Physical and chemical formula

V line ÷V object =P object ÷P liquid (F floating =G object)

V Lou ÷V Pai =P liquid -P substance ÷P substance.

V dew point ÷V object =P liquid -P object ÷P liquid.

When line V =V object, G÷F float =P object ÷P liquid.

Table of physical theorems, laws and formulas

First, the motion of the particle (1)- linear motion

1) moving in a straight line at a uniform speed

1. average speed Vping = s/t (definition)

2. Useful inference vt 2-VO 2 = 2as

3. Intermediate speed vt/2 = Vping = (vt+VO)/2.

4. Terminal speed vt = VO+at

5. Intermediate position speed vs/2 = [(VO 2+vt 2)/2] (1/2)

6. Displacement S = V level T = VOT+(at 2)/2 = vt/2t.

7. Acceleration A =(vt-Vo)/t {With Vo as the positive direction, A and Vo are in the same direction (accelerating) a>0; On the other hand, a < 0}

8. It is inferred from experiments that δs = at 2 {δs is the displacement difference of continuous adjacent equal time (t)}

9. Main physical quantity and unit: initial velocity (VO): m/s; Acceleration (a): m/s2; Terminal speed (vt): m/s; Time (t) seconds (s); Displacement (s): m; Distance: meters; Speed unit conversion:1m/s = 3.6km/h.

note:

(1) The average speed is a vector;

(2) When the speed of the object is high, the acceleration is not necessarily high;

(3)a=(Vt-Vo)/t is only a measure, not a judgment;

(4) Other related contents: particle, displacement and distance, reference system, time and moment [see Volume I P 19]/S-T diagram, V-T diagram/speed and speed, instantaneous speed [see Volume I P24].

2) Free falling body movement

1. Initial speed VO = 0

2. Final speed vt = gt

3. Falling height H = GT2/2 (calculated downward from Vo position)

4. Inference vt 2 = 2gh

note:

(1) Free falling body is a uniformly accelerated linear motion with zero initial velocity, which follows the law of uniformly variable linear motion.

(2) A = G = 9.8m/S2 ≈ 10m/S2 (the gravity acceleration near the equator is small, and the mountain is smaller than the flat, and the direction is vertical downward).

3) Vertical throwing movement

1. displacement s = VOT-(gt 2)/2

2. Final speed vt = vo-gt (g = 9.8m/s2 ≈10m/s2)

3. Useful inference VT2-VO2 =-2GS

4. Maximum rising height hmax = VO 2/2g (from the throwing point)

5. Round trip time t = 2vo/g (time from throwing back to original position)

note:

(1) whole process: it is a straight line motion with uniform deceleration, with positive upward direction and negative acceleration;

(2) subsection treatment: the upward movement is a straight line movement with uniform deceleration, and the downward movement is a free fall, which is symmetrical;

(3) The process of ascending and descending is symmetrical, for example, at the same point, the speed is equal and the direction is opposite.

Second, the motion of particles (2)-curve motion, gravity

1) flat throwing motion

1. Horizontal speed: VX = VO

2. Vertical speed: vy = gt

3. Horizontal displacement: x = VOT

4. Vertical displacement: y = gt 2/2

5. Exercise time t = (2 y/g) 1/2 (usually expressed as (2h/g) 1/2)

6. Closing speed vt = radical sign (VX 2+vy 2) = radical sign [VO 2+(gt) 2] (the angle between the closing speed direction and the horizontal plane is β: TG β = vy/VX = gt/v0).

7. Combined displacement: S = root sign (x 2+y 2) (included angle between displacement direction and horizontal plane α: tgα = y/x = gt/2vo)

8. Horizontal acceleration: ax = 0；; Vertical acceleration: ay = g

note:

(1) Flat throwing motion is a curvilinear motion with uniform change, and the acceleration is g, which can usually be regarded as the synthesis of uniform linear motion in horizontal direction and free falling motion in vertical direction;

(2) The movement time is determined by the falling height h(y) and has nothing to do with the horizontal throwing speed;

(3) The relationship between θ and β is TGβ= 2tgα；; ;

(4) The time t of flat throwing is the key to solving the problem; (5) An object moving along a curve must have acceleration. When the direction of velocity and the direction of resultant force (acceleration) are not in a straight line, the object moves in a curve.

