the ladder is used as an insulator, its stress diagram is shown in Figure l.Where T is the tension of the rope;G is the gravity of the ladder;NA is the reaction force of the smooth wall;NB is the ground reaction force;F is the friction force.When the ladder is about to slide, F reaches the maximum friction μ NR, and F<μ NB.
Figure 1 Stress diagram of ladder leaning against smooth wall
Figure 1 Stress diagram of ladder leaning against smooth wall
If the force diagram of the whole object is not enough to solve the problem (the number of equations is less than the number of unknown forces), it can be divided into two isolators according to the characteristics of the internal structure of the object, and the interaction force at the separation meets the law of action and reaction.From the force diagram of these two isolators, the increased number of equations can be written to achieve the purpose of solving problems.
For example, the three hinged arch in Figure 2 has four support reactions XA, YA, XB and YB (Figure 3a) because two fixed hinge supports are used.The three equilibrium equations listed as a whole are not enough to solve the four unknowns.At this time, it can be disassembled into two parts from the middle hinge C, and two force diagrams can be drawn (Fig. 3b).At hinge C, X α and Y σ on the two graphs are equal in size and opposite in direction.In this way, the six unknown quantities XA, XB, XO, YA, YB, yC can be solved by the six equilibrium equations of the two isolators.If it cannot be solved by splitting it into two parts, it can be split into several parts.
Figure 2 Three hinged arch
Figure 2 Three hinged arch
Figure 3 Stress Diagram of Three hinged Arch
Figure 3 Stress Diagram of Three hinged Arch
To calculate the force on a component inside an object, it is necessary to disassemble the component.When calculating the internal force of truss member, the member can be cut off and attached with the force along the member.[2]
Problem solving method
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solutionDynamicsAn important part of the problem is the correct force analysis of objects.Since the interaction between objects is interactive, any mechanical problem cannot involve only one object, and the force cannot exist independently of the object.Therefore, when solving a problem, draw a sketch according to the requirements of the problem, and use“Isolation method”（Holistic approachIt is also the isolation method) for stress analysis.Since matter is divided into entity and field, the action mode of force can also be divided into two types. One is the effect of object on the research object, which is characterized by direct contact between the force applying object and the research object (such asfriction、air resistance、Elastic forceEtc.);The other is the effect of the object on the research object through the field it excites, which is characterized by that the object of the excitation field does not directly contact the research object (such as gravityElectrostatic forceEtc.).In mechanics, the force acting on the research object in the form of field is often gravity.From this, the rule of force analysis is drawn: when studying the forces on an object, except gravity, only look at the object that the object touches. Any object that contacts the research object may have a powerful effect on the research object.
onelevelA wooden block on thedesktopThe wood block is subjected to two forces.One is the gravity G, which is attracted by the earthVertical Down；The other is that the wooden block pressed on the desktop causes extremely small deformation of the desktopSupportabilityN，The direction is vertically upward.As shown in Figure 1-8, since the wood block is stationary, G and N are mutually balanced forces acting on the wood block. They are equal in size and opposite in direction.
Stress analysis can also be usedHypothesis。That is, if a force does not exist, look at themotion state Whether it has an impact.If there is no effect, the force does not exist.Principle: force is to change objectsmotion state Reason for.
Figure 1-9
staylevelThe wood block moving upward is not only affected by gravity G and support force N, but also affected bysliding friction Function of f.sliding friction Direction of f and wood blockDirection of movementcontrary.The force diagram of wood block is shown in Figure 1-9.Wood blockair resistanceDirection of and wood blockDirection of movementcontrary.The size of the air resistance is consistent with that of the objectMovement speed, and the size of the object's cross section.
Figure 1-10
If the horizontal rope is used to pull the wooden block forward, the wooden block is not only affected by gravity G, support force N and sliding friction force f, but also by the pull force F of the rope. The wooden block is subject to four forces in total, as shown in Figure 1-10.
Example 2: Objects moving on a slope
Figure 1-11
2. Objects moving on the slope: as shown in Figure 1-11, a wooden block slides along the slopeVertical DownThe gravity G.The wood blocks press the inclined plane, and the inclined plane is deformed to produce a supporting force N for the wood blocks, and the direction is perpendicular to the inclined plane and points to the supported wood blocks.The wood block is also affected byDirection of movementOn the contrary, upward along the slopesliding friction f。The component force of gravity along the slope causes the object to accelerate and slide along the slope, without a so-called "independent of gravity"“Gliding force”。
Example 3: A light rope passes throughFixed pulley
Figure 1-12
3. A light rope passes throughFixed pulley, use a horizontal force F to pull object A to move it to the right, B falls on Afriction coefficientIs μ 1, and the friction coefficient between A and the table top is μ 2. The force on A and B is analyzed without considering the air resistance.As shown in Figure 1-12.
