You need to know the point of application and direction of each force. It is important to be able to determine which forces are acting on the body and in which direction. Force is denoted as, measured in Newtons. In order to distinguish between forces, they are designated as follows
Below are the main forces at work in nature. It is impossible to invent non-existent forces when solving problems!
There are many forces in nature. Here are considered the forces that are considered in the school physics course in the study of dynamics. Other forces are also mentioned, which will be discussed in other sections.
Gravity
Every body on the planet is affected by the gravity of the Earth. The force with which the Earth attracts each body is determined by the formula
The point of application is at the center of gravity of the body. Gravity always points straight down.
Friction force
Let's get acquainted with the force of friction. This force arises when bodies move and two surfaces come into contact. The force arises from the fact that the surfaces, when viewed under a microscope, are not as smooth as they appear. The friction force is determined by the formula:
The force is applied at the point of contact between the two surfaces. Directed in the opposite direction to the movement.
Support reaction force
Imagine a very heavy object lying on a table. The table flexes under the weight of the object. But according to Newton's third law, a table acts on an object with exactly the same force as an object on a table. The force is opposite to the force with which the object pushes against the table. That is, up. This force is called the support reaction. The name of the force "speaks" support reacts... This force always arises when there is an impact on the support. The nature of its occurrence at the molecular level. The object, as it were, deformed the usual position and bonds of molecules (inside the table), they, in turn, tend to return to their original state, "resist".
Absolutely any body, even a very light one (for example, a pencil lying on the table), deforms the support at the micro level. Therefore, a support reaction occurs.
There is no special formula for finding this force. It is designated by a letter, but this force is just a separate type of elastic force, therefore it can be designated as
The force is applied at the point of contact of the object with the support. Directed perpendicular to the support.
Since the body is represented as a material point, the force can be depicted from the center
Elastic force
This force arises as a result of deformation (change in the initial state of matter). For example, when we stretch a spring, we increase the distance between the molecules of the spring material. When we compress the spring, we decrease it. When we twist or shift. In all these examples, a force arises that prevents deformation - the elastic force.
Hooke's law
The elastic force is directed opposite to the deformation.
Since the body is represented as a material point, the force can be depicted from the center
When connecting springs in series, for example, the stiffness is calculated by the formula
Parallel connection stiffness
The rigidity of the sample. Young's modulus.
Young's modulus characterizes the elastic properties of a substance. This is a constant value that depends only on the material, its physical state. It characterizes the ability of a material to resist tensile or compressive deformation. Young's modulus is tabular.
Learn more about properties of solids.
Body weight
Body weight is the force with which an object acts on a support. You say, it's gravity! The confusion is as follows: indeed, often the weight of the body is equal to the force of gravity, but these forces are completely different. Gravity is a force that results from interaction with the Earth. Weight is the result of interaction with the support. The force of gravity is applied at the center of gravity of the object, while the weight is the force that is applied to the support (not to the object)!
There is no formula for determining weight. This force is designated by a letter.
The reaction force of the support or the elastic force arises in response to the action of the object on the suspension or support, therefore the weight of the body is always numerically the same as the elastic force, but has the opposite direction.
The reaction force of the support and the weight are forces of the same nature, according to Newton's 3 law they are equal and oppositely directed. Weight is a force that acts on the support, not on the body. The force of gravity acts on the body.
Body weight may not be equal to gravity. It can be either more or less, or it can be such that the weight is zero. This state is called weightlessness... Weightlessness is a state when an object does not interact with a support, for example, a state of flight: there is gravity, and the weight is zero!
It is possible to determine the direction of acceleration if we determine where the resultant force is directed
Note, weight is force, measured in Newtons. How to correctly answer the question: "How much do you weigh"? We answer 50 kg, naming not the weight, but our own mass! In this example, our weight is equal to gravity, which is approximately 500N!
Overload- the ratio of weight to gravity
Archimedes' strength
Force arises as a result of the interaction of a body with a liquid (gas), when it is immersed in a liquid (or gas). This force pushes the body out of the water (gas). Therefore, it is directed vertically upward (pushes). Determined by the formula:
We neglect the power of Archimedes in the air.
If the force of Archimedes is equal to the force of gravity, the body floats. If the force of Archimedes is greater, then it rises to the surface of the liquid, if less, it sinks.
Electrical forces
There are forces of electrical origin. Occur when there is an electrical charge. These forces, such as the Coulomb force, the Ampere force, the Lorentz force, are discussed in detail in the Electricity section.
Schematic designation of forces acting on a body
The body is often modeled with a material point. Therefore, in the diagrams, various points of application are transferred to one point - to the center, and the body is depicted schematically as a circle or rectangle.