2) Uniform circular motion

1. linear velocity v = s/t = 2π r/t.

2. Angular velocity ω = φ/t = 2π/t = 2π f

3. centripetal acceleration a = v2/r = ω 2r = (2π/t) 2r.

4. Centripetal force f = mv2/r = mω 2r = mr (2π/t) 2 = mω v = f.

5. Period and frequency: t = 1/f 6. Relationship between angular velocity and linear velocity: v = ω r.

7. The relationship between angular velocity and rotational speed ω = 2 π n (frequency and rotational speed have the same meaning here).

8. Main physical quantities and units: arc length (s): meter (m); Angle (φ): radian (rad); Frequency (f): Hertz; Period (t): seconds (s); Rotational speed (n): rpm; Radius (r): meter (m); Linear speed (v): m/s; Angular velocity (ω): radians per second; Centripetal acceleration: m/s2.

note:

(1) The centripetal force can be provided by a specific force, resultant force or component force, and the direction is always perpendicular to the speed direction and points to the center of the circle;

(2) The centripetal force of an object moving in a uniform circular motion is equal to the resultant force, and the centripetal force only changes the direction of the speed, not the size of the speed, so the kinetic energy of the object is unchanged, and the centripetal force does not do work, but the momentum is constantly changing.

3) Gravity

1. Kepler's third law: t2/r3 = k (= 4π 2/gm) {r: orbital radius, t: period, k: constant (independent of the mass of the planet, depending on the mass of the central celestial body)}.

2. Law of gravitation: f = g (m1m2)/r 2 (g = 6.67×10-1n? M2/kg2, the direction is on their connection)

3. Gravity and gravity acceleration on celestial bodies: GMM/R2 = mg; G = GM/R2 {R: celestial radius (m), m: celestial mass (kg)}

4. Orbital speed, angular velocity and period of the satellite: v = root sign (GM/r); ω = root sign (GM/R3); T = radical sign ((4 π 2r 3)/GM) {m: mass of central celestial body}

5. The first (second and third) cosmic velocity V 1 = (G and r)1/2 = (GM/r)1/2 = 7.9 km/s; V2 = 1 1.2km/s； V3 =16.7km/s

6. Geosynchronous satellite GMM/(R+H) 2 = M4 π 2 (R+H)/T2 {H ≈ 36,000 km, H: height from the earth's surface, R: radius of the earth}

note:

(1) The centripetal force required for celestial motion is provided by gravity, and the F direction = F million;

(2) The mass density of celestial bodies can be estimated by applying the law of universal gravitation.

(3) Geosynchronous satellites can only run over the equator, and the running period is the same as the earth's rotation period;

(4) When the orbit radius of the satellite decreases, the potential energy decreases, the kinetic energy increases, the speed increases and the period decreases.

(5) The maximum circling speed and minimum launching speed of the Earth satellite are 7.9 km/s. ..

III. Force (common force, composition and decomposition of force)

1) ordinary force

1. Gravity G = mg (vertical downward direction, G = 9.8m/S2 ≈ 10m/S2, the point of action is at the center of gravity, which is applicable to the vicinity of the earth's surface).

Hooke's law f = kx {direction is along the direction of recovery deformation, k: stiffness coefficient (N/m), x: deformation variable (m)}

3. Sliding friction force f =μFN {opposite to the relative motion direction of the object, μ: friction coefficient, FN: positive pressure (n)}

4. Static friction force 0≤f Static ≤fm (contrary to the relative motion trend of objects, fm is the maximum static friction force)

5. Gravity F = GM1m2/R2 (g = 6.67×10-11n? M2/kg2, the direction is on their connection)

6. Electrostatic force F = kq1Q2/R2 (k = 9.0×109N? M2/C2, the direction is on their connecting line)

7. electric field force f = eq (e: field strength N/C, q: electric quantity c, the electric field force applied to the positive charge is in the same direction as the field strength).

8. Ampere force f = bilsin θ (θ is the angle between b and l, when L⊥B: f = Bil, when B//L: f = 0).

9. Lorentz force f = qvbin θ (θ is the included angle between B and V, when V⊥B: f = qvb, when V//B: f = 0).

note:

(1) The stiffness coefficient k is determined by the spring itself;

(2) The friction coefficient μ has nothing to do with pressure and contact area, but is determined by the material characteristics and surface conditions of the contact surface.

