§1.20. rectilinear motion with constant acceleration. Movement with constant acceleration
ABSTRACT
Physics lectures
MECHANICS
Kinematics
Kinematics is the branch of mechanics that studies mechanical motion without analyzing the causes of its causes.
mechanical movement- simplest form movement of bodies, which consists in changing over time the position of some bodies relative to others, or the position of body parts relative to each other. In this case, the bodies interact according to the laws of mechanics.
Basic concepts:
Material point- a body, the size and shape of which can be neglected.
Reference body– the body relative to which the motion of the investigated body (other bodies) is considered.
reference system- a set of a reference body, a coordinate system associated with it, and clocks that are fixed relative to the reference body.
Radius-Vect op is a vector connecting the origin of coordinates with the location of the body at a given time.
Trajectory- the line that describes the body ( center of gravity) in the course of its movement,
Path – scalar a physical quantity equal to the length of the trajectory described by the body over the considered time interval. ( , m)
Speed is a vector physical quantity that characterizes the speed of the particle moving along the trajectory, and the direction in which the particle moves at each moment of time, i.e. position changes with time (υ, m/s).
Acceleration – vector physical quantity, equal to the ratio body speed increment some period of time to the value of this gap, i.e. speed (speed) of change in speed ( A, m/s 2).
The acceleration vector can change by changing its direction, magnitude, or both. If the speed decreases, then the term "deceleration" is used.
Point speed
Types of movements:
Uniform movement –
the movement of a body in which it travels the same paths in any equal intervals of time.
1 - The coordinate of the point at the moment of time t.
2 - Point coordinate at the initial moment of time t= 0
3 - Projection of the velocity vector on the coordinate axis
Movement with constant acceleration
a= = S = υ 0 t ± υ = υ 0 ± a t
Uniform circular motion
Dynamics
Dynamics the branch of mechanics that studies the causes occurrence mechanical movement.
Weight- a scalar physical quantity, which is a quantitative measure of the inertia of the body, and also characterizes the amount of substance (m, kg),
Force- a vector physical quantity, which is a measure of the interaction of bodies and leads to the appearance of an acceleration in the body or to deformation of the body. Force is characterized by magnitude, direction and application point (F, N).
FORCE
Newton's laws:
Newton's first law:
V inertial systems reference, the closed system continues to remain in a state of rest or rectilinear uniform motion.
Classical Newtonian mechanics is applicable in a special class inertial frames of reference.
All inertial frames of reference move relative to each other in a straight line and uniformly.
Newton's second law:
the force acting on the system from the outside leads to the acceleration of the system.
Newton's third law:
the force of action is equal in absolute value and opposite in direction to the force of reaction; forces are of the same nature, but applied to different bodies and are not compensated.
Gravitational force
Forces in nature:
Law of conservation of momentum
Impulse is a vector physical quantity, equal to the product body mass to its speed:
Law of conservation of momentum:
Law of energy conservation
Energy- a characteristic of the movement and interaction of bodies, their ability to make changes in the outside world (E, J).
The total mechanical energy is understood as the sum of kinetic and potential energies:
Total mechanical energy
Potential energy
Kinetic energy
Potential energy of the body- a scalar physical quantity characterizing the ability of a body (or material point) to perform work due to its being in the field of action of forces.
Kinetic energy of the body- energy mechanical system, depending on the velocities of its points.
The law of conservation of mechanical energy:
Absolute temperature scale
English introduced. physicist W. Kelvin
- no negative temperatures
Absolute temperature unit in SI: [T] = 1K (Kelvin)
The zero temperature of the absolute scale is absolute zero (0K = -273 C), the most low temperature in nature. At present, the lowest temperature has been reached - 0.0001K.
1K is equal to 1 degree Celsius.
Relationship of the absolute scale with the Celsius scale: in the formulas, the absolute temperature is denoted by the letter "T", and the temperature on the Celsius scale by the letter "t".
Basic equation of MKT gas
The basic equation of the MKT relates the microparameters of particles (the mass of the molecule, the average kinetic energy of the molecules, the average square of the velocity of the molecules) with the macroparameters of the gas (p - pressure, V - volume, T - temperature).
average kinetic energy of the translational motion of molecules root-mean-square velocity
average kinetic energy of the translational motion of molecules
Root mean square speed: =
Internal energy of a monatomic ideal gas: U = pV
Gases are characterized by a complete disorder in the arrangement and movement of molecules.
The distance between gas molecules many times more sizes molecules. Small forces of attraction cannot keep molecules near each other, so gases can expand indefinitely.
The pressure of the gas on the walls of the vessel is created by the impacts of moving gas molecules.
Liquid
The thermal motion of molecules in a liquid is expressed by oscillations around the position of stable equilibrium within the volume provided to the molecule by its neighbors.
Molecules cannot move freely throughout the entire volume of a substance, but transitions of molecules to neighboring places are possible. This explains the fluidity of the liquid, the ability to change its shape.
In a liquid, the distance between molecules is approximately equal to the diameter of the molecule. With a decrease in the distance between molecules (compressing a liquid), the repulsive forces sharply increase, so liquids are incompressible.
The thermal motion of molecules in a solid is expressed only by oscillations of particles (atoms, molecules) around the position of stable equilibrium.
Most solids have a spatially ordered arrangement of particles that form a regular crystal lattice. Particles of matter (atoms, molecules, ions) are located at the vertices - the nodes of the crystal lattice. The nodes of the crystal lattice coincide with the position of stable equilibrium of the particles.
Air humidity:
Dew point is the temperature at which steam becomes saturated
Solid
Fundamentals of thermodynamics
Basic concepts:
Thermodynamics- a theory of physics that studies the thermal properties of macroscopic systems, without referring to the microscopic structure of the bodies that make up the system.
Thermodynamic system is a physical system consisting of a large number particles (atoms and molecules) that make thermal motion, and interacting with each other, exchange energies.
Thermodynamics considers only equilibrium states.
equilibrium states– states in which the parameters of the thermodynamic system do not change with time.
Thermodynamic process- the transition of the system from the initial state to the final state through a sequence of intermediate states (any change in the thermodynamic system).
Thermodynamic processes
Internal energy is the energy consisting of the sum of the energies of molecular interactions and the energy thermal motion molecules, depending only on the thermodynamic state of the system.
Ways to change internal energy :
- committing mechanical work.
- Heat transfer (heat transfer)
Heat exchange- the transfer of internal energies from one body to another.
Heat exchange
desublimation
sublimation
vaporization
condensation
crystallization
melting
The amount of heat (Q, J)- a measure of energy
Quantity of heat:
First law of thermodynamics
Formulation of the first law of thermodynamics:
Getting the job done
Q 2 - given energy (the "remainder" of energy is transferred)
The heat engine must operate cyclically. At the end of the cycle, the body returns to its original state, while the internal energy takes its initial value. The work of the cycle can be performed only due to external sources that supply heat to the working fluid.
Real heat engines operate in an open cycle, i.e. after expansion, the gas is ejected, and a new portion of gas is introduced into the machine.
Efficiency
efficiency ( η ) – work ratio A perfect working fluid per cycle, to the amount of heat Q obtained by the working fluid for the same cycle.
η = 100% = 100% = 100%
Efficiency characterizes the degree of efficiency of the heat engine, depends only on the temperature of the heater and refrigerator.
ü To increase the efficiency of a heat engine, you can increase the temperature of the heater and reduce the temperature of the refrigerator;
ü Efficiency always< 1
Second law of thermodynamics
The second law of thermodynamics determines the direction of the processes occurring in nature and associated with the transformation of energy.
Statements of the second law of thermodynamics:
- There is no thermodynamic process that would result in the transfer of heat from a cold body to a hotter one, without any other changes in nature.
- In nature, a process is not possible, the only result of which is the conversion of all the heat received from a certain body into work.
The second law of thermodynamics denies the possibility of using the internal energy reserves of any source without transferring it to a lower level, i.e. without refrigerator.
BASICS OF ELECTRODYNAMICS
Electrodynamics- the science of properties electromagnetic field.
1. ELECTROSTATICS
- a branch of electrodynamics that studies electrically charged bodies at rest.
Elementary particles may have email charge, then they are called charged; interact with each other with forces that depend on the distance between the particles, but many times exceed the forces of mutual gravitation (this interaction is called electromagnetic).
Electric charge
- the main scalar physical quantity that determines the intensity of electromagnetic interactions (q, C).
1 C - a charge passing in 1 second through the cross section of the conductor at a current strength of 1 A.
There are 2 signs of electric charges: positive and negative.
Particles with like charges repel, and particles with opposite charges attract.
The proton has a positive charge, the electron has a negative charge, and the neutron is electrically neutral.
elementary charge- the minimum charge that cannot be divided.
Body charged, if it has an excess of charges of any sign:
negatively charged - if there is an excess of electrons;
positively charged - if the lack of electrons.
Electrification of bodies
- one of the ways to get charged bodies.
In this case, both bodies are charged, and the charges are opposite in sign, but equal in magnitude.
MAGNETS
Magnets have two poles: S (southern) and N (northern), which have the greatest force attraction.
Like poles of a magnet repel each other, while opposite poles attract.
Magnetic field characteristics:
magnetic flux(F, Wb) - the number of magnetic induction lines penetrating the area.
Magnetic field strength(N, A / m) - a value that characterizes the magnetic field at any point in space, created by macrocurrents (currents flowing in the wires of an electrical circuit) in conductors, regardless of the environment.
B \u003d μ with H
For rectilinear current: H = ;
in the center of the circular current: H = ;
in the center of the solenoid: H = .
Magnetic permeability of a substance
The value of magnetic induction depends on the environment in which the magnetic field exists. The ratio of the magnetic induction B of the field in a given medium to the magnetic induction B o in vacuum characterizes magnetic properties of this medium and is called the relative magnetic permeability of the substance - µ.
ELECTROMAGNETIC INDUCTION
Methods for obtaining induction current:
The phenomenon of electromagnetic induction- occurrence electric current in a closed conducting circuit, which is either at rest in a time-varying magnetic field, or moves in a constant magnetic field so that the number of magnetic induction lines penetrating the circuit changes. The faster the number of lines of magnetic induction changes, the greater the induction current.
LAW OF ELECTROMAGNETIC INDUCTION:
Electric current in the circuit is possible if external forces act on the free charges of the conductor. The work of these forces to move a unit positive charge along a closed loop is called emf. When it changes magnetic flux through the surface bounded by the contour, external forces appear in the circuit, the action of which is characterized by the induction EMF.
Given the direction of the induction current, according to Lenz's rule:
The induction emf in a closed loop is equal to the rate of change of the magnetic flux through the surface bounded by the loop, taken with the opposite sign.
VORTEX ELECTRIC FIELD
The reason for the occurrence of electric current in a fixed conductor is electric field.
Any change in the magnetic field generates an induction electric field, regardless of the presence or absence of a closed circuit, while if the conductor is open, then a potential difference arises at its ends; if the conductor is closed, then an induction current is observed in it.
Eddy currents:
Induction currents in massive conductors are called Foucault currents. Foucault currents can reach very large values, because resistance of massive conductors is small. Therefore, the cores of transformers are made of insulated plates.
In ferrites - magnetic insulators, eddy currents practically do not occur.
The use of eddy currents
Heating and melting of metals in vacuum, dampers in electrical measuring instruments.
Harmful effects of eddy currents
These are energy losses in the cores of transformers and generators due to the release of a large amount of heat.
SELF-INDUCTION
The phenomenon of self-induction- the occurrence of induction EMF in the circuit, which is caused by a change in the magnetic field of the current flowing in the same circuit.
Own magnetic field in the circuit direct current changes at the moments of closing and opening of the circuit and when the current strength changes.
Inductance
(self-induction coefficient) - a physical quantity showing the dependence EMF self-induction on the size and shape of the conductor and on the environment in which the conductor is located.
The inductance of a coil depends on:
the number of turns, the size and shape of the coil, and the relative magnetic permeability of the medium (a core is possible).
ENERGY OF THE MAGNETIC FIELD OF THE CURRENT
Around a conductor with current there is a magnetic field that has energy.
The energy of the magnetic field is equal to the self-energy of the current.
The self-energy of the current is numerically equal to the work that the current source must do to overcome the self-induction EMF in order to create a current in the circuit.
Alternating current
Alternating current- current, changing in direction and magnitude according to the harmonic law.
Effective current value- the strength of the direct current, which releases in the conductor for the same time the same amount of heat as the alternating current. I=
The instantaneous value of the current is proportional to the instantaneous value of the voltage and is in phase: i = = I m cos ωt
The effective value of the alternating voltage is determined similarly to the effective value of the current U=
The instantaneous value of the voltage varies according to the harmonic law: u = U m cos ωt
Active resistances – electrical devices, converting electrical energy into internal (high-resistance wires, heating coils, resistors).
AC power.
If the phases of the oscillations of the current and voltage coincide, the instantaneous power of the alternating current is equal to:
p \u003d iu \u003d i 2 R \u003d I m U m cos 2ωt
The average power value for an alternating current period is: p=
Inductance and capacitance in the AC circuit:
1. Inductance
In a coil connected to an alternating voltage circuit, the current strength is less than the current strength in the DC voltage circuit for the same coil. Therefore, a coil in an AC circuit creates more resistance than a coil in a DC circuit.
Voltage leads current in phase by π/2
The inductive reactance is : Х L = ωL = 2πνL
Ohm's law: I m = , where Lω is the inductive reactance.
2. Capacity
When a capacitor is connected to a DC voltage circuit, the current strength is zero, and when a capacitor is connected to an AC voltage circuit, the current strength is not zero. Therefore, a capacitor in an AC voltage circuit creates less resistance than in a DC circuit.
The capacitance is: X C = =
Resonance in an electrical circuit.
Resonance in an electric circuit - the phenomenon of a sharp increase in the amplitude of forced current oscillations when the frequencies ω 0 \u003d ω coincide, where ω 0 is the natural frequency of the oscillatory circuit, ω is the frequency of the supply voltage.
The operating principle is based on the phenomenon of electromagnetic induction.
The principle of operation at idle, i.e. without R n:
ε ind1/ε ind2= ω 1 / ω 2 = k, where ε ind1 And ε ind2- EMF of induction in the windings, ω 1 and ω 2 - the number of turns in the windings,
k is the transformation ratio.
If k > 1 , then the transformer steps down the voltage; If k< 1 , then the transformer steps up the voltage. When idling, the transformer consumes a small amount of energy from the network, which is spent on remagnetization of its core.
Transformers for converting alternating currents of high power have a high efficiency.
Broadcast electrical energy:
5. Electromagnetic oscillations and waves
Oscillatory circuit- a circuit in which energy electric field could be converted into magnetic field energy and vice versa.
Electric oscillation circuit- a system consisting of a capacitor and a coil connected to each other in a closed electrical circuit
Free electromagnetic oscillations- periodically repeating changes in the current strength in the coil and the voltage between the capacitor plates without energy consumption from external sources.
If the contour is "perfect", i.e. electrical resistance is 0 X L = X C ω =
T \u003d 2π - Thomson formula (period of free electromagnetic oscillations in an electrical circuit)
Electromagnetic field – special form matter, the totality of electric and magnetic fields.
Variable electrical and magnetic fields exist simultaneously and form a single electromagnetic field.
ü At the rate of charge, zero, there is only an electric field.
ü At a constant charge rate, an electromagnetic field arises.
ü With the accelerated movement of the charge, an electromagnetic wave is emitted, which propagates in space at a finite speed.
Materiality of the electromagnetic field:
u can register
ü exists independently of our will and desires
ü has a large but finite speed
Electromagnetic waves
An electromagnetic field changing in time and propagating in space (vacuum) at a speed of 3 · 10 8 m/s forms an electromagnetic wave. The finite speed of propagation of the electromagnetic field leads to the fact that electromagnetic oscillations in space propagate in the form of waves.
Away from the antenna, the values of the vectors E and B are in phase.
The main condition for the emergence of an electromagnetic wave is the accelerated movement of electric charges.
Electromagnetic wave speed: υ = νλ λ = = υ2π
Wave properties:
Ø reflection, refraction, interference, diffraction, polarization;
Ø pressure on the substance;
Ø absorption by the medium;
Ø final propagation velocity in vacuum With;
Ø causes the phenomenon of photoelectric effect;
Ø the speed in the medium decreases.
6. WAVE OPTICS
Optics The branch of physics that studies light phenomena.
According to modern concepts, light has a dual nature (particle-wave dualism): light has wave properties and is electromagnetic waves, but at the same time it is also a stream of particles - photons. Depending on the light range, they appear in more certain properties.
Speed of light in vacuum:
When solving problems for calculations, the value c = 3 · 10 8 km/s is usually taken.
LIGHT REFLECTION
A wave surface is a set of points oscillating in the same phase.
Huygens' principle: Each point, to which the perturbation has reached, itself becomes a source of secondary spherical waves.
Laws of light reflection
MN - reflective surface
AA 1 and BB 1 - rays of the incident plane wave
AA 2 and BB 2 - rays of the reflected plane wave
AC - the wave surface of the incident plane wave is perpendicular to the incident rays
DB - wave surface of the reflected plane wave perpendicular to the reflected rays
α - angle of incidence (between the incident beam and the perpendicular to the reflecting surface)
β - angle of reflection (between the reflected beam and perpendicular to the reflecting surface)
Laws of reflection:
1. The incident ray, the reflected ray and the perpendicular restored at the point of incidence of the ray lie in the same plane.
2. The angle of incidence is equal to the angle of reflection.
LIGHT REFRACTION
Refraction of light is a change in the direction of propagation of light when passing through the interface between two media.
Laws of refraction of light:
1. The incident beam and the refracted beam lie in the same plane with the perpendicular to the interface between two media, restored at the point of incidence of the beam.
2. The ratio of the sine of the angle of incidence to the sine of the angle of refraction for two given media is a constant value 
where n is the relative refractive index (otherwise, the refractive index of the second medium relative to the first)
Refractive index
physical meaning: it shows how many times the speed of light in the medium from which the beam exits is greater than the speed of light in the medium into which it enters.
TOTAL INTERNAL LIGHT REFLECTION
Let the absolute refractive index of the first medium be greater than the absolute refractive index of the second medium
, that is, the first medium is optically denser. 
Then, if he directs
Motion with constant acceleration is a motion in which the acceleration vector remains constant both in magnitude and in direction. An example of this type of movement is the movement of a point in the field of gravity (both vertically and at an angle to the horizon).
Using the definition of acceleration, we obtain the following relation
After integration, we have the equality 
.
Given that the instantaneous velocity vector is 
, we will have the following expression
Integration of the last expression gives the following relation
. From where we get the equation of motion of a point with constant acceleration
.
Examples of vector equations of motion of a material point
Uniform rectilinear motion (
):
. (1.7)
Movement with constant acceleration ( 
):
. (1.8)
The dependence of speed on time when a point moves with constant acceleration has the form:
.
(1.9)
Questions for self-control.
Formulate the definition of mechanical motion.
Define a material point.
How is the position of a material point in space determined in the vector way of describing motion?
What is the essence of the vector method for describing mechanical motion? What characteristics are used to describe this movement?
Give definitions of vectors of average and instantaneous speed. How is the direction of these vectors determined?
Define the mean and instantaneous acceleration vectors.
Which of the relations is the equation of motion of a point with constant acceleration? What relationship determines the dependence of the velocity vector on time?
§1.2. Coordinate way of describing motion
In the coordinate method, a coordinate system (for example, Cartesian) is chosen to describe the movement. The reference point is rigidly fixed with the selected body ( reference body). Let 
unit vectors directed to the positive sides of the axes OX, OY and OZ, respectively. The position of the point is given by the coordinates 
.
The instantaneous velocity vector is defined as follows:
Where 
projections of the velocity vector on the coordinate axes, and 
derivatives of coordinates with respect to time.
The length of the velocity vector is related to its projections by the relation:
. (1.11)
For the instantaneous acceleration vector, the relation is true:
Where 
projections of the acceleration vector on the coordinate axes, and 
time derivatives of velocity vector projections.
The length of the instantaneous acceleration vector is found by the formula:
. (1.13)
Examples of equations of point motion in a Cartesian coordinate system
. (1.14)
Motion equations: 
. (1.15)
Dependences of the projections of the velocity vector on the coordinate axes on time:
(1.16)
Questions for self-control.
What is the essence of the coordinate method of describing motion?
What ratio determines the instantaneous velocity vector? What formula is used to calculate the magnitude of the velocity vector?
What ratio determines the instantaneous acceleration vector? What formula is used to calculate the magnitude of the instantaneous acceleration vector?
What relations are called the equations of uniform motion of a point?
What relationships are called equations of motion with constant acceleration? What formulas are used to calculate the projections of the instantaneous velocity of a point on the coordinate axes?
With uniformly accelerated motion, the following equations are valid, which we give without derivation:
As you understand, the vector formula on the left and the two scalar formulas on the right are equal. From the point of view of algebra, scalar formulas mean that with uniformly accelerated motion, the projections of displacement depend on time according to a quadratic law. Compare this with the nature of the instantaneous velocity projections (see § 12-h).
Knowing that sx = x – xo u sy = y – yo (see § 12-e), from the two scalar formulas from the upper right column we obtain equations for the coordinates:
Since the acceleration during uniformly accelerated motion of the body is constant, the coordinate axes can always be arranged so that the acceleration vector is directed parallel to one axis, for example, the Y axis. Consequently, the equation of motion along the X axis will be noticeably simplified:
x = xo + υox t + (0) and y = yo + υoy t + ½ ay t²
Please note that the left equation coincides with the equation of uniform rectilinear motion (see § 12-g). This means that uniformly accelerated motion can "compose" of uniform motion along one axis and uniformly accelerated motion along the other. This is confirmed by the experience with the cannonball on a yacht (see § 12-b).
Task. Stretching out her arms, the girl tossed the ball. He rose to 80 cm and soon fell at the girl's feet, flying 180 cm. With what speed was the ball thrown and what speed did the ball have when it hit the ground?
Let us square both sides of the equation for the projection onto the Y-axis of the instantaneous velocity: υy = υoy + ay t (see § 12-i). We get the equality:
υy² = ( υoy + ay t )² = υoy² + 2 υoy ay t + ay² t²
Let us take the factor 2 ay out of brackets only for two right-hand terms:
υy² = υoy² + 2 ay ( υoy t + ½ ay t² )
Note that in parentheses we get a formula for calculating the displacement projection: sy = υoy t + ½ ay t². Replacing it with sy , we get:
Solution. Let's make a drawing: point the Y axis up, and place the origin on the ground at the girl's feet. Let's apply the formula we derived for the square of the velocity projection first at the top point of the ball's ascent:
0 = υoy² + 2 (–g) (+h) ⇒ υoy = ±√¯2gh = +4 m/s
Then, at the beginning of the movement from the top point down:
υy² = 0 + 2 (–g) (–H) ⇒ υy = ±√¯2gh = –6 m/s
Answer: the ball was thrown upwards with a speed of 4 m/s, and at the moment of landing it had a speed of 6 m/s directed against the Y axis.
Note. We hope you understand that the formula for the square of the instantaneous velocity projection will be true by analogy for the X axis:
If the movement is one-dimensional, that is, it occurs only along one axis, you can use either of the two formulas in the framework.
Movement. Warmth Kitaygorodsky Alexander Isaakovich
Rectilinear motion with constant acceleration
Such a movement occurs, according to Newton's law, when a constant force acts on the body in total, driving or slowing down the body.
Although not entirely accurate, such conditions occur quite often: it is decelerated under the action of approximately constant strength friction, a car moving with the engine off falls from a height under the action of constant gravity a weighty object.
Knowing the magnitude of the resulting force, as well as the mass of the body, we will find by the formula a = F/m the amount of acceleration. Because
Where t- travel time v- final, and v 0 is the initial speed, then using this formula it is possible to answer a number of questions of such a nature, for example: after how long will the train stop if the braking force, the mass of the train and the initial speed are known? To what speed will the car accelerate if the motor force, the resistance force, the mass of the car and the acceleration time are known?
Often we are interested in knowing the length of the path traveled by the body in uniformly accelerated motion. If the movement is uniform, then the distance traveled is found by multiplying the speed of movement by the time of movement. If the movement is uniformly accelerated, then the distance traveled is calculated as if the body were moving at the same time t uniformly at a speed equal to half the sum of the initial and final speeds:
So, with uniformly accelerated (or slowed down) movement, the path traveled by the body is equal to the product of half the sum of the initial and final velocities and the time of movement. The same distance would have been traveled in the same time uniform motion with speed (1/2)( v 0 + v). In this sense, about (1/2)( v 0 + v) can be said to be average speed uniformly accelerated motion.
It is useful to draw up a formula that would show the dependence of the distance traveled on the acceleration. Substituting v = v 0 + at in the last formula, we find:
or, if the movement occurs without initial velocity,
If in one second the body has passed 5 m, then in two seconds it will pass (4? 5) m, in three seconds - (9? 5) m, etc. The distance traveled increases with the square of the time.
According to this law, a heavy body falls from a height. Free fall acceleration is g, and the formula looks like this:
If t substitute in seconds.
If the body could fall without interference for some 100 seconds, then it would have covered a huge distance from the beginning of the fall - about 50 km. In this case, in the first 10 seconds, only (1/2) km will be covered - this is what accelerated movement means.
But what speed will the body develop when falling from a given height? To answer this question, we need formulas that relate the distance traveled to acceleration and speed. Substituting in S = (1/2)(v 0 + v)t travel time value t = (v ? v 0)/a, we get:
or, if the initial velocity is zero,
Ten meters is the height of a small two- or three-story house. Why is it dangerous to jump to Earth from the roof of such a house? A simple calculation shows that the speed free fall reaches the value v= sqrt(2 9.8 10) m/s = 14 m/s? 50 km / h, but this is the city speed of a car.
Air resistance will not reduce this speed much.
The formulas we have derived are used for the most various calculations. Let's apply them to see how the motion on the moon occurs.
Wells' novel The First Men in the Moon tells of the surprises experienced by travelers on their fantastic walks. On the Moon, the acceleration of gravity is about 6 times less than on Earth. If on Earth a falling body passes 5 m in the first second, then on the Moon it will “float” down only 80 cm (acceleration is approximately 1.6 m / s 2).
High jump h time lasts t= sqrt(2 h/g). Since the lunar acceleration is 6 times less than the terrestrial one, on the Moon you will need sqrt(6) to jump? 2.45 times more time. By how many times does the final speed of the jump decrease ( v= sqrt(2 gh))?
On the moon, you can safely jump from the roof of a three-story building. The height of a jump made with the same initial speed increases six times (formula h = v 2 /(2g)). A jump that exceeds the earth's record will be within the power of a child.
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From the book Systems of the World (from the ancients to Newton) author Gurev Grigory AbramovichMovement along a circle If a point moves along a circle, then the movement is accelerated, if only because at each moment of time the speed changes its direction. In magnitude, the speed can remain unchanged, and we will focus on just such
From book 1. modern science about nature, the laws of mechanics author Feynman Richard PhillipsJet propulsion Man moves by pushing off the ground; the boat floats because the rowers push off the water with their oars; the ship is also repelled from the water, but not with oars, but with propellers. Also, a train running on rails and a car are repelled from the ground, -
From the book of Faraday. Electromagnetic induction[High Voltage Science] author Castillo Sergio RarraVI. Motion of rigid bodies Moment of force Try to turn a heavy flywheel by hand. Pull on the needle. It will be difficult for you if you grab your hand too close to the axis. Move your hand to the rim, and things will go easier. What has changed? After all, the force in both cases
From the author's bookWhat thermal motion looks like The interaction between molecules can be of greater or lesser importance in the "life" of molecules. The three states of matter - gaseous, liquid and solid - differ from one another in the role that interaction plays in them
From the author's bookTURN ELECTRICITY INTO MOTION Faraday noticed one small detail in Oersted's experiments that seemed to hold the key to understanding the problem. He guessed that the magnetism of electric current always deflects the compass needle in one direction. For example, if
