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MindMap Gallery Force and motion (objects)
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Force and motion (objects)
This is a mind map about force and motion, which introduces gravity and interaction, elasticity, friction, synthesis and decomposition of force, equilibrium of common force points, Newton's first law, etc.
Edited at 2024-02-15 23:50:34
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Force and motion (objects)
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- Outline
force and motion
Gravity and interaction
gravity and center of gravity
The force exerted on an object due to the attraction of the Earth.
G=mg, which is usually taken as 9.8m/s², and is larger toward the poles, and smaller toward the equator.
Direction: vertically downward
Point of action: Because all parts of the object are affected by gravity, it can be considered that the point where the gravity effect is concentrated is the center of gravity of the object. The location of the center of gravity is related to the mass distribution and geometric shape of the object. The center of gravity is not necessarily on the object, but can be outside the object.
Forces and interactions
Forces are interactions between objects.
nature of force
Materiality: Force cannot exist apart from objects.
Reciprocity: The effects of forces are reciprocal.
Vectorality: The vector of a force has both magnitude and direction.
The unit of force: cow, represented by N.
Classification of forces
According to properties: can be divided into elasticity, gravity, friction, etc.
According to the effect: it can be divided into support, power, resistance, pressure, etc.
Effect: Deform the object and gain acceleration.
Three elements of force: magnitude, direction, and point of action
Determines the effect of force
Representation method of force: diagram of force, schematic diagram of force
Measuring Tool: Spring Dynamometer
interaction
Gravitational interactions exist between all objects. The force of gravity experienced by terrestrial objects is only one manifestation of gravity near the Earth's surface.
The interaction between charges and magnets is essentially different manifestations of electromagnetic interaction.
Strong interaction and weak interaction exist in the nucleus. When the distance between them increases, the intensity of both decreases rapidly. As long as the size of the nucleus, the strength of the strong interaction is 10¹² times that of the weak interaction.
Elasticity
Concept and conditions of production
Definition: An object that undergoes elastic deformation exerts a force on the object in contact with it because it wants to return to its original shape. This force is called elastic force.
Conditions for production: direct contact between objects and elastic deformation
The presence or absence of elasticity
Elastic force does not necessarily exist in contact. Elastic force only exists between two objects that are in contact with each other and undergo elastic deformation.
method
When the deformation effect is obvious, the presence or absence of elastic force can be directly judged from the deformation situation.
Assume there is elastic force between the interacting objects and see if the state of the object under study changes. If it changes, then there is; if it does not change, then there is nothing
Remove the object in contact with it and see if the state of the object under study changes. If it changes, then there is; if it does not change, then there is nothing
Several common elastic directions
The direction of the elastic force is opposite to the direction of deformation of the object. It acts on the object that forces the object to deform. The elastic force is a normal force and is perpendicular to the contact surface of the two objects.
The direction of the elastic force of a light rope or rubber strip on an object points along the rope in the direction of rope contraction, that is, it can only be a pulling force.
The direction of the elastic force at both ends of the spring coincides with the central axis of the spring and points in the direction of the spring returning to its original shape. It can be tension or pressure. The elastic force of the spring dynamometer can only be the tensile force
elasticity of contact surface
When a point contacts a surface, the direction of the elastic force or the contact point is perpendicular to the contact surface or the tangent direction of the contact surface, and points towards the force-bearing object.
When surfaces contact each other, the direction of the elastic force is perpendicular to the contact surface and directed toward the object receiving the force.
When the ball comes into contact with the surface, the direction of the elastic force is on the line connecting the contact point and the center of the ball, and points towards the object receiving the force.
When the ball is in contact with the ball, the direction of the elastic force is perpendicular to the cutting plane of the contact point, passing through the centers of the two balls and pointing towards the force-bearing object.
Light rods can be subjected to pressure, and they can be affected by pressure. They can be along or not along the rod. The direction depends on the meaning of the question.