(3)fm is slightly larger than μFN, which is generally considered as FM ≈ μ fn;

(4) Other related contents: static friction (magnitude and direction) [see P7]; In the first volume];

(5) Symbol and unit of physical quantity B: magnetic induction intensity (T), L: effective length (M), I: current intensity (A), V: charged particle velocity (m/s), Q: charged particle (charged body) electric quantity (C);

(6) The directions of Ampere force and Lorentz force are determined by the left-hand rule.

2) Composition and decomposition of force

1. The resultant force on the same straight line has the same direction: f = f 1+F2, and the opposite direction: f = f 1-F2 (f 1 > F2).

2. Composition of mutually angled forces:

When f = (f12+f22+2f1f2cos α)1/2 (cosine theorem) f1⊥ F2: f = (f12+f22)/kloc.

3. resultant force range: | f1-F2 |≤ f≤| f1+F2 |

4. Orthogonal decomposition of force: FX = FCOS β, FY = FSIN β (β is the included angle between the resultant force and the X axis TG β = FY/FX).

note:

The synthesis and decomposition of (1) force (vector) follow the parallelogram law;

(2) The relationship between resultant force and components is equivalent substitution, and resultant force can be used to replace the * * * interaction of components, and vice versa;

(3) In addition to the formula method, it can also be solved by drawing method. At this time, we must choose the scale and draw strictly;

(4) When the values of F 1 and F2 are constant, the greater the included angle (α angle) of F 1 and F2, the smaller the resultant force;

(5) The combination of forces on the same straight line can be taken along the positive direction of the straight line, and the direction of forces is represented by symbols, which is simplified as algebraic operation.

Four. Dynamics (motion and force)

1. Newton's first law (law of inertia): An object has inertia and always keeps moving in a straight line at a uniform speed or at rest until an external force forces it to change this state.

2. Newton's second law of motion: f = ma or a = f/ma (determined by external force and consistent with the direction of external force)

3. Newton's third law of motion: f =-F' (the negative sign indicates that the directions are opposite, and f and f' interact, and the balance force is different from the reaction force. Practical application: recoil movement).

4. The balance f of * * * point force is equal to 0, which summarizes the {orthogonal decomposition method and the intersection principle of three forces}.

5. Overweight: FN>g, weightlessness: fn

6. Applicable conditions of Newton's law of motion: it is suitable for solving low-speed motion problems, for macroscopic objects, for dealing with high-speed problems, and for microscopic particles [see Volume I P57].

Note: the equilibrium state means that the object is at rest or moving in a straight line at a uniform speed, or rotating at a uniform speed.

Verb (abbreviation of verb) vibration and wave (mechanical vibration and propagation of mechanical vibration)

1. Simple harmonic vibration f =-kx {f: restoring force, k: proportional coefficient, x: displacement, and the negative sign indicates that the direction of f is always opposite to x}

2. The period of a simple pendulum t = 2π (l/g) 1/2 {l: pendulum length (m), g: local gravity acceleration value, provided that the pendulum angle θ.

3. Vibration frequency characteristics: F = F driving force

4. Conditions for occurrence of * * * vibration: F driving force = F solid, A = Max * * * Prevention and application of vibration [see Volume I, P 175].

5. Mechanical waves, shear waves and longitudinal waves [see P2 Volume II]

6. Wave velocity v = s/t =λf =λ/t {In the process of wave propagation, one period propagates forward by one wavelength; The wave velocity is determined by the medium itself.

7. Sound wave velocity (in air) 0℃; 332 m/s; 20℃； 344 m/s; 30℃； 349 m/s; (Sound waves are longitudinal waves)

8. Conditions for obvious diffraction of waves (waves continue to propagate around obstacles or holes): the size of obstacles or holes is less than the wavelength, or there is little difference.

9. Interference conditions of waves: the two waves have the same frequency (constant phase difference, similar amplitude and the same vibration direction).