First study object A.As shown in Figure 1-13.A is attracted by the earth (downward), and people, objects, ropes, tabletops, and air come into contact with A.Through analysis, it is found that the tension between people and A (to the right), B and APositive pressure(downward), the friction force B gives A (leftward), the pull force of the rope (leftward), the positive pressure of the table top on A (upward, also called the support force), and the friction force exerted by the table top on A (leftward).
Figure 1-13
Secondly, object B is taken as the research object.As shown in Figure 1-14.
Figure 1-14
B is gravitated by the earth (downward), and objects A, rope and air contact with B.The positive pressure of A against B (upward), the friction of A against B (rightward), and the tension of the rope (leftward).
N1 and N1 'are a pair of forces and reactions.While f1=μ 1N1, f2=μ 2N2.
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In teaching, it should be noted that although the pressure of the weight on the ground is numerically equal to the gravity of the object when the object is stationary on the horizontal ground, in some cases, the pressure is not equal to gravity.It is not necessary for two objects to contact to produce gravity effect, but pressure can only be produced when two objects contact.It should also be made clear that the pressure of the object on the slope is not equal to the gravity of the object.When the object on the inclined plane slides, the gravity G is decomposed into parallel along the inclined planeComponent forceF1 and the component force F2 perpendicular to the slope.F1 can be called sliding force, and F2 is called positive pressure.
General order
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Process Introduction
1. Definition of force analysis: find out all external forces on the specified object (research object) in a specific physical scenario and draw a force diagram, which is called force analysis.
(1) Select the research object: that is, determine the object for force analysis.The research object can be a single object or a system combination of objects.
(2) Isolation object analysis: isolate the research object from the surrounding objects, and then analyze the gravityelastic force, frictionElectric field force、Magnetic forceCheck which objects around exert force on it.
(3) Draw the force diagram: carry out force analysis according to a certain order. Generally, analyze gravity first;Then, circle around the object, find out the object in contact with the research object, and analyze the elastic force and friction force one by one;Finally, other field forces are analyzed.In the process of force analysis, it is necessary to draw stress diagram while analyzing (form a good habit of drawing stress diagram)Property force, do not drawEffect force。
(4) Check whether the force analysis is wrong: after the force analysis, check whether each force drawn can find its force application object, and check whether the analysis result can make the research object in the given positionmotion state Otherwise, force leakage, excessive force or wrong force will inevitably occur.
matters needing attention
① Only the force applied to the research object is analyzed, and the force applied to other objects is not analyzed.Remember not to mistake the force acting on other objects for "force transmission".
② Only forces named according to nature are analyzed, and forces named according to effect are not analyzed (sliding force, centripetal forceRestoring force）。
③ Every time a force is analyzed, the force applying object should be found to prevent the analysis of some non-existent force.
④Resultant forceAnd the component force cannot be regarded as the force on the object at the same time.
1. Specify the research object
Before carrying out force analysis, it is necessary to make clear the force objects.We always say“Isolation method”、“Holistic approach”It refers to whether the object under force is a single object or a whole composed of multiple objects.aboutConnectomeIn the process of force analysis, it is often necessary to change the research object several times before solving the problem.
Sometimes, it is difficult to find the force when the force bearing object is selected as the research object. At this time, the object can be transferred, the force applying object can be selected as the research object, and its reaction force can be calculated according toNewton's Third Law, find the force.
2. Analyze the stress orderly
Students should develop the habit of carrying out force analysis according to certain steps, so as to avoid missing or adding force.Generally, there are three steps: first, analyze gravity, then find out the object in contact with the research object, and analyzeContact force, such as elastic force, friction force, etc., and finally analyze electric field force, magnetic field force, etc.
There are three common methods to determine whether an object is subject to force:
After the stress analysis, we should carefully check to see whether each force drawn can find out the force applying object and whether they can find outReaction force, whether the research object can be in themotion state 。
Finally, it should be emphasized to the students that understanding the concept of force and mastering the characteristics of force are the basis and basis for correct analysis of force.If you want to master it skillfully, you need a certain amount of practice to constantly deepen your understanding of the laws of object movement, experience the methods repeatedly, and summarize skills.