Hooke's law and its applications
Within the elastic limit, the elastic force of a spring is proportional to its deformation (length of extension or shortening)
F=kx (K is the spring stiffness coefficient, x is the spring variable, f is the elastic force)
From the end point of the spring, compare the actual position with the end point position when the spring is at its original length, determine the deformation form and amount of the spring, and thereby determine the direction of the elastic force.
Features of light springs
The rope only produces tension. The tension of the tension rope is along the direction of the rope and points to the contraction direction of the rope. It cannot produce a supporting effect.
Negligible quality
law
The force on the light rope is equal everywhere, and the direction of the pulling force is along the rope
The light rope cannot be stretched
For systems connected by light ropes, the mechanical energy of the system will be lost when the light ropes collide or impact.
The elasticity of the light rope will change suddenly
light spring
Features: It can be compressed or stretched, and its elastic force is related to the amount of elongation or contraction of the spring.
law
The force on the light spring is equal everywhere, and its direction is opposite to the direction of elastic deformation.
The elastic force of the spring will not change suddenly
Series and parallel relationship
Series connection: When two identical springs are connected in series, the progress coefficient is only half of the progress coefficient of one spring. This is because the number of spring coils increases.
Parallel connection: If two identical springs are connected in parallel, their progress coefficient is twice that of one spring. This is because the spring wire becomes thicker.
Friction
Concept and conditions of production
When an object moves relatively or has a tendency to move relative to the surface of another object, the force that hinders the relative movement or the tendency of relative movement is called friction, which can be divided into static friction and sliding friction.
Generate conditions
Rough contact surface
There is elasticity between objects in contact with each other
There is relative movement or relative movement tendency between contact surfaces
The presence or absence of friction (method)
Conditional method: There is pressure between the contact surfaces, they are rough and have a tendency of relative movement.
"Oil coating method": Assume that a layer of ideal smooth oil is applied between the contact surfaces. If the motion state remains unchanged, there will be no friction. If the motion state changes, there will be friction, and the direction is opposite to the relative motion direction.
State method: the motion state of an object is related to the force on the object
Interaction method of forces: When it is difficult to determine the direction of the friction force on an object, it can be judged based on the friction force on another object that interacts with it. According to the characteristics of two equal and opposite forces,
Direction of Static Friction (Method)
Assumption method: Assume that the contact surface between two objects is smooth (The direction of static friction is opposite to the direction of relative motion of the object)
If two objects do not move relative to each other, it means that they have no tendency of relative motion and no static friction.
If two objects move relative to each other, it means that they originally had a relative movement tendency, and the direction of the original relative movement trend is the same as the direction of relative movement based on the assumption that the contact surface is smooth
Balance method: According to the conditions of the balance of two forces, the direction of static friction can be judged
Inverse deduction method: from studying the motion state and force conditions of an object, infer the conditions it must have
The magnitude of static friction (the strength of the relative motion trend)
The stronger the trend, the greater the friction, but it cannot exceed the maximum static friction.
It has no direct relationship with the mutual extrusion force f of the contact surfaces. The specific size can be determined by the motion state of the object combined with the dynamic laws.
The maximum static friction rate is greater than the sliding friction force
The effect of static friction is to hinder the relative movement trend of objects, but it does not necessarily hinder the movement of objects. It can be power or resistance.
sliding friction
The direction of sliding friction is always opposite to the object, and the direction of motion is opposite.
in conclusion
When two objects moving in the same direction are superposed together, the friction force on the fast-moving object is resistance, and the friction force on the slow-moving object is power.
When two objects are superimposed and moving toward each other, the friction force experienced by both objects is resistance.
calculate
Distinguish between static friction and sliding friction
Calculate using the definition: F=μFn
Calculate using equilibrium equations
Calculated using Newton’s second law (when in non-equilibrium state, dynamic equations can be used to calculate)
The size of the sliding friction force has nothing to do with the size of the contact surface, the speed and acceleration of the object's movement, and is only determined by the kinetic friction factor and positive pressure. The kinetic friction factor is related to the properties and roughness of the contact surface material.
sudden change in friction
Changes in the force or motion of an object (leading to sudden changes in the force and motion properties of the object)
Static friction is a passive force (its presence, magnitude, and direction depend on the tendency of relative motion between objects and the conditions of other forces)
Friction has a maximum value
The state of zero friction is the critical state of direction change
Static friction reaches its maximum value, which is the critical state where the object just remains relatively stationary.
Sliding friction exists between objects in relative motion (when two objects have the same speed, sliding friction may change suddenly)
Within the maximum static friction range of the friction force, if the two objects can be kept relatively stationary (the acceleration is equal), then the force will change to static friction or disappear, otherwise there will be no change.
Synthesis and decomposition of force
The synthesis of forces and the parallelogram rule
Resultant force: The effect produced by one force can be the same as the effect produced by several original forces acting together. Synthesis of forces: Find the resultant of several forces Resultant force and component force are an equivalent relationship.
parallelogram rule
subtopic
calculate
Pythagorean theorem
tan (angle)
subtopic
In a parallelogram, the component forces are certain. The greater the angle between the component forces, the smaller the resultant force.
The relationship between the change of the resultant force and the size of the component forces
When the angle between two force components is an acute angle, if one of the force components increases from zero, the resultant force increases
When the angle between two component forces is an obtuse angle, and one of the component forces increases from zero, the resultant force first decreases and then increases.
decompose, resolve
The object on the ground is subject to an oblique upward pulling force F. On the one hand, the pulling force F makes the object advance along the horizontal ground, and on the other hand, it lifts the object upward. Therefore, the pulling force F can be decomposed into a horizontal forward force F1 and a vertical upward force F2·F1= Fcosα, F2=Fsinα
When an object of mass m is stationary on an incline, its gravity produces two effects. One is the component force F1 that causes the object to slide down the incline. The other is the component force F2 that causes the object to press the incline. F2=mg•sinα, F2 =mg·cosα
A smooth ball with mass m is blocked by a vertical baffle. When it is stationary on the inclined surface, its gravity produces two effects: one is the component force F1 that presses the ball against the baffle, and the other is the force component F1 that causes the ball to press against the inclined surface. Force F2·F1=mg·tanα
orthogonal decomposition
Decompose the known force into two mutually perpendicular directions
Establish coordinate axes: Generally, the action point of the common point force is selected as the origin.
In statics, the principle is to have few decomposed forces and easy to decompose forces (as many forces as possible on the coordinate axis)
In dynamics, it is customary to use the acceleration direction and the vertical acceleration direction as the coordinate axes to establish a coordinate system.
An object is subjected to multiple forces. When finding the resultant force F, each force can be decomposed along the mutually perpendicular x-axis and y-axis.
optimal value problem
common force point balance
Equilibrium state and equilibrium conditions
Common-point force balance refers to several forces acting on the same point on an object or whose lines of action intersect at one point, keeping the object in uniform linear motion or in a stationary state.
Condition: F = 0
inference
Two-force balance: If an object is in equilibrium under the action of two common force points, the two forces must be equal in magnitude and opposite in direction.
Three-force equilibrium: If an object is in equilibrium under the action of three common-point forces, any one of the forces is equal in magnitude and opposite in direction to the resultant force of the other two forces, and the vectors of these three forces can form a closed vector triangle.
Multi-force equilibrium: If an object is in equilibrium under the action of multiple common-point forces, any one of the forces is equal in magnitude and opposite in direction to the resultant force of the other forces.
The number of forces on an object
Holistic approach first, then isolation approach
1. Field forces (gravity, electric field force, magnetic field force) 2. Contact force (elasticity, friction) 3. Other forces
method
Orthogonal decomposition method
Vector triangle method (similar triangles)
Multi-body balance, space balance
First integrate (known external forces) and then isolate (find internal forces)
First isolate (known internal forces) and then the whole (find external forces)
When the forces are not in the same plane but are balanced, the solid will be flattened
critical extreme value
Critical problem: the transition state when a certain physical phenomenon (or physical state) changes to another physical phenomenon (or another physical state)
hypothetical reasoning
extremum
maximum
minimum value
comprehensive
Limit analysis: pushing a certain physical quantity to an extreme
At the critical point, analyze and calculate using the method of equilibrium problem
Newton's first law
content and understanding
All objects always maintain a state of uniform linear motion or a state of rest unless a force acting on it forces it to change this state.
1. The state of motion of an object when no force is applied remains a state of uniform linear motion or a state of rest. 2. Force is not what maintains the motion of an object. The motion of an object does not require force to maintain it. 3. Force is the cause of changing the motion state of an object (the acceleration or force of an object whose motion state changes is the cause of acceleration of the object)
Point out that all objects have inertia (Newton’s first law is also called the law of inertia)
Understanding and applying inertia
The object has the ability to maintain uniform linear motion or rest.
Measurement: Mass (objects with large mass have large inertia, objects with small mass have small inertia)
The size of the object's inertia has nothing to do with position, force, motion state, etc.
Universality: Inertia is an inherent property of objects, and all objects have inertia
Newton's second law
Contents and basic calculations
The acceleration of an object is directly proportional to the force on it and inversely proportional to the mass of the object. The direction of acceleration is the same as the direction of the force.
nature
Causality: Force is what produces acceleration. If there is no force, there is no acceleration
Vectoriality: both force and acceleration are vectors. The direction of an object’s acceleration is determined by the direction of the net external force on the object (F=ma. The equal sign not only means that the values on the left and right sides are equal, but also means that the direction is consistent - the direction of the object’s acceleration is the same as the direction of the net external force on the object. same direction)
Instantaneousness: When the force on an object (with a constant mass) changes suddenly, the acceleration will also suddenly change at the same time; when the net external force is zero, the acceleration will be zero at the same time. The acceleration and the net external force maintain a one-to-one correspondence (instantaneous effect of force)
Relativity: There is a coordinate system in nature. In this coordinate system, when an object is not subject to force, it will maintain uniform linear motion or rest. Such a coordinate system is called an inertial reference system (the ground and the object are at rest relative to the ground). Or an object that moves in a straight line at a uniform speed can be regarded as an inertial reference system. Newton's law is only in the inertial reference system Sinoma City)
Independence: The acceleration generated by the forces on an object does not interfere with each other. The actual acceleration of the object is the vector sum of the acceleration generated by each force. The component relationship between the component force and the component acceleration in each direction also follows Niu Er.
Identity: a and F correspond to a certain state of the same object
image
F-t image
As shown in the figure, graph 1 shows that the force F does not change with the change of time: , that is, the force on the object is a constant force; graph 2 shows that the force F changes uniformly with the change of time: , that is, the force on the object is variable. Force and acceleration also change.
Above the time x-axis, the force F is positive, indicating that the direction of the force exerted on the object is positive; below the time: axis, the force F is negative. Indicates that the direction of the force on the object is the negative direction.
The intersection of two F-t graph lines indicates that the forces on the two objects are the same, and the slope of the graph indicates how quickly the force changes with time.
The area enclosed by the F-t graph and the time coordinate axis is equal to the impulse of force F within a period of time, that is, I = Fr. If force F is a constant force, then the area enclosed by the graph is S1 = I1 = Ft; if force F is a variable force. Using the microelement method, we can get S2=I2=ΣFntn. Therefore, regardless of whether the force on the object is a constant force or a variable force, the F-t image can be used to find the impulse.
After obtaining the impulse from the F-t image, we can use the definition of impulse to find the average force in this elbow section.
F-a image
Meaning: reflects the change of the object's acceleration with time.
If the image is parallel to the t-axis, it means that the object is moving in a straight line with uniform speed; if the image is a curve or an inclined straight line, it means that the object is moving with variable acceleration.