In order to correctly designate the forces, it is necessary to list all the bodies with which the investigated body interacts. Determine what happens as a result of interaction with each: friction, deformation, attraction, or perhaps repulsion. Determine the type of force, correctly indicate the direction. Attention! The number of forces will coincide with the number of bodies with which the interaction takes place.
The main thing to remember
1) Forces and their nature;
2) Direction of forces;
3) Be able to identify the acting forces
Distinguish between external (dry) and internal (viscous) friction. External friction occurs between touching solid surfaces, internal - between layers of liquid or gas during their relative motion. There are three types of external friction: static friction, sliding friction, and rolling friction.
Rolling friction is determined by the formula
The resistance force arises when a body moves in a liquid or gas. The magnitude of the resistance force depends on the size and shape of the body, the speed of its movement and the properties of the liquid or gas. At low speeds of movement, the resistance force is proportional to the speed of the body
At high speeds, it is proportional to the square of the speed
Consider the mutual attraction of an object and the Earth. Between them, according to the law of gravity, there is a force 
Now let's compare the law of gravity and the force of gravity 
The magnitude of the acceleration due to gravity depends on the mass of the Earth and its radius! Thus, you can calculate with what acceleration objects will fall on the Moon or on any other planet, using the mass and radius of that planet.
The distance from the center of the Earth to the poles is less than to the equator. Therefore, the acceleration of gravity at the equator is slightly less than at the poles. At the same time, it should be noted that the main reason for the dependence of the acceleration of gravity on the latitude of the area is the fact of the Earth's rotation around its axis.
With distance from the surface of the Earth, the force of gravity and the acceleration of gravity change in inverse proportion to the square of the distance to the center of the Earth.
Investigating the normal acceleration that occurs when the Moon moves around the Earth, I. Newton came to the conclusion that all bodies in nature are attracted to each other with a certain force, called the force of gravity. In this case, the acceleration, which is caused by the action of this force, is inversely proportional to the square of the distance between the bodies under consideration, acting on each other.
Suppose that two point bodies with masses $ m_1 \ and \ m_2 $ are at a distance $ r $ from each other. These bodies interact with forces:
In accordance with Newton's third law, the moduli of forces are equal:
From what was said above about acceleration and on the basis of (2) we get:
\ [\ frac (m_1K_1) (r ^ 2) = \ frac (m_2K_2) (r ^ 2) \ left (3 \ right). \]
Formula (3) will be valid if $ K_1 $ = $ \ gamma m_2 $, and $ K_2 $ = $ \ gamma m_1 $, where $ \ gamma $ is some constant. Then:
where $ \ gamma = 6.67 \ cdot (10) ^ (- 11) \ frac (H \ cdot m ^ 2) ((kg) ^ 2) $ is the gravitational constant.
Formulation of the law of universal gravitation
Definition
The force of attraction between two material points is directly proportional to the product of the masses of these points and inversely proportional to the square of the distance between them:
Strictly speaking, formula (4) can be used to calculate the gravitational force between homogeneous balls with masses $ m_1 (\ and \ m) _2 $, assuming that $ r $ is the distance between the centers of the balls.
In order to find the forces of gravity that act on one body from the side of another body, while the bodies cannot be considered point-like, proceed as follows. Both bodies are theoretically divided into elements that can be mistaken for point masses. The forces of gravity that act on one selected element of the first body from the side of all elements of the other body are found, and a force is obtained that acts on the considered point of the first body. Then the operation is repeated for each point of the first body. The resulting forces are added taking into account their directions. The result is a gravitational force with which the second body acts on the first. This is a very difficult task.
Gravity
Definition
Gravity(the force of attraction to the Earth) is a special case of the appearance of the force of universal gravity. Let's denote the force of gravity as $ F_t $. In accordance with the law of universal gravitation, this force is equal to:
where $ m $ is the mass of the body attracted to the Earth; $ M $ is the mass of the Earth; $ R $ - radius of the Earth; $ h $ - body height above the Earth's surface.
The force of gravity is directed towards the Center of the Earth. In problems, if the size of the Earth is much larger than the bodies under consideration, it is considered that the force of gravity is directed vertically downward.
The force of gravity imparts an acceleration to bodies located near the Earth's surface, which is called the acceleration of gravity, denoted as $ \ overline (g) $. According to Newton's second law, we have:
\ [\ overline (g) = \ frac ((\ overline (F)) _ t) (m) \ left (6 \ right). \]
Taking into account expression (5), we have:
\ [\ left | \ overline (g) \ right | = \ gamma \ frac (M) ((\ left (R + h \ right)) ^ 2) \ left (7 \ right). \]
Directly on the surface of the Earth (at $ h = 0 $) the value of the acceleration due to gravity is:
the value of the gravitational acceleration calculated from (8) is approximately equal to $ g \ approx 9.8 \ \ frac (m) (s ^ 2). $ You should be aware that even at the Earth's surface, the gravitational acceleration modulus is not the same everywhere, since The Earth is not a perfect ball, and it rotates on its axis and moves in a curved path around the Sun.
