Consider the movement of a car. For example, if a car travels 15 km in every quarter hour (15 minutes), 30 km in every half hour (30 minutes), and 60 km in every hour, it is considered to be moving uniformly.
Uneven movement.
If a body covers equal distances in any equal intervals of time, its motion is considered to be uniform.
Uniform movement is very rare. The Earth revolves almost uniformly around the Sun; in a year, the Earth makes one revolution around the Sun.
Almost never the driver of the car fails to maintain uniformity of movement - for various reasons, it is necessary to speed up or slow down the ride. The movement of the hands of the clock (minutes and hours) only seems to be uniform, which is easy to verify by watching the movement of the second hand. She moves and then stops. The other two arrows move in exactly the same way, only slowly, and therefore their jerks are not visible. Molecules of gases, hitting each other, stop for a while, then accelerate again. During the next collisions, already with other molecules, they again slow down their movement in space.
These are all examples of uneven movement. This is how the train moves, moving away from the station, passing for the same intervals of more and more ways. A skier or skater travels equal paths in different times in competitions. This is how a plane taking off, an opening door, a falling snowflake move.
If a body travels different paths in equal intervals of time, then its motion is called uneven.
Uneven movement can be observed experimentally. The figure shows a trolley with a dropper, from which drops fall at regular intervals. When the trolley moves under the action of a load on it, we see that the distances between the traces of drops are not the same. And this means that for the same intervals of time the cart travels different paths.
Speed. Speed units.
We often say that some bodies move faster, others slower. For example, a tourist walks along the highway, a car rushes, an airplane flies in the air. Suppose that they all move uniformly, nevertheless, the movement of these bodies will be different.
A car is faster than a pedestrian and an airplane is faster than a car. In physics, the quantity that characterizes the speed of movement is called speed.
Suppose that a tourist travels 5 km in 1 hour, a car 90 km, and the speed of an airplane is 850 km per hour.
The speed with a uniform motion of the body shows what distance the body has traveled per unit time.
Thus, using the concept of speed, we can now say that a tourist, a car, and an airplane are moving at different speeds.
With uniform motion, the speed of the body remains constant.
If a cyclist travels for 5 s a distance equal to 25 m, then his speed will be equal to 25m/5s = 5m/s.
To determine the speed during uniform motion, it is necessary to divide the path traveled by the body in a certain period of time by this period of time:
speed = path/time.
The speed is denoted by the letter v, the path is s, the time is t. The formula for finding the speed will look like this:
The speed of a body in uniform motion is the quantity equal to the ratio path to the time for which this path is passed.
In the International System (SI), speed is measured in meters per second (m/s).
This means that the unit of speed is the speed of such a uniform movement, in which in one second the body travels a distance equal to 1 meter.
The speed of a body can also be measured in kilometers per hour (km/h), kilometers per second (km/s), centimeters per second (cm/s).
Example. A train moving uniformly covers a distance of 108 km in 2 hours. Calculate the speed of the train.
So, s = 108 km; t = 2 h; v=?
Solution. v = s/t, v = 108 km/2 h = 54 km/h. Simply and easily.
Now, let's express the speed of the train in SI units, i.e. we will translate kilometers into meters, and hours into seconds:
54 km/h = 54000 m/ 3600 s = 15m/s.
Answer: v = 54 km/h, or 15 m/s.
Thus, the numerical value of the speed depends on the selected unit.
Speed, in addition to a numerical value, has a direction.
For example, if you want to specify where the plane will be located after 2 hours, taking off from Vladivostok, then you need to specify not only the value of its speed, but also its destination, i.e. his direction. Values that, in addition to a numerical value (modulus), also have a direction, are called vector.
Velocity is a vector physical quantity.
All vector quantities are denoted by the corresponding letters with an arrow. For example, the speed is denoted by the symbol v with an arrow, and the speed modulus by the same letter, but without the arrow v.
Some physical quantities have no direction. They are characterized only by a numerical value. These are time, volume, length, etc. They are scalar.
If during the movement of the body its speed changes from one section of the path to another, then such movement is uneven. To characterize the non-uniform movement of the body, the concept of average speed is introduced.
For example, a train from Moscow to St. Petersburg travels at a speed of 80 km/h. What speed do you mean? After all, the speed of the train at stops is zero, after stopping it increases, and before stopping it decreases.
In this case, the train moves unevenly, which means that the speed equal to 80 km/h is the average speed of the train.
It is defined in much the same way as speed in uniform motion.
To determine average speed bodies with uneven movement, it is necessary to divide the entire distance traveled by the entire time of movement:
It should be recalled that only with uniform motion, the ratio s / t for any period of time will be constant.