The image in the first quadrant indicates that the acceleration direction of the object is positive; the image in the fourth quadrant indicates that the acceleration direction of the object is negative.
The area enclosed by the image and the t-axis represents the change in the object's speed. The area in the first quadrant represents the increase in the object's speed in the positive direction, and the area in the fourth quadrant represents the increase in the object's speed in the negative direction.
Mechanical unit system
Base and derived units
warning
It is an international unit, not necessarily a basic unit (in the International System of Units, units other than the seven basic units are derived units)
The relationship between units of physical quantities may be derived through corresponding physical formulas, but not all units of physical quantities can be derived from each other.
nature
Isotropy: The direction of acceleration is the same as the direction of the external force acting on the object.
Vector properties (parallelogram rule, triangle rule, establishment of rectangular coordinate system)
Decomposition power
Decomposed acceleration
instantaneity
mutation problem
Thin wire and rod (contact surface): The amount of deformation is extremely small, deformation recovery does not take time, and the elastic force changes suddenly in an instant
Spring or rubber rope: The amount of deformation is extremely small, it takes time to recover from the deformation, and the elastic force does not change suddenly in an instant.
linear motion with variable acceleration
Raindrop falling model: resistance changes with speed, so acceleration changes with the resultant external force
Bungee jumping and trampoline models: The elastic force will change with the change of the deformation amount, and the deformation amount will change with the movement.
Locomotive starting process: During the constant power starting process, the locomotive traction force will decrease as the speed increases.
connectome problem
isolation method, holistic method
Holistic method: If the objects in the connected body have the same acceleration and there is no need to find the interaction force between the objects, they can be regarded as a whole and the total external force on the whole body can be analyzed.
Isolation method: If the acceleration of each object in the connected body is different, or if the force between objects in the system is required, the object needs to be isolated from the system.
Alternate application: If connected objects have the same acceleration and the force between the objects is required, you can first use the overall method to find the acceleration, and then use the isolation method to select the appropriate research object (first find the acceleration as a whole, and then find the isolation method internal force)
When the acceleration is different
Force characteristics of connectors
In any case, the tension in the rope is equal, and the elastic forces on both ends of the rope, rod and spring are also equal.
When two objects are connected by contact, the elastic forces exerted on each other by the contacting objects are equal and opposite in magnitude.
Movement characteristics (different acceleration)
Spring connection: During the deformation process of the spring, the velocity and acceleration of the connectors at both ends are not necessarily equal. When the spring deformation is maximum, the velocity of the connectors at both ends is equal, but the acceleration is still not necessarily equal.
Contact connection: When two stacked blocks are in contact and slide relative to each other, the acceleration may be different.
Basic application (the bridge between force and motion is acceleration)
Knowledge of strength and movement/Knowledge of movement and strength
Force analysis: It is required to draw the force diagram of the object in proportion
Motion analysis: determined based on the combined external force and initial velocity of the object
Analyze the force on the object and use Niu to find the acceleration According to the motion characteristics, use kinematic formulas to determine the motion of the object
multiple processes
It consists of multiple small processes. The final state of the previous process is the initial state of the next process. Analyze each process (acceleration may change, but speed remains unchanged)
Common models
Linear motion: linear motion on the horizontal plane, linear motion on the inclined plane, linear motion on the conveyor belt
Circular motion: circular motion of the rope model, circular motion of the circular motion rod model, circular motion of the arched bridge model
Flat throwing motion: flat throwing motion related to the inclined plane, flat throwing motion related to the circular orbit
Newton's third law
concepts and understanding
The interaction between objects is mutual. Among two objects, when one object exerts a force on the other object, the latter object must exert a force (reaction force) on the object at the same time. In other words, one object is exerting force. An object is also a force-receiving object (the interaction between two objects is called action force and reaction force)
Newton's third law: The action and reaction forces between two objects are always equal in magnitude, opposite in direction, and act on the same straight line.