10. Doppler effect: Due to the mutual movement between the wave source and the observer, the transmitting frequency of the wave source is different from the receiving frequency (the receiving frequency increases when they are close to each other, and decreases when they are opposite [see Volume II P2 1]].

note:

(1) The natural frequency of an object has nothing to do with amplitude and driving force frequency, but depends on the vibration system itself;

(2) The strengthened area is the place where the peaks meet or the valleys meet, and the weakened area is the place where the peaks meet;

(3) The wave only propagates vibration, and the medium itself does not migrate with the wave, which is a way to transfer energy;

(4) Interference and diffraction are Porter's;

(5) Vibration image and fluctuation image;

(6) Other related contents: Ultrasonic wave and its application [see the second volume P62]/Energy transformation in vibration [see the second volume P63].

Impulse and momentum of intransitive verbs (the change of force and momentum of an object)

1. momentum: p = mv {p: momentum (kg/s), m: mass (kg), v: speed (m/s), which is in the same direction as speed}

3.Impulse: I = ft {I: Impulse (n？ S), f: constant force (n), t: action time of force (s), and the direction is determined by f}

4. Momentum theorem: I = Δ P or FT = MVT–MVO {Δ P: momentum change Δ δP = MVT-MVO, which is a vector type}

5. Law of conservation of momentum: p = p after the total or p'' can also be m1v1+m2v2 = m1v1'+m2v2'

6. Elastic collision: δ p = 0; Ek = 0 (i.e. conservation of momentum and kinetic energy of the system)

7. Inelastic collision δ p = 0; 0 & ltEK & ltδ EKm {δ ek: kinetic energy loss, EKm: maximum kinetic energy loss}

8. Completely inelastic collision δ p = 0; Δ δek =δekm {connected into a whole after contact}

9. The object m 1 collides with the stationary object m2 elastically at the initial velocity of v 1;

v 1′=(m 1-m2)v 1/(m 1+m2)v2′= 2m 1v 1/(m 1+m2)

10. Inferred from 9-the exchange speed (kinetic energy conservation, momentum conservation) between them in elastic collision of equal mass.

1 1. The mechanical energy loss when the horizontal velocity vo of the bullet M shoots at the long wooden block M resting on the horizontal smooth ground and is embedded in it to move together.

E loss = mvo2/2-(m+m) vt2/2 = fs relative to {vt:* * * * same speed, f: resistance, s relative to the displacement of the bullet relative to the long block}

note:

(1) frontal collision is also called centripetal collision, and the speed direction is on the line connecting their "centers";

(2) The above expressions are all vector operations except kinetic energy, which can be transformed into one-dimensional algebraic operations;

(3) Condition of momentum conservation of the system: If the resultant force is zero or the system is not subjected to external force, the momentum of the system is conserved (collision, explosion, recoil, etc. );

(4) The collision process (a system composed of colliding objects in a very short time) is regarded as momentum conservation, and momentum conservation occurs when the nucleus decays;

(5) The explosion process is regarded as momentum conservation, when chemical energy is converted into kinetic energy, and the kinetic energy is increased; (6) Other related contents: recoil movement, development of rocket and space technology, and space navigation [see Volume I, p 128].

Seven, work and energy (work is a measure of energy conversion)

1. work: w = fscos α (definition) {w: work (j), f: constant force (n), s: displacement (m), α: angle between f and s}

2. Gravity work: WAB = mghab {m: mass of the object, g = 9.8m/S2 ≈ 10m/S2, hab: height difference between A and B (hab = ha-HB)}

3. Work done by electric field force: WAB = QUAB {Q: electric quantity (C), UAB: potential difference between A and B (V), that is, UAB = φ A-φ B}

4. Electric power: w = UIT (universal) {U: voltage (V), I: current (A), T: power-on time (S)}

5. power: p = w/t (definition) {p: power [w], w: work done in time (j), t: time spent doing work (s)}

6. Automobile traction power: p = FvP level = Fv level {P: instantaneous power, P: average power}

7. The car starts at constant power and constant acceleration, and the maximum running speed of the car (VMAX = P /f)

8. Electric power: P = UI (universal) {U: circuit voltage (V), I: circuit current (A)}

9. Joule's Law: q = i2rt {q: electrothermal (j), i: current intensity (a), r: resistance value (Ω), t: electrifying time (s)}

10. I = u/r in pure resistance circuit; p = UI = U2/R = I2R； Q=W=UIt=U2t/R=I2Rt

1 1. kinetic energy: ek = mv2/2 {ek: kinetic energy (j), m: m/s)} object (kg), v: instantaneous velocity of object (m/s)}

12. gravitational potential energy: EP = mgh {EP: gravitational potential energy (j), g: gravitational acceleration, h: vertical height (m) (from zero potential energy surface)}

13. potential: ea = q φ a {ea: point a charged body potential (j), q: electric quantity (c), φ a: point a potential (v) (from zero potential plane)}

14. kinetic energy theorem (positive work is done on an object, and the kinetic energy of the object increases);

W = mvt2/2-mvo2/2 or w = δ ek.

{W = total work done by external force on an object, Δ ek: kinetic energy change Δ ek = (MVT2/2-MVO2/2)}

15. conservation law of mechanical energy: δe = 0 or EK 1+EP 1 = EK2+EP2, or mv12+mgh1= mv22/2+mgh2.

16. Variation of gravitational work and gravitational potential energy (gravitational work is equal to the negative value of the increment of gravitational potential energy of an object) WG =-δ EP.

note:

(1) power indicates how fast work is done, and how much work is done indicates how much energy is converted;

(2)O0≤α& lt； 90O do positive work; 90O & ltα≤ 180O does negative work; α = 90o does no work (when the direction of force is perpendicular to the direction of displacement (velocity), the force does no work);

(3) When gravity (elasticity, electric field force and molecular force) does positive work, the potential energy of gravity (elasticity, electricity and molecule) decreases.

(4) Gravity work and electric field force work are independent of the path (see Equations 2 and 3); (5) Condition of conservation of mechanical energy: Except gravity (elasticity), other forces do not do work, but only convert between kinetic energy and potential energy; (6) Conversion of energy in other units: 1kWh (degree) = =3.6× 106J,1ev =1.60×10-19j; *(7) Spring elastic potential energy E = kX2/2, which is related to stiffness coefficient and deformation.

Eight, molecular dynamics theory, law of conservation of energy

1.Avon gadro constant na = 6.02×1023/mol; The molecular diameter is in the order of 10- 10 meter.

2. Measurement of molecular diameter by oil film method d=V/s {V/s {V: single molecule oil film volume (m3), S: oil film surface area (m) 2}

3. Content of molecular dynamics theory: Matter is composed of a large number of molecules; A large number of molecules do random thermal motion; There are interactions between molecules.

4. Intermolecular attraction and repulsion (1) r

(2) r = r0, f citation = f repulsion, f molecular force = 0, and e molecular potential energy = =Emin (minimum value).

(3)r & gt； R0，f quote >； F repulsion and f molecular force represent gravity.

(4)r & gt； 10r0, f = F repulsion ≈0, f molecular force ≈0, e molecular potential energy ≈0.

5. The first law of thermodynamics w+q = Δ u {(work and heat transfer, two ways to change the internal energy of an object, the effect is equivalent),

W: the positive work done by the outside world on the object (J), Q: the heat absorbed by the object (J), and δ U: the increased internal energy (J), which involves that the perpetual motion machine of the first kind cannot be built (see Volume II P40).

6. The second law of thermodynamics

Kirkhner's statement: it is impossible to transfer heat from a low-temperature object to a high-temperature object without causing other changes (directionality of heat conduction);

Kelvin's statement: it is impossible to absorb heat from a single heat source and use it all to do work without causing other changes (directionality of mechanical energy and internal energy transformation) {it involves that the second type of perpetual motion machine cannot be built [see Volume II P44]}.

7. The third law of thermodynamics: thermodynamic zero cannot be reached (lower limit temperature of the universe: -273. 15 degrees Celsius (thermodynamic zero)).

note:

(1) Brownian particles are not molecules. The smaller the Brownian particle, the more obvious Brownian motion, and the higher the temperature, the more intense Brownian motion.

(2) Temperature is a sign of average kinetic energy of molecules;

3) The intermolecular attraction and repulsion exist at the same time, and decrease with the increase of intermolecular distance, but the repulsion decreases faster than the attraction;

(4) When the molecular force does positive work, the molecular potential energy decreases, and at r0, F attraction = F repulsion, and the molecular potential energy is the smallest;

(5) The gas expands, and the outside world does negative work on the gas W.

(6) The internal energy of an object refers to the sum of all kinetic energy of molecules and molecular potential energy of an object. For an ideal gas, the intermolecular force is zero and the molecular potential energy is zero;

(7)r0 is the distance between molecules at molecular equilibrium;

(8) Other related contents: energy transformation and invariance law [see p 4 1]/ energy development and utilization, environmental protection [see P47]/ internal energy, kinetic energy of molecules and molecular potential energy [see p 47].

Nine, the nature of gas

1. State parameters of gas:

Temperature: macroscopically, the degree of heat and cold of an object; Microscopically, it is a sign of the irregular motion intensity of molecules inside an object.

Relationship between thermodynamic temperature and celsius temperature: t = t+273 {t: thermodynamic temperature (k), t: celsius temperature (℃)}

Volume V: the space occupied by gas molecules, and the unit is1m3 =103l =106ml.

Pressure P: In unit area, a large number of gas molecules frequently hit the impactor wall, resulting in continuous and uniform pressure. The standard atmospheric pressure is1ATM =1.013x105pa = 76hg (1pa =1n/m2).

2. Characteristics of gas molecular movement: large intermolecular gap; Except the collision moment, the interaction force is weak; The molecular motion rate is very high.

3. Equation of state of ideal gas: p1v1/t1= p2v2/t2 {PV/t = constant, t is thermodynamic temperature}

Formula: F=PS S: stress area, the common part of two objects in contact; Unit: square meters.

1 standard atmospheric pressure = 76 cm mercury column height =1.01×105pa =10.336m water column height.

The vertical height from the liquid surface to a certain point of the liquid. ]

Formula: p = P=ρgh h: unit: meter; ρ: kg/m3; G=9.8 N/kg

2. Archimedes principle: An object immersed in a liquid is subjected to upward buoyancy, and the buoyancy is equal to the gravity when the object displaces the liquid.

That is, f float = G liquid discharge = ρ liquid gV discharge. (Line V represents the volume of liquid discharged by the object)

3. Buoyancy calculation formula: F float = G-T = ρ gV drainage = F up-down pressure difference.

4. When the object floats: F float = G object and ρ object.

When the object floats: f floats >; G and ρ < ρ liquid when the object sinks: ρ liquid when F floats.

1. Lever balance condition: f 1L 1 = f2l2. Force arm: the vertical distance from the fulcrum to the line of force action.

The purpose of keeping the lever in the water position by adjusting the nuts at both ends of the lever is to facilitate the direct measurement of the length of the power arm and the resistance arm.

Crown block: equivalent to an arm. It can't save energy, but it can change the direction of force.

Moving pulley: it is equivalent to a lever with twice the power arm as the resistance arm, which can save half of the force, but cannot change the direction of the force.

Work: two necessary factors: ① the force acting on the object; ② The passing distance of the object in the direction of force. W = W unit =FS Work: Joule.

3. Power: the work done by an object in unit time. A physical quantity indicating the speed at which an object does work, that is, an object with high power does work quickly.

W = unit W = Pt P:watt；; Unit of w: joule; Unit of t: seconds.

3. The imaging law of convex lens;

Properties of object distance U image distance V image Application of light path diagram

U & gt2f f<v & lt2f Inverted Micro Reality Camera

F<u & lt2f v & gt2f Inverted Amplification Real Slide Projector

U< magnifying glass

⒌ Convex lens imaging experiment: Put the candle, convex lens and light screen on the optical bench in turn, so that the centers of the candle flame, convex lens and light screen are at the same height.

Physics compulsory formula (in the field of curriculum reform)

Speed: v=s/t

Density: ρ = m/v

Gravity: G=mg

Pressure: p=F/s (liquid pressure formula is not directly tested)

Buoyancy: F float = G row = ρ liquid gV row

When floating and floating: f floating = G object.

Lever balance condition: F 1× L 1 = F2× L2.

Work: W=FS

Power: p = w/t = Fv

Mechanical efficiency: η = w useful /W total = GH/fs = g/fn (n is the number of pulley blocks)

Heat: q = cm △ t