MindMap Gallery force and motion
This is a mind map about force and motion. By studying this mind map, we can better understand the phenomena and laws in nature.
Edited at 2024-02-14 22:07:56This article discusses the Easter eggs and homages in Zootopia 2 that you may have discovered. The main content includes: character and archetype Easter eggs, cinematic universe crossover Easter eggs, animal ecology and behavior references, symbol and metaphor Easter eggs, social satire and brand allusions, and emotional storylines and sequel foreshadowing.
[Zootopia Character Relationship Chart] The idealistic rabbit police officer Judy and the cynical fox conman Nick form a charmingly contrasting duo, rising from street hustlers to become Zootopia police officers!
This is a mind map about Deep Analysis of Character Relationships in Zootopia 2, Main content: 1、 Multi-layer network of relationships: interweaving of main lines, branch lines, and hidden interactions, 2、 Motivation for Character Behavior: Active Promoter and Hidden Intendant, 3、 Key points of interaction: logic of conflict, collaboration, and covert support, 4、 Fun Easter eggs: metaphorical details hidden in interactions.
This article discusses the Easter eggs and homages in Zootopia 2 that you may have discovered. The main content includes: character and archetype Easter eggs, cinematic universe crossover Easter eggs, animal ecology and behavior references, symbol and metaphor Easter eggs, social satire and brand allusions, and emotional storylines and sequel foreshadowing.
[Zootopia Character Relationship Chart] The idealistic rabbit police officer Judy and the cynical fox conman Nick form a charmingly contrasting duo, rising from street hustlers to become Zootopia police officers!
This is a mind map about Deep Analysis of Character Relationships in Zootopia 2, Main content: 1、 Multi-layer network of relationships: interweaving of main lines, branch lines, and hidden interactions, 2、 Motivation for Character Behavior: Active Promoter and Hidden Intendant, 3、 Key points of interaction: logic of conflict, collaboration, and covert support, 4、 Fun Easter eggs: metaphorical details hidden in interactions.
force and motion
force
gravity
produce
The force on an object due to the attraction of the earth (Gravity is not the universal gravitation force, but a vertical downward component of the universal gravitation force)
size
G=mg
direction
always straight down
Elasticity
definition
When a deformed object returns to its original shape, it exerts a force on the object in contact with it.
Generate conditions
direct contact between objects
Elastic deformation occurs at the contact point
direction
Always opposite to the direction of deformation of the object exerting force
hooke's law
F=kx
k is called the stiffness coefficient of the spring The unit is Newton per meter The symbol is N/m The size of K is determined by the properties of the spring itself
X is the change in spring length, not the length of the spring after deformation
Friction
static friction
definition
friction between two relatively stationary objects
Generate conditions
Rough contact surface
There is pressure on the contact surface
There is a tendency for relative motion between two objects
direction
The direction opposite to the relative motion trend of the force-bearing object
sliding friction
definition
friction between two objects in relative motion
Generate conditions
Rough contact surface
There is pressure on the contact surface
There is relative motion between two objects
direction
Opposite to the direction of relative motion of the object under force
dynamic friction factor
definition
The ratio of friction to normal pressure when objects in contact move relative to each other
μ=Ff/FN
determining factors
Material and roughness of contact surfaces
Effect
Always hinders the relative movement trend between objects
Synthesis and decomposition of force
Resultant force and component force
definition
Assuming that the effect of several forces acting together is the same as the effect of a force acting alone, This force is called the resultant force of those forces, and those forces are called the components of this force.
relation
equivalent substitution
synthesis of force
parallelogram rule
Find the resultant force of two component forces that are at an angle to each other. If you make a parallelogram with the directed line segments representing these two forces as adjacent sides, The diagonal between these two adjacent sides represents the magnitude and direction of the resultant force.
triangle rule
Connect the two vectors head to tail in sequence, the starting point of the first vector The directed line segment to the end point of the second vector is the sum vector
decomposition of force
parallelogram rule
triangle rule
Effect decomposition method
Orthogonal decomposition method
A method of decomposing a known force into two mutually perpendicular directions
definition
Force is the effect of one object on another object
Effect
Deform an object or change its state of motion
nature
Force has the characteristics of materiality, mutuality, vectority, independence and other characteristics
force balance
An object is at rest or moving in a straight line at a constant speed
sports
Displacement and distance
Displacement
Represents the position change of the particle, which is from the out position to the end position. It is a directed line segment (displacement).
distance
The length of the object’s trajectory (scalar)
the difference
Displacement is a vector quantity, and distance is a scalar quantity. Only in one-way linear motion, the magnitude of displacement is equal to the distance.
speed
definition
The ratio of the displacement of an object to the time it takes for this displacement to occur , is a physical quantity that describes how quickly the position of an object changes.
direction
The average velocity direction is the same as the displacement direction, Instantaneous speed direction and direction of object motion
average rate
definition
The ratio of the distance an object travels within a certain period of time to the time it takes
is a scalar
average speed
definition
The ratio of the displacement completed by an object within a certain period of time to the time taken
is a vector Same as displacement direction
instantaneous speed
definition
The speed of an object at a certain moment or when it passes through a certain position
is a vector Same as the direction of motion of the object, Along the tangential direction of the motion trajectory
acceleration
definition
The ratio of the change in an object's speed to the time it takes for this change to occur , is a physical quantity that describes how fast an object’s speed changes.
direction
Consistent with the direction of velocity change, The direction of the speed change determines It has nothing to do with the direction of the initial and final velocities.
Laws of uniformly variable linear motion
Basic rules
v=v. at
x=v. t 1/2·at^2
v^2-v. ^2=2ax
Three corollaries
The displacement differences within consecutive equal adjacent time intervals T are equal, that is, x2-x1=x3-x2=…=xn-x(n-1)=aT^2
Average speed (time)
V=(v. v)·1/2
Displacement midpoint speed
V=root (v.^2 v^2)/2
Four Corollaries for Uniformly Accelerated Linear Motion with an Initial Velocity of Zero
The ratio of the instantaneous speed at the end of T, the end of 2T, the end of 3T...nT is v1:v2:v3:…:vn=1:2:3:…:n
Within the first T, within the first 2T, within the first 3T,…, the ratio of the displacements within the first nT is x1:x2:x3:…:xn=1^2:2^2:3^2:…:n^2
The ratio of the displacements in the first T, the second T, the third T,...the nth T is x1:x2:x3:...:xn=1:3:5:...:(2n- 1)
The ratio of the time taken to pass through consecutive equal displacements is t1:t2:t3:…:tn=1:root 2-1:root 3-root 2:…:root n-root (n-1)
circular motion
Angular velocity
v=2πr/t
Line speed
ω=2π/t
centripetal acceleration
(ω^2)r
cycle
T=2π/ω
centripetal force
Effect
Centripetal force produces centripetal acceleration, which only changes the direction of the speed but does not change the magnitude of the speed.
Fn=m(v^2)/r=mωv=m(ω^2)r=m4(π^2)r/(T^2)=4π^2mf^2r
direction
Always points to the center of the circle along the radius, changing all the time
Aerospace and celestial operations
Kepler's three laws
Kepler's first law
content
The orbits of all love stars relative to the sun are ellipses, and the sun is at an intersection of the ellipses.
Kepler's second law
content
For any planet, the line connecting it to the sun sweeps out equal areas in equal time.
Kepler's third law
content
The ratio of the cube of the semi-major axis of all planetary orbits to the square of its orbital period is equal.
formula
a^3/T^2=k,k is a fixed value
law of universal gravitation
content
Any two objects in nature attract each other, and the direction of gravity is on the line connecting them. The magnitude of the gravitational force is directly proportional to the product of the object's masses M1 and M2, and inversely proportional to the square of the distance r between them.
expression
F=G(m1m2)/r^2, G is the gravitational constant
First cosmic velocity
It is the minimum launch speed of artificial satellites and the maximum orbit speed, with a size of 7.9km/s.
second cosmic speed
The minimum speed to leave the earth’s orbit is 11.2km/s
third cosmic speed
The minimum speed away from the sun is 16.7km/s
GMm/r^2=ma=mv^2/r=mω^2·r=4π^2r/T^2
GM=gR^2
central body mass
M=4π^2r^3/GT^2=v^2r/G=v^3T/2πG
central body density
ρ=3πr^3/GT^2R^3=3g/4πGR
The further away, the slower
v=root under GM/r
ω=GM/r^3 under the root sign
T=root root 4π^2r^3/GM
a=GM/r^2
double star problem
T1=T2,ω1=ω2
m1/m2=r2/r1
T=Radix L^3/G(m1 m2)
m1 m2=4π^2L^3/T^2G
The relationship between motion and force
Newton's first law
content
All objects always maintain uniform linear motion or rest. Unless a force acting on it forces it to change this state
significance
Point out that force is not what maintains motion, It’s the reason that changes the state of motion of an object That is, force is the cause of acceleration
Pointed out that all objects have inertia, Therefore Newton's first law is also called the law of inertia
inertia
definition
An object has the property of maintaining its original state of uniform linear motion or resting state
measure
Mass is the only measure of the inertia of an object Objects with large mass have large visual properties. Objects with large mass have small inertia.
universality
Inertia is an inherent property of an object
Newton's second law
content
The acceleration of an object is proportional to the external force it experiences. Inversely proportional to the mass of the object, the direction of acceleration is the same as the direction of the external force
F=ma
Scope of application
Newton's second law only applies to inertial reference frames, That is, a reference frame that is at rest relative to the ground or moving in a straight line at a uniform speed.
Newton's second law only applies to macroscopic objects and low-speed motion
Overweight and weightlessness
overweight
definition
The phenomenon that the pressure of an object on a support or the pulling force on a suspended object is greater than the gravity on the object
Generate conditions
acceleration upward
weightlessness
definition
The pressure of an object on a support or the pulling force on a suspended object is less than the gravity of the object
Generate conditions
acceleration downward
Complete weightlessness
definition
The phenomenon that an object exerts no force on a support or suspended object at all
Generate conditions
The object has downward acceleration, and the acceleration is equal to the acceleration due to gravity g
Newton's third law
Action and reaction forces
content
The interaction between two objects is always reciprocal, One object exerts a force on another object, Another object also exerts a force on this object at the same time
Features
equal size
opposite direction
act on the same straight line
significance
Establish connections between interacting objects and The interdependence between action force and positive force