Formula: F=-F'
Action and reaction forces and equilibrium forces
relation
Three characteristics: size, nature, changes
Three differences: direction, force-receiving object, and effect
Three irrelevances: object type, object motion state, and whether the object interacts with other objects
Compare
difference
Forced object
Action and reaction forces: Act on two interacting objects
Balanced force: acting on the same object
Dependencies
Action force and reaction force: appear at the same time, disappear at the same time, change at the same time, and cannot exist alone.
Balanced force: no dependence. If one force is withdrawn, the other force class will still exist, but the force on the object is no longer balanced.
nature of force
Action and reaction forces: must be the same
Balance: can be the same or different
Same point
Action and reaction forces: magnitude and direction
Balanced forces: equal in magnitude, opposite in direction, acting on the same straight line
Overweight and weightlessness
concept
Overweight: The pressure of an object on the support (the pulling force on the suspended object) is greater than the gravity of the object
Weightlessness: the phenomenon that the pressure of an object on the support (the pulling force on the suspended object) is less than the gravity of the object
Complete weightlessness
When the downward acceleration of the object is equal to g, the pressure of the object on the support (the pulling force on the suspended object) is equal to zero.
When there is complete weightlessness, all phenomena related to gravity disappear.
Note: When an object is in a state of complete weightlessness, there is no elastic force between it and other objects in contact. At this time, the object is only affected by gravity or gravity. The effect of gravity is completely used to change the motion state of the object without deforming the object, that is, the apparent weight of the object is zero
Actual weight: The actual gravity exerted by an object, that is, the true gravity Visual weight: the measured gravity, that is, the focus of the expression
Computing and Applications
overweight
The acceleration direction of an object is vertically upward
Movement status: accelerating up or decelerating down
Equation: F-mg=ma F=m(g a)
weightlessness
The acceleration direction of an object is vertically downward
Movement status: accelerating down or decelerating up
Equation: mg-F=ma F=mg-ma
Complete weightlessness
The acceleration direction of an object is vertically downward, and its magnitude is equal to the acceleration due to gravity g.
Decrease or decelerate to rise with a=g acceleration
Equation: mg-F=ma F=0
Comprehensive application of Newton's laws of motion
isochrones
law
(A) An object slides down from rest along all smooth chords located on the same vertical circle, and the time it takes to reach the lowest point of the circle is equal.
(B) The time it takes an object to travel from rest to every point on the circle along different smooth chords from the highest point of the same vertical circle is equal
condition
vertical circle
smooth
The starting point is the highest point or the end point is the lowest point
subtopic
The trajectory length is the chord length
Features
The time it takes for the block to move along the string is equal to the time it takes for the block to fall freely along the diameter.
The starting point and midpoint of the motion of an object that satisfies the isochronous law are on the same circle
Critical state (conditions that produce critical values and extreme values)
Conditions for separation of contacting objects: the elastic force of interaction is zero and the acceleration is equal
The critical condition for the rope to relax (break): the tension in the rope is zero (maximum)
The critical conditions for relative sliding between two objects: static friction reaches the maximum value and the acceleration is equal
The condition for maximum acceleration: maximum total external force
The conditions for the maximum value of the speed: when the acceleration is zero, the speed takes the maximum value (in most cases)
Application to plate problems
Features: Involves two objects, and there is relative sliding between the objects
Law analysis
Pay attention to the two displacement relationships: when the slider moves from one end of the skateboard to the other end If the slider and the skateboard move in the same direction, the difference in displacement is equal to the length of the board If the slider and the skateboard move in opposite directions, the sum of the displacements is equal to the length of the board
If the board length is L, the displacement of the slider is x1, and the displacement of the skateboard is x2 When moving in the same direction: L=x1-x2 During reverse movement: L=x1 x2
step
Draw a force diagram
Analyze the movement process (painting the initial and final movement states)
Grasp the plate connection (time, speed, displacement)
series of equations
conveyor belt
level
tilt
model synthesis
energy, momentum
Mechanics (F=ma)
Kinesiology