With uneven body movement, the average speed characterizes the movement of the body over the entire period of time. It does not explain how the body moved at different times of this interval.
Table 1 shows the average speeds of movement of some bodies.
Table 1
Average speeds of movement of some bodies, the speed of sound, radio waves and light.
Calculation of the path and time of movement.
If the speed of the body and time are known for uniform motion, then the path traveled by it can be found.
Since v = s/t, the path is determined by the formula
To determine the path traveled by a body in uniform motion, it is necessary to multiply the speed of the body by the time of its movement.
Now, knowing that s = vt, we can find the time during which the body moved, i.e.
To determine the time for uneven movement, it is necessary to divide the path traveled by the body by the speed of its movement.
If the body moves unevenly, then, knowing its average speed of movement and the time during which this movement occurs, they find the path:
Using this formula, you can determine the time for an uneven body movement:
Inertia.
Observations and experiments show that the speed of a body cannot change by itself.
Experience with carts. Inertia.
The soccer ball lies on the field. A football player sets him in motion with a kick. But the ball itself will not change its speed and will not start moving until other bodies act on it. A bullet inserted into the barrel of a gun will not fly out until it is pushed out by powder gases.
Thus, both the ball and the bullet do not have their own speed until other bodies act on them.
A soccer ball rolling on the ground stops due to friction on the ground.
The body reduces its speed and stops not by itself, but under the influence of other bodies. Under the action of another body, there is also a change in the direction of velocity.
A tennis ball changes direction after hitting the racket. The puck after hitting the hockey stick also changes direction. The direction of motion of a gas molecule changes when it hits another molecule or the walls of a vessel.
Means, a change in the speed of a body (magnitude and direction) occurs as a result of the action of another body on it.
Let's do an experiment. Let's set the board at an angle on the table. Pour on the table, at a short distance from the end of the board, a hill of sand. Place the trolley on the sloping board. The cart, having rolled down from the inclined board, quickly stops, hitting the sand. The speed of the trolley decreases very quickly. Her movement is uneven.
Let's level the sand and again release the cart from its previous height. The cart will now travel a greater distance on the table before it stops. Its speed changes more slowly, and the movement becomes closer to uniform.
If you completely remove the sand from the path of the cart, then only friction on the table will be an obstacle to its movement. The cart to the stop is even slower, and it will travel more than the first and second times.
So, the smaller the action of another body on the cart, the longer the speed of its movement is maintained and the closer it is to uniform.
How will a body move if other bodies do not act on it at all? How can this be determined by experience? Thorough experiments on the study of the motion of bodies were first carried out by G. Galileo. They made it possible to establish that if no other bodies act on the body, then it is either at rest or moves in a straight line and uniformly relative to the Earth.
The phenomenon of maintaining the speed of a body in the absence of other bodies acting on it is called inertia.
Inertia- from Latin inertia- immobility, inactivity.
Thus, the movement of a body in the absence of the action of another body on it is called inertia.
For example, a bullet fired from a gun would have flown, maintaining its speed, if it had not been acted upon by another body - air (or rather, the gas molecules that are in it.). As a result, the speed of the bullet decreases. The cyclist, having stopped pedaling, continues to move. He would be able to maintain the speed of his movement if the force of friction did not act on him.
So, If no other bodies act on the body, then it moves at a constant speed.
Phone interaction.
You already know that with uneven motion, the speed of the body changes over time. A change in the speed of a body occurs under the action of another body.
Experience with carts. The carts move relative to the table.
Let's do an experiment. We attach an elastic plate to the cart. Then bend it and tie it with a thread. The trolley is at rest relative to the table. Will the cart move if the elastic plate is straightened?
To do this, cut the thread. The plate will straighten out. The cart will remain in the same place.
Then, close to the bent plate, we put another similar cart. Let's burn the thread again. After that, both carts start moving relative to the table. They go in different directions.
To change the speed of the cart, a second body was needed. Experience has shown that the speed of a body changes only as a result of the action of another body (the second cart) on it. In our experience, we observed that the second cart also began to move. Both began to move relative to the table.
Boat experience. Both boats are moving.
trolleys act on each other, i.e. they interact. This means that the action of one body on another cannot be one-sided, both bodies act on each other, that is, they interact.
We have considered the simplest case of the interaction of two bodies. Both bodies (carts) before interaction were at rest relative to each other, and relative to the table.
Boat experience. The boat departs in the direction opposite to the jump.
For example, the bullet was also at rest relative to the gun before being fired. When interacting (during the shot), the bullet and the gun move in different directions. It turns out the phenomenon - returns.
If a person sitting in a boat pushes another boