There is a huge variety of concepts of “power”. It is used in various fields of science and life. The most extensive definition is given in physics.
Definition 1
In physics, force is a measure of the interaction of different bodies.
All bodies in the surrounding world mutually influence each other. Such interaction is generated by certain forces. These power processes are directly related:
- with changing speed;
- with body deformation.
The force formula forms a certain mathematical model, according to which the history of the study of the dependence of force on basic parameters occurs. The result of the research should be experimental evidence of the existence of such a dependence.
Force has its own unit of measurement in the SI system. To determine this indicator, special scientific equipment is used. The simplest device for measuring force is a dynamometer.
This device compares the force that acts on the body with the elastic force of the spring installed in the force meter.
Force is a vector quantity and is defined:
- application point;
- direction of action;
- absolute value.
Definition 2
A force of 1 newton (N) is the force under the influence of which a body of 1 kilogram changes its own speed by 1 meter in one second.
When describing a force, its parameters must be indicated.
Pressure force
There are several types of interactions that have a natural origin:
- gravitational interaction;
- electromagnetic interactions;
- weak and strong interactions.
They surround any body that has mass. Gravity is the force of universal gravitation, including its varieties. Currently, the interaction of gravitational fields in the Universe is being actively studied, and research cannot yet provide accurate answers to many questions, including those regarding the nature of the emergence and existence of such forces. The source of the global field has not yet been found, but it is known that a significant part of gravitational forces arises from electromagnetic interaction at the atomic level. As you know, all substances consist of atoms and molecules. This fact has become the basis of all modern research in this area.
When bodies interact with the Earth's surface, gravitational forces exert pressure. The pressure force is determined by the mass of the body (m) and can be seen in the formula $P=mg$, where g is the acceleration of gravity. This value has different indicators at different latitudes of the planet.
The vertical pressure force is equal in absolute value, but opposite in relation to the direction of the elastic force. In this case, the force formula will change based on the movement of the body.
The weight of a body is usually represented as the action of the body on support after interaction with the Earth. The amount of body weight depends on the acceleration of movement that occurs in the vertical direction. An increase in weight is observed when the direction of acceleration changes. It must act in the opposite direction to the acceleration of gravity. A decrease in weight is observed when the body accelerates. It must coincide with the direction of free fall.
Elastic force
When the shape of the body is deformed, another force appears. It is aimed at returning the body to its original state. An elastic force can arise from the electrical interaction of particles. There are two main types of deformation: compression and tension. When stretched, the linear dimensions of the body increase. Compression is characterized by a reverse process, during which a decrease in the linear dimensions of the body is observed.
The elastic force formula is as follows:
It is used only for elastic deformation processes.
Interaction of magnetic field with current
Ampere's law describes the effect of a magnetic field on a current-carrying conductor that is placed in it.
Force manifestations are caused by the interaction of a magnetic field and an electric charge in motion.
Ampere power is determined by the formula:
- $I$ is the current strength in the conductor,
- $l$ – length of the active part of the conductor,
- $В$ – magnetic induction.
This dependence suggests that the vector of action of the magnetic field changes when the conductor turns, as well as when the direction of the current changes.
Lorentz force
In the study of elementary particles, data from spectrographs are actively used, where the level of interaction of the magnetic field with the charge is recorded. In such a process, another force arises, which was characterized by Lorentz using his equation. It occurs when a charged particle enters a magnetic field and moves at a certain speed.
The Lorentz force is determined by the formula in the form:
$F = vBqsinα$, where:
- $v$ is the particle velocity module,
- $В$ – magnetic field induction,
- $q$ is the electric charge of the particle being studied.
This force causes a charged particle to move in a circle.
The interaction of a magnetic field and matter is used in cyclotrons, where they are trying to give birth to the process of a thermonuclear reaction, but there is still no effective way to create a new source of energy.
Current strength and work of force
Definition 3
Current strength is the main quantity that characterizes the flow of current in a conductor.
The formula $I = q/t$, where $q$ is the charge, $t$ is the flow time, includes the charge flowing per unit time through the cross section of the conductor.
The work of force is a physical quantity that is numerically equal to the product of force and displacement. It must be achieved through influence. The force exerted on a substance is accompanied by the performance of work.
The work force is expressed by the following formula $A = FScosα$, which includes the magnitude of the force. The action of the body itself occurs when the speed of the body changes, as well as possible deformation. This means that there are simultaneous changes in energy. The work done by a force is directly dependent on its magnitude.
When solving problems of dynamics, we will mainly consider the following constant or variable forces (the laws of change of variable forces, as a rule, are established experimentally).
Gravity. This is a constant force P acting on any body located near the earth’s surface (for more details, see § 92). The modulus of gravity is equal to the weight of the body.
Experience has established that under the influence of force P, any body freely falling to the Earth (from a small height and in airless space) has the same acceleration g, called the acceleration of gravity, and sometimes the acceleration of gravity
Then from equation (D) it follows that
These equalities make it possible, knowing the mass of a body, to determine its weight (the modulus of the force of gravity acting on it) or, knowing the weight of a body, to determine its mass. Body weight or gravity, like the value of g, changes with latitude and altitude; mass is a constant quantity for a given body.
Friction force. This is what we will briefly call the sliding friction force acting (in the absence of liquid lubricant) on a moving body. Its modulus is determined by the equality (see § 23)
where f is the friction coefficient, which we will consider constant; N - normal reaction.
The force of gravity. This is the force with which two material bodies are attracted to each other according to the law of universal gravitation discovered by Newton. The force of gravity depends on the distance and for two material points with masses located at a distance from each other, it is expressed by the equality
where f is the gravitational constant (in).
Elastic force. This force also depends on the distance. Its value can be determined based on Hooke's law, according to which stress (force per unit area) is proportional to deformation. In particular, for the elastic force of the spring we obtain the value
where is the elongation (or compression) of the spring; c is the so-called spring stiffness coefficient (in SI measured in ).
Viscous friction force. This speed-dependent force acts on a body when it moves slowly in a very viscous medium (or in the presence of a liquid lubricant) and can be expressed by the equality
where v is the speed of the body; - resistance coefficient. A dependence of the form (7) can be obtained based on the law of viscous friction discovered by Newton.
Aerodynamic (hydrodynamic) drag force.
This force also depends on speed and acts on a body moving in, for example, a medium such as air or water. Usually its value is expressed by the equality
where is the density of the medium; - area of projection of the body onto a plane perpendicular to the direction of movement (midsection area); - dimensionless drag coefficient, usually determined experimentally and depending on the shape of the body and how it is oriented during movement.
Inertial and gravitational masses. To experimentally determine the mass of a given body, one can proceed from law (1), where mass is included as a measure of inertia and is therefore called inertial mass. But we can also start from law (5), where mass is included as a measure of the gravitational properties of a body and is called, accordingly, gravitational (or heavy) mass. In principle, it does not follow from anywhere that the inertial and gravitational masses represent the same quantity. However, a number of experiments have established that the values of both masses coincide with a very high degree of accuracy (according to experiments carried out by Soviet physicists (1971), with an accuracy of ). This experimentally established fact is called the principle of equivalence. Einstein based it on his general theory of relativity (theory of gravity).
Based on the above, in mechanics they use the single term “mass”, defining mass as a measure of the inertia of a body and its gravitational properties.
There are four types of forces in nature: gravitational, electromagnetic, nuclear and weak.
Gravitational forces or gravity, act between all bodies. But these forces are noticeable if at least one of the bodies has dimensions comparable to the size of the planets. The forces of attraction between ordinary bodies are so small that they can be neglected. Therefore, the forces of interaction between planets, as well as between planets and the Sun or other bodies that have a very large mass, can be considered gravitational. These can be stars, satellites of planets, etc.
Electromagnetic forces act between bodies having an electric charge.
Nuclear forces(strong) are the most powerful in nature. They act inside the nuclei of atoms at distances of 10 -13 cm.
Weak forces, like nuclear ones, act at short distances of the order of 10 -15 cm. As a result of their action, processes occur inside the nucleus.
Mechanics considers gravitational forces, elastic forces and frictional forces.
Gravitational forces
Gravity is described law of universal gravitation. This law was outlined by Newton in the middle XVII V. in the work “Mathematical principles of natural philosophy.”
By gravitycalled the force of gravity with which any material particles attract each other.
The force with which material particles attract each other is directly proportional to the product of their masses and inversely proportional to the square of the distance between them .
G – gravitational constant, numerically equal to the modulus of the gravitational force with which a body having unit mass acts on a body having the same unit mass and located at a unit distance from it.
G = 6.67384(80) 10 −11 m 3 s −2 kg −1, or N m² kg −2.
On the surface of the Earth, the force of gravity (gravitational force) manifests itself as gravity.
We see that any object thrown in a horizontal direction still falls down. Any object thrown up also falls down. This happens under the influence of gravity, which acts on any material body located near the surface of the Earth. The force of gravity acts on bodies and on the surfaces of other astronomical bodies. This force is always directed vertically downwards.
Under the influence of gravity, a body moves towards the surface of the planet with acceleration, which is called acceleration of free fall.
The acceleration of gravity on the Earth's surface is denoted by the letter g .
Ft = mg ,
hence,
g = Ft / m
g = 9.81 m/s 2 at the Earth’s poles, and at the equator g = 9.78 m/s 2 .
When solving simple physical problems, the value g is considered to be equal to 9.8 m/s 2.
The classical theory of gravity is applicable only to bodies whose speed is much lower than the speed of light.
Elastic forces
Elastic forces are called forces that arise in a body as a result of deformation, causing a change in its shape or volume. These forces always strive to return the body to its original position.
During deformation, particles of the body are displaced. The elastic force is directed in the direction opposite to the direction of particle displacement. If the deformation stops, the elastic force disappears.
The English physicist Robert Hooke, a contemporary of Newton, discovered a law establishing a connection between the force of elasticity and the deformation of a body.
When a body is deformed, an elastic force arises that is directly proportional to the elongation of the body and has a direction opposite to the movement of particles during deformation.
F = k ∆ l ,
Where To – body rigidity, or elasticity coefficient;
∆ l – the amount of deformation showing the amount of elongation of the body under the influence of elastic forces.
Hooke's law applies to elastic deformations when the elongation of the body is small, and the body restores its original dimensions after the forces that caused this deformation disappear.
If the deformation is great and the body does not return to its original shape, Hooke's law does not apply. At Very large deformations cause destruction of the body.
Friction forces
Friction occurs when one body moves on the surface of another. It is of electromagnetic nature. This is a consequence of the interaction between atoms and molecules of contacting bodies. The direction of the friction force is opposite to the direction of movement.
Distinguish dry And liquid friction. Friction is called dry if there is no liquid or gaseous layer between the bodies.
A distinctive feature of dry friction is static friction, which occurs when bodies are at relative rest.
Magnitude static friction forces always equal to the magnitude of the external force and directed in the opposite direction. The force of static friction prevents the movement of a body.
In turn, dry friction is divided into friction slip and friction rolling.
If the magnitude of the external force exceeds the magnitude of the friction force, then slippage will occur, and one of the contacting bodies will begin to move forward relative to the other body. And the friction force will be called sliding friction force. Its direction will be opposite to the direction of sliding.
The force of sliding friction depends on the force with which the bodies press on each other, on the state of the rubbing surfaces, on the speed of movement, but does not depend on the area of contact.
The sliding friction force of one body on the surface of another is calculated by the formula:
F tr. = k N ,
Where k – sliding friction coefficient;
N – normal reaction force acting on the body from the surface.
Rolling friction force occurs between a body that rolls over a surface and the surface itself. Such forces appear, for example, when car tires come into contact with the road surface.
The magnitude of the rolling friction force is calculated by the formula
Where Ft – rolling friction force;
f – rolling friction coefficient;
R – radius of the rolling body;
N – pressing force.
During this lesson “Types of Forces” we will become familiar with the different forces that operate around us, learn how to describe them and solve problems. We will learn about the resultant force of several forces at once and about the interaction of bodies.
Bodies interact, and these interactions affect whether and how the body moves. Interaction forces determine acceleration. What is the nature of these forces? You can push the body with your hand, and it will move - with such an action everything is clear. But there are many other interactions. For example, if we unclench our fingers, the body will fall down. A body will fall faster in air than it would sink in water. This means that some forces are acting on the body. The body lies on the table and presses on it - also interaction. Substances consist of structural particles - these particles somehow interact with each other. The question arises of how to take all this into account and calculate, because we have to answer the question: “What if...?”, predict phenomena.
Any two bodies attract. The phenomenon of attraction is also called gravity. We feel it by the fact that the Earth attracts bodies: we overcome gravity when we lift something heavy, and observe its effect when the body falls. The force of attraction depends on the masses of the bodies and the distance between them. The mass of the Earth is enormous, so bodies are noticeably attracted to it. Two books on a shelf are also attracted to each other, but so weakly due to their small masses that we do not notice it.
Does the Moon attract us? And the Sun? Yes, but much smaller than Earth due to the great distance. We do not feel the attraction of the Moon on ourselves, but the ebb and flow of tides occur due to the attraction of the Moon and the Sun. And black holes have so much mass that they even attract light: rays passing by are bent.
All bodies attract. Let's take a body that lies on the table. It is attracted to the Earth, but remains in place. To maintain a state of rest, the forces acting on the body must be balanced. This means there must be a force that balances the force of gravity. In this case, this is the force with which the table acts on the body. This force was called ground reaction force(see Fig. 1).
At the same time, the body presses on the table. If we consider how the body moves, we don't care what happens to the table. But if we consider what will happen to the table, then we will need to take this effect into account. The force with which a body acts on a support or suspension is called weight:
Rice. 1. Interaction between the weight and the table
To move any body, you need to apply force. This is where inertia lies. If we try to move a weight on a table, it will not move at all until a certain limit. This means that a certain force arises here that balances our impact. That power - friction force:
Rice. 2. Friction force
Something similar happens when we lift a weight. It, too, does not rise at first until our strength exceeds the threshold: here this threshold is the gravitational force of the Earth.
If there is a spring instead of a table, it will compress and will also act on this body. The body acts on the table or spring, they bend, their molecules are displaced (see Fig. 3), and when the molecules are displaced, repulsive forces arise between them, preventing further deformation:
Rice. 3. Repulsion force
The difference is that the deformation of the table is most often so small that it is difficult to notice, and some bodies are deformed much more, like a spring or an elastic band. Moreover, by the deformation of such a body one can judge the force that arose in it. This is convenient for calculations, so this force is studied separately - it was called elastic force.
What if the body is placed on the surface of the water? In water, many objects become lighter, which means there is a force that “lifts” them. For some bodies, it is enough for them to float on the surface - this is a piece of foam or wood, or a ship. Thanks to this force, we can swim at all. This force was called by the power of Archimedes.
Of course, this classification is quite arbitrary. The nature of the support reaction force and the elastic force is the same, but it is convenient to study them separately. Or consider this case: a weight lies on a support and is pulled upward by a thread. The weight acts on both the support and the thread - which of these forces is considered a weight and what is the second force called? It is important to consider the two forces, what they act on, and solve the problem regardless of the names. By and large, there is only the interaction of atoms, but for convenience we have come up with several models.
You can conduct an experiment: hang two weights on a crossbar on a thread so that they are balanced. If we bring a weight to one of the weights, the system will rotate, which means that the weight and the weight attract each other. The law of universal gravitation applies.
Law of Gravity
Isaac Newton formulated the law of universal gravitation:
Any two bodies are attracted to each other, and the force of attraction is directly proportional to the masses of these bodies, and inversely proportional to the distance between their centers of mass. Mathematically, the law of universal gravitation is written as follows:
where m (1,2) are the masses of interacting bodies, and R- the distance between their centers of mass. The forces of universal gravitation are also called gravitational forces, and the proportionality coefficient G in the law of universal gravitation is called the gravitational constant. It is equal.
The law of universal gravitation can be used to calculate the forces of attraction between any bodies. Imagine you are sitting in front of a monitor. Let's say the mass of the monitor is 2 kg, and the mass of a person is 70 kg, let's take the distance to be 1 m. Then the interaction force according to the formula will be . This is so small that we absolutely do not notice such a weak interaction. The proportionality coefficient G in the formula takes a very small value, . If there is a nail lying on the ground and we bring a magnet to it, then the nail will be attracted to the small magnet more strongly than to the planet. However, if we take the interaction of two celestial bodies, for example, planets, then huge masses will have to be substituted into the formula, then the force will be much greater, despite the large distances. And the Earth has a significant influence on the movement of small bodies near the Earth’s surface.
Gravity is the force with which a body is attracted to the Earth . Of course, other planets also enter into gravitational interaction and gravity can also be calculated for them. Gravitational forces, and hence the force of gravity, are directed along a segment connecting the centers of mass of interacting bodies. We are used to calling the direction towards the center of the Earth “down”.
Galileo Galilei established experimentally: all bodies near the surface of the Earth fall with the same acceleration. Let us consider the case when only the force of gravity acts on the body. This force gives the body acceleration, according to Newton's second law. The fact is that if we increase the mass of a body, the force of gravity will increase by the same amount, and from the formula we will see that the body will move with the same acceleration: That is, to accelerate heavier bodies with the same acceleration, more force is needed, and on them It is precisely the greater force of gravity that acts. This is called the acceleration due to gravity. For Earth it is approximately 9.8 m/.
It is customary to denote this acceleration by the letter “ g" The force of gravity itself is most often designated as F gravity, or briefly F t. And by the acceleration that the force creates, you can find the force itself:
Why does paper fall slower than iron?
We considered the movement of bodies that are acted only by gravity. This force imparts equal acceleration to all bodies. But the action of other forces cannot always be neglected. For example, with a certain body shape, the force of air resistance becomes significant. Take an iron ball and a crumpled sheet of paper of the same mass. The forces of gravity on them are the same, but the paper is additionally affected by air resistance, which cannot be neglected, and therefore the paper moves with a different acceleration. If you throw iron and paper in airless space, then you can again consider a situation where only the force of gravity acts on the body, and both bodies fall with the same acceleration.
Even if the body lies on the table, it is acted upon by the same force of gravity, which we also calculate using the formula: mass times the acceleration of gravity. It would seem, what does acceleration have to do with it when the body is not moving? So, this is the acceleration with which the body would move if only gravity acted on it. From this acceleration you can calculate the force, it will be the same: .
"Acceleration of free fall in different parts of the Earth"
It is generally accepted that the value of “g”, that is, the acceleration of free fall, is a constant value equal to about 9.8 m/s 2 . But with a caveat: “for our planet.” On other celestial bodies, gravitational forces also act, but the acceleration of free fall there is different from ours. For example, on Mars the acceleration due to gravity is only 3.71 m/s 2 .
But in fact, even on our own planet, this acceleration will have different values in different places on Earth.
The known number 9.8 is the average value for the entire planet. Our planet, as you know, is not round, but slightly flattened at the poles. And it is at these poles that the acceleration of gravity is slightly greater than at other latitudes: at the poles g = 9.832 m/s 2 , and at the equator - 9.78 m/s 2 .
This is explained by the fact that the acceleration of gravity depends on the distance to the center of the Earth.
The formula by which you can find acceleration: (the force of gravity acting on a body, divided by the mass of this body). The force of gravitational interaction: . is the distance from the center of the Earth to the body if R is the radius of the Earth and the body is at a height h above the surface. Divide the force by the mass of the body and get the acceleration of gravity:
The greater the distance, the lower the acceleration due to gravity. Therefore, in the mountains it is less than at the surface of the Earth.
The greater the distance from the body to the planet, the weaker the force of gravity acts on it and the lower the acceleration of free fall. Near the surface, we can assume that h is equal to zero, then g will be constant and equal to . What height can we still consider “near”, and what height can no longer be considered? Accuracy is dictated by the purpose of the task. For some problems we can assume g is constant at altitudes of hundreds of kilometers. If we are looking at a book lying on a table in a flying airplane, then it is not so important to us that the acceleration of gravity will differ by several hundredths. And if we calculate the launch of a satellite, we need greater accuracy; these few hundredths cannot be omitted; we even have to take into account the differences in the radius of the Earth at the equator and at the poles. For many tasks, the usual value or even .
If a body rests on some surface (support), then the force of gravity and the reaction force of the support act on it, and they are balanced.
Ground reaction force- this is the force with which the support acts on the body.
The forces of gravity and ground reaction are applied to and act on our body. In the example considered, when the body lies on a horizontal surface, the support reaction force is equal to the force of gravity and is directed in the opposite direction, that is, vertically upward:
Rice. 4. Ground reaction force
The ground reaction force is usually denoted by the letter N.
The support acts on the body, and the body acts on the support (or thread, if it hangs on a thread).
Body weight- this is the force with which the body acts on the support or suspension:
Rice. 5. Body weight
The weight of a body is most often denoted by the letter “P”, and in modulus it is equal to the support reaction force (according to Newton’s third law: with the force one body acts on another, with the same force the second body acts on the first): P=N.
If a body is at rest on a horizontal surface, it is acted upon by the force of gravity and the reaction force of the support. They are balanced. Then the weight is equal.
The concept of “body weight” is often confused with body weight. This has already become the norm for colloquial speech: “weigh”, “how much do you weigh”, “scales”. Weight is the force with which a body acts, and mass is a characteristic of the body itself, a measure of inertia. It’s easy to check: standing on the scales, we see the mass value, which is calculated from the weight. If you jump a little, the number will change. But the mass has not changed. This has changed the weight, the force with which we press on the surface of the scale. And on the ISS, the astronaut does not put pressure on the scales at all, his weight is zero - and this state is called weightlessness.
The body also attracts the Earth, but this force does not affect the movement of the huge Earth, so it is not considered. Touching the support, the body presses on the support with its weight, and the support on the body presses with the reaction force of the support. This is the second pair of forces in this system. If we describe the motion of a particular body, we consider the forces that act on it, for example, gravity and ground reaction force.
Let's consider the force that arises when some bodies move relative to others, coming into contact with them - the force of friction.
Friction force- a force that arises at the point of contact of bodies and prevents them from moving relative to each other:
Rice. 6. Friction force
If you kick a ball, it will roll and stop after some time. The sled, no matter how high the hill it slides down, will also stop.
Let's consider two types of friction. The first is when one body slides over the surface of another - for example, when sledding down a mountain, it is called sliding friction. Secondly, when one body rolls on the surface of another, for example, a ball on the ground, it is called rolling friction.
Designate friction force, and is calculated by the formula:
where N is the support reaction force, which we have already become familiar with, and µ is the coefficient of friction between these two surfaces.
The stronger the bodies are pressed against each other, the greater the friction force will be, that is, the friction force is proportional to the reaction force of the support.
Friction occurs due to the interaction of the particles that make up a substance. The surface cannot be perfectly smooth; there are always protrusions and roughness. The protruding parts of the surfaces touch each other and impede the movement of the body. This is why moving on smooth (polished) surfaces requires less force than moving on rough ones.
Does friction always decrease when polishing?
By polishing, we reduce the number and size of irregularities that impede the relative movement of the two surfaces. This means that the better the surfaces are polished, the better they will slide over each other and the less frictional force between them will be. Is it possible to polish so that the friction force is zero? At some point, the irregularities will become so insignificant that a huge number of particles of the two surfaces will come into contact, and not just particles of roughness, and all these particles will interact and impede movement. It turns out that there is a limit to which the friction force decreases when polishing surfaces, and then the number of interactions between particles, and therefore the friction force, increases. This is why we sometimes notice that surfaces that are too smooth “stick together.”
For bodies made of the same materials, the rolling friction force will be less than the sliding friction force. People have known this for a long time, so they came up with the wheel.
But whatever friction there is, the friction force is directed in the direction opposite to the relative displacement of the surfaces. Moreover, it is directed along the line along which the bodies touch.
"Different types of friction"
There are different types of friction forces.
For example, there is a heavy book on the table. It will take some effort to move it. And if you press the book too weakly, it will not move. We are applying force, why is there no acceleration? The force with which we push the book is balanced by the frictional force between the bottom cover of the book and the table. This frictional force prevents solid bodies from moving. Therefore it is called the static friction force.
The force of static friction is also directed against movement - that movement that should yet arise:
Rice. 7. Static friction force
To move something, you need to apply a force that is greater than the maximum static friction force.
When a liquid or gas moves, individual layers of these substances move one relative to the other. Forces of internal or viscous friction arise between them.
At a low flow speed, in the absence of vortices, the fluid will flow in layers. That is, the liquid can be mentally divided into parallel layers, each layer has its own speed. The layer located directly at the bottom will be motionless. The next layer will "slide" over the stationary layer. Then a layer with an even greater speed relative to the bottom, sliding over the previous one, etc. (see Fig. 8). And thus, a viscous friction force will act between the faster and slower layers of the liquid. It arises due to the interaction of atoms and molecules of liquids and gases moving at different speeds: fast molecules will collide with slow ones, thereby slowing down.
Rice. 8. Movement of water near the wall of the vessel
Why do objects move with a jerk?
When we try to move something, a static friction force arises. It balances the force F that we apply, and the body remains in place. The greater the force we apply, the greater the static friction force arises. The static friction force cannot increase indefinitely; it has a limit. The body will move: the friction force will be less than the force F we applied. When the body moves, a sliding friction force arises. It is slightly less than the maximum static friction force. That is, at the moment of shift, we applied a force equal to the maximum static friction force, the body moved - and the friction force decreased sharply. As sharply as we can reduce our F force for balance. Therefore, at this moment a jerk usually occurs: to shift the body, to lift it off, we apply more force than is needed later during movement. Try moving a book on the table one millimeter with one finger. It may not work the first time; due to the jerk it will move a couple of centimeters.
All bodies immersed in a liquid or gas, and in particular in water, are subject to a buoyant force. The force is directed upward, against gravity:
Rice. 9. Buoyancy force
This force is called the Archimedes force, after the ancient Greek physicist and mathematician who discovered it.
Archimedes' force is a buoyant force acting on a body immersed in a liquid (gas) and equal to the weight of the liquid (gas) displaced by the body. It is usually designated Farchimeda, or Fa.
To calculate it, use the formula.
where ρ is the density of the liquid, g is the acceleration of gravity and V is the volume of the immersed part of the body.
The Archimedes force is equal to the weight of the displaced fluid. This is similar to a scale, only the counterweight to our body is not the weight on the second pan of the scale, but the water around the body.
Weight of displaced water at rest: . The mass of displaced water is calculated through density and volume: . The volume of displaced water is equal to the volume of the body part immersed in it, . If we substitute all the expressions:
In the formula for gravity (), we can also express mass through density, then we can write: .
Let's immerse any body in water and release it. It is acted upon by gravity and the Archimedes force. If the force of gravity is greater, then the body begins to move downward. When a body is completely immersed in water, the comparison of gravity and the Archimedes force comes down to a comparison of the densities of the body and the liquid. That is, a body sinks when its density is greater than the density of the liquid. And if the density of the body is less, then the body will float until it appears from under the surface. Then the volume of the immersed part will decrease until the force of gravity becomes equal to the force of Archimedes. And then the body will float in a state of equilibrium on the surface.
In the same way, the Archimedes force acts in any liquid and gas, in particular in air. It is neglected if it is small compared to the force of gravity acting on the body. But, for example, a helium balloon has very little mass due to the low density of helium, so the force of gravity is even less than the Archimedean force with which the air pushes the balloon. In this case, the Archimedean force is taken into account, because thanks to it the helium balloon takes off.
Elastic force- this is the force that arises during the deformation of a body, which tends to return it to its previous size and shape:
Rice. 10. Elastic force
The more we deform the body, the more force we apply, the more the body will resist deformation, that is, an elastic force will arise (see Fig. 11). The magnitude of the elastic force depends on how much the body has lengthened or compressed relative to its original state.
Rice. 11. Greater elastic force with greater deformation
Let us consider a small deformation at which the body returns to its original state. This deformation is called elastic. Let's look at an example: if we stretched a hair tie and it became longer by 3 cm, then this is called absolute elongation, this is usually written as Δx or Δl.
It is convenient to denote the elastic force F exr, and it is calculated using the formula, which is a notation of “Hooke’s law”:
The elastic force that arises during elastic deformation of a body is proportional to the magnitude of the deformation.
k is the stiffness coefficient of the material from which the body is made, and Δх is the difference between the length of the body before and after deformation ().
Fig. 12. Elastic force
For example, if for an elastic band, then to stretch it by 3 cm, you need to apply a force of 15 N. Using this formula, you can calculate the force modulus. The force is directed opposite to the direction of deformation.
What we neglect when describing the interaction of bodies
Let's replace the body with a point - introduce a model and call it a material point. In this case, we neglect where exactly the force is applied to the body. When the donut lies on the table, each part of it is acted upon by the force of gravity and the reaction force of the support, but we can replace it with a point and assume that the forces acting on the donut are applied to it. Such a point will describe the movement of the entire body, without taking into account where exactly the force is applied to the body.
An infinite number of forces act on every body, so it is simply impossible to take them all into account. For example: a child is sliding down a slide - does the Moon influence him? It somehow influences: it has mass, is located at some distance... But the influence is so weak that it can be ignored. If we solve the problem of the flight of a spacecraft, then of course we need to take into account the forces with which nearby space objects act on it. We often don’t even notice what we discard: everything except what we consider essential for the movement of the body. For a child on a sled, this is interaction with the Earth (gravity) and with the surface (ground reaction force and friction force). Some problems immediately tell you to ignore some forces or influences on the body. Therefore, depending on the goals, we choose a model that is convenient for us, including all the necessary forces. When taking measurements, we also discard the unnecessary. If we want to measure the distance from home to school, we will measure it in kilometers, or meters if it is close. But we won’t measure it in millimeters. But when making a key, every millimeter is important. These limits can be compared to the accuracy of writing a number. For example, we take the number Pi for ordinary problems to be 3.14. This is the correct value, but rounded because we don't need maximum precision. After all, if you write Pi = 3.14159, then only the third decimal place will change in the answer, and this is one thousandth of the answer. Thus, the accuracy of the calculations depends on the purpose.
Several such forces can act on a body simultaneously. We consider a material point and believe that all forces are applied to it, in which case the overall result of the action of these forces on the body can be replaced by the action of one. This force has the same effect on the body and leads to the same result as the action of all forces applied to the body. It shows the final effect of all forces applied to the body. This force is called the resultant force and is usually denoted by the letter R.
Let's consider forces that act along one straight line. If two forces act in one direction, then they “help” each other, add up, and the resultant is equal to . And if they are opposite, then, on the contrary, they “interfere” with each other, and their actions are subtracted. If the forces are equal, then the resultant is equal.
We assign opposite signs to opposite directions. And before which force should we put a minus, or:
Rice. 13. Opposite forces
For each specific task, we can choose a direction that we will consider positive, and then no matter how many forces there are, we will simply arrange the pros and cons in front of them depending on the directions, and add them up. And if, for example, the resultant turns out to be negative, then it is directed against the chosen direction, and vice versa.
Let's apply our model, where the sign + or - corresponds to the direction to Hooke's law: . The elastic force is directed opposite to the deformation, which means you need to put a minus sign:
Task
Determine the weight of a person with mass m = 50 kg in an elevator moving with acceleration a = 0.8 m/s 2:
a) up; b) down.
The problem describes the accelerated movement of a person in an elevator. This obeys Newton's second law: a resultant force produces an acceleration, .
A person is acted upon by the force of gravity of the Earth, let's denote it by , and the reaction force of the support with which the floor of the elevator acts on a person, let's denote it by , it is directed upward. Gravity can be easily calculated using the formula.
Let's first solve part a), the elevator accelerates upward
Now let's solve part b), the elevator moves down.
In the equation, we put a minus sign in front of ma (the acceleration is directed against the selected positive direction). Let's write down:
The problem is solved.
- Sokolovich Yu.A., Bogdanova G.S. Physics: a reference book with examples of problem solving. - 2nd edition, revision. - X.: Vesta: Ranok Publishing House, 2005. - 464 p.
- Peryshkin A.V. Physics: textbook 7th grade. - M.: 2006. - 192 p.
- Internet portal “files.school-collection.edu.ru” ()
- Internet portal “files.school-collection.edu.ru” ()
Homework
- Explain from a physical point of view why logs were used in ancient Egypt during the construction of the pyramids, namely when moving concrete blocks.
- Make your own observations of the action of various forces in everyday life and describe some examples.
General characteristics of strength
Any human motor actions are the result of coordinated activity of the central nervous system (CNS) and peripheral parts of the motor system, in particular the musculoskeletal system. Excitatory impulses are produced in the central nervous system, which enter muscle fibers through motor neurons and axons. As a result, the muscles tense with a certain force, which allows individual parts of the body or the body as a whole to be moved in space. The speed and nature of movement change depending on the magnitude and direction of application of force. Thus, without the manifestation of muscle strength, a person cannot perform any motor actions. In this sense, strength is an integral motor quality, on which the manifestation of all other physical qualities (speed, endurance, etc.) depends to one degree or another.
In physiology, muscle strength is understood as the maximum tension that they are capable of developing. The external manifestation of muscle tension (force) is measured in newtons.
In the theory of physical culture the concept of “strength” expresses one of the qualitative characteristics of human voluntary movements aimed at solving a specific motor task.
Thus:
FORCE- this is the ability to overcome a certain resistance or counteract it due to muscle tension.
As resistance The forces of gravity, the reaction of the support when interacting with it, the resistance of the environment, the weight of objects and sports equipment, the inertial forces of one’s own body or its links and other bodies, the resistance of a partner, etc. can act.
The more resistance a person can overcome, the stronger he is.
Depending on the motor task and the nature of the work of the musculoskeletal system, the force exerted by the muscles acquires specific characteristics, which become more pronounced as a person’s physical fitness increases.
Main specific for different motor actions types of manifestation of power are:
1) actual strength qualities (these include the concepts of “absolute” and “relative” strength);
2) speed-strength qualities (these include the concepts of “speed” and “explosive” strength);
3) strength endurance.
This identification of types of force is rather arbitrary. Despite their specificity, they are interconnected in a certain way both in their manifestation and in their development. In their pure form they appear extremely rarely. As a rule, they are all components of most human motor actions.
· The absolute power of man is this is his ability to overcome the greatest resistance or counteract it with voluntary muscle tension.
It is interesting that a person can develop the greatest amounts of strength in muscle tensions that are not accompanied by external manifestations of movement, or in slow movements: for example, in a barbell press with two hands in a supine position. The manifestation of absolute strength is dominant when it is necessary to overcome great external resistance.
Example:
Granite slab lifting competitions are popular in Iceland. In 1992, a resident of the country, I. Perurena, set a unique record for displaying absolute strength: he lifted a stone weighing 315 kg above his head.
To compare the strength of people who have different body weights, the relative strength indicator is used.
· Relative strength - This is the amount of absolute strength a person has per kilogram of his body weight.
Relative strength is critical in motor actions that involve moving one's own body in space. The more force per 1 kg of your own body weight, the easier it is to move it in space or hold a certain position. For example, placing the arms to the sides on gymnastic rings (“cross”) can only be performed by those athletes whose relative strength of the corresponding muscle groups is close to 1 kg per kilogram of body weight. Relative strength is also of great importance in sports where athletes are divided into weight categories.
· Speed force - is the ability of a person to overcome moderate resistance as quickly as possible .
At first glance, it may seem that speed strength is a complex manifestation of speed and strength. However, in reality, this is still a specific manifestation of force in a certain range of external resistance. This range has been established by scientists and ranges from 15-20% to 70% of the maximum force in a specific motor action.
Example:
If a person can lift a maximum weight of 100 kg, then the range of manifestation of his speed strength in this exercise will be 15-70 kg;
If a person can perform a maximum of 40 flexions-extensions of the arms in a prone position (push-ups), then, depending on the increase in the speed of movements, he will be able to perform from 6 to 28 flexions-extensions of the arms in a prone position.
Speed strength is dominant in ensuring effective motor activity at sprint distances in cyclic exercises. In particular, the length of steps in running depends on the level of development of speed strength of the leg muscles.
Example:
It has been established that at the same running speed, qualified athletes have longer step lengths than less qualified ones, and for runners of the same qualifications, running speed increases in a fairly close relationship with the increase in step length.
· Explosive force - It is a person's ability to exert the greatest effort in the least amount of time.
Explosive strength is crucial in motor actions that require a large amount of muscle tension: for example, when starting sprinting, jumping, throwing, striking actions in boxing, etc. In most physical exercises, where explosive strength is of leading importance, the manifestation of explosive muscle contraction in the main phase of movement is preceded by mechanical stretching. For example, before throwing a javelin or grenade, an athlete makes an energetic swing. The manifestation of a powerful force immediately after intense mechanical stretching of the muscles, i.e. the rapid switching from inferior to overcoming work is called “muscle reactivity.”
Example:
There has been a high correlation between reactive ability and results in running triple jumps, hurdles, weightlifting exercises, etc.
· Strength endurance is a person’s ability to overcome moderate external resistance for a long time with the greatest efficiency.
This refers to the diverse nature of muscle functioning: long-term maintenance of the required posture (for example, holding a grip in a fight), repeated repeated explosive efforts (for example, training in a triple jump, pole vaulting), cyclic work of a certain intensity (ex. ., swimming, kayaking), etc.
By and large, it would be advisable to classify strength endurance as one of the types of endurance, but in the specialized literature this quality is traditionally considered as a type of strength.
Depending on the muscle work mode a distinction is also made between static and dynamic force:
· Static force manifests itself when the muscles tense, and there is no movement of the body, its parts or objects with which the person interacts (eg, holding a weight).
· Dynamic force manifests itself when overcoming resistance is accompanied by movement of the body or its individual parts in space (for example, lifting a weight).
Loading...