Using Newton's second law and expression (8), gravity is written as:
\ [(\ overline (F)) _ t = m \ overline (g) \ left (9 \ right). \]
Examples of tasks with a solution
Example 1
Exercise. What is the gravitational force of two bodies whose masses are equal to $ (m = 10) ^ 4 \ kg, $ if the distance between their centers is $ r = 100 $ m? Consider the bodies as uniform balls.
Solution. Since, according to the condition of the problem, the mass of bodies has spherical symmetry (homogeneous balls), then to calculate the gravitational force, you can use the formula:
Taking into account the equality of the masses of the bodies, the expression (1.1) is transformed to the form:
Calculate the required force:
Answer.$ F = 6.67 \ cdot (10) ^ (- 7) $ H
Example 2
Exercise. Some body, located at the Earth's pole, was thrown vertically upward at a speed of $ v_0 $. How high ($ h $) will this body rise? Assume that the radius of the Earth ($ R $) and the acceleration of gravity ($ g $) are known. Do not take air resistance into account.
Solution. We will solve the problem on the basis of the law of conservation of mechanical energy, since there are no resistance forces, the system is conservative. The body at the moment of throwing has kinetic energy:
The potential energy of interaction between the body and the Earth on the surface of the latter is equal to:
where $ M $ is the mass of the Earth. When the body reaches the point of maximum lift, it has only potential energy:
From the law of conservation of energy we have:
Taking into account that
Answer.$ h = \ frac (R) (\ frac (2gR) (v ^ 2_0) -1) $
1. What letter denotes the force of gravity and in what units is it measured in C? 2. What letter denotes body weight and in what units is it measured in C? 3. What letter denotes density and in what units in C is it measured? 4. Write down the formula for calculating the force of gravity. 5. In what units is body mass measured in C? 6. Formula for calculating body weight? 7. What force is called gravity? 8. What is deformation? 9. In what units in C is the volume of a body measured and what letter is indicated? 10. What is called body weight? 11. What is the measure of the interaction of bodies? 12. What is the acceleration due to gravity? 13. Write down the formula for calculating the elastic force? 14. What device is used to measure force?
Answers: 1) Ftyazh. (H) 2) P (H) 3) p (kg / m 3) 4) F = gm 5) (kg) 6) P = gm 7) The force with which the Earth attracts the body. 8) Changing the shape and size of the body. 9) V (m 3) 10) The force with which the body, as a result of attraction to the Earth, acts on a support or suspension. 11) Force 12) g = 9.8N / kg = 10N / kg 13) Fcont. = K (ll 0) 14) Dynamometer For 14 (+) - 3 points For 12 (+) - 2 points For 10 (+) - 1 point Less than 10 (+) - 0 points
A woman with a cart makes it easier for a mare; If you do not grease, you will not go; It went smoothly; You can't hold an eel in your hands; Skis glide according to the weather; A rusty plow is cleaned only on plowing; What is round rolls easily; The well rope is fraying; Mow, scythe, while the dew is, the dew is gone - and we are home.
1) R = 20H + 80H = 100H R = 80H-20H = 60H Answer: 100H; 60H. 2) Given: Solution: F 1 = 1000H R = F 1 - F 2 R = 1000H - 700H = 300H F 2 = 700H Answer: R = 300H R-? 3) Given: SI: Solution: m = 500 g. 0.5 kg Fty. = Gm Fty. = 10N / kg * 0.5 kg = 5H g = 10H / kg N / kg Fty. N Answer: Ftyazh = 5N. 4) Given: SI Solution: P = 600H N m = P / g m = 600H / 10H / kg = 60 kg g = 10H / kg H / kg Answer: m = 60 kg m-? kg 5) Given: SI Solution: V = 20 l 0.02 m 3 P = mg m = 800 kg / m 3 * 0.02 m 3 = 16 kg p = 800 kg / m 3 kg / m 3 m = pV P = 16 kg * 10N / kg = 160N. g = 10H / kg H / kg Answer: P = 160H P-? H
In physics, there is a huge number of laws, terms, definitions and formulas that explain all natural phenomena on earth and in the Universe. One of the main is the law of universal gravitation, which was discovered by the great and well-known scientist Isaac Newton. Its definition looks like this: any two bodies in the Universe are mutually attracted to each other with a certain force. The formula of universal gravitation, which calculates this force, will be: F = G * (m1 * m2 / R * R).
In contact with
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History of the discovery of the law
For a very long time, people have been studying the sky... They wanted to know all of its features, all that reign in an unattainable space. A calendar was drawn up in the sky, important dates and dates of religious holidays were calculated. People believed that the center of the entire Universe is the Sun, around which all celestial subjects revolve.
A truly stormy scientific interest in space and astronomy in general appeared in the 16th century. Tycho Brahe, the great scientist astronomer, during his research, observed the movements of the planets, recorded and systematized observations. By the time Isaac Newton discovered the law of the force of universal gravitation, the Copernican system had already been established in the world, according to which all celestial bodies revolve around the star in certain orbits. The great scientist Kepler, on the basis of Brahe's research, discovered the kinematic laws that characterize the motion of the planets.
Based on Kepler's laws, Isaac Newton opened his own and found out, what:
- The motions of the planets indicate the presence of a central force.
- The central force causes the planets to move in their orbits.
Parsing the formula
Five variables appear in the formula for Newton's law:
How accurate are the calculations
Since Isaac Newton's law refers to mechanics, calculations do not always accurately reflect the real force with which bodies interact. Moreover , this formula can be used only in two cases:
- When two bodies, between which interaction occurs, are homogeneous objects.
- When one of the bodies is a material point, and the other is a homogeneous ball.
Gravitational field
According to Newton's third law, we understand that the forces of interaction of two bodies are the same in value, but opposite in direction. The direction of forces occurs strictly along a straight line that connects the centers of mass of two interacting bodies. The interaction of attraction between bodies is due to the gravitational field.
Description of interaction and gravity
Gravity has very long-range interaction fields... In other words, its influence extends over very large, cosmic-scale distances. Thanks to gravity, people and all other objects are attracted to the earth, and the earth and all the planets of the solar system are attracted to the sun. Gravity is the constant impact of bodies on each other, this is a phenomenon that determines the law of universal gravitation. It is very important to understand one thing - the more massive the body, the more gravity it has. The Earth has a huge mass, so we are attracted to it, and the Sun weighs several million times more than the Earth, so our planet is attracted to the star.
Albert Einstein, one of the greatest physicists, argued that gravity between two bodies is due to the curvature of space-time. The scientist was sure that space, like a fabric, can be pressed through, and the more massive the object, the more it will press this fabric. Einstein became the author of the theory of relativity, which states that everything in the Universe is relative, even such a value as time.
Calculation example
Let's try, using the already known formula of the law of universal gravitation, solve a physics problem:
- The radius of the Earth is approximately 6350 kilometers. We take the acceleration of free fall for 10. It is necessary to find the mass of the Earth.
Solution: The acceleration of gravity at the Earth will be equal to G * M / R ^ 2. From this equation we can express the mass of the Earth: M = g * R ^ 2 / G. It remains only to substitute the values in the formula: M = 10 * 6350000 ^ 2/6, 7 * 10 ^ -11. In order not to suffer with degrees, we bring the equation to the form:
- M = 10 * (6.4 * 10 ^ 6) ^ 2 / 6.7 * 10 ^ -11.
After calculating, we get that the mass of the Earth is approximately equal to 6 * 10 ^ 24 kilograms.
Gravity is the force with which the Earth attracts a body close to its surface. .
The phenomena of gravitation can be observed everywhere in the world around us. A ball thrown upwards falls down, a stone thrown in a horizontal direction will find itself on the ground after a while. An artificial satellite launched from the Earth does not fly in a straight line due to gravitation, but moves around the Earth.
Gravity always directed vertically downward towards the center of the earth. It is denoted by a Latin letter F t (T- severity). The force of gravity is applied to the center of gravity of the body.
To find the center of gravity of an arbitrary shape, you need to hang the body on threads at its different points. The intersection point of all directions marked by the thread will be the center of gravity of the body. The center of gravity of regularly shaped bodies is at the center of symmetry of the body, and it does not need to belong to the body (for example, the center of symmetry of a ring).
For a body near the surface of the Earth, the force of gravity is:
where is the mass of the Earth, m- body mass , R is the radius of the Earth.
If only this force acts on the body (and all others are balanced), then it makes a free fall. The acceleration of this free fall can be found by applying Newton's second law:
(2)
From this formula, we can conclude that the acceleration of gravity does not depend on body weight m therefore, it is the same for all bodies. According to Newton's second law, gravity can be defined as the product of body mass and acceleration (in this case, the acceleration of gravity g);
Gravity acting on a body is equal to the product of the body's mass by the acceleration of gravity.
Like Newton's second law, formula (2) is valid only in inertial reference frames. On the surface of the Earth, inertial reference systems can only be systems associated with the poles of the Earth, which do not take part in its daily rotation. All other points on the earth's surface move in circles with centripetal accelerations and the frames of reference associated with these points are non-inertial.
Due to the rotation of the Earth, the acceleration of gravity is different at different latitudes. However, the acceleration due to gravity in different regions of the globe differs very little and differs very little from the value calculated by the formula
Therefore, in rough calculations, the non-inertial axis of the reference frame associated with the Earth's surface is neglected, and the acceleration of gravity is assumed to be the same everywhere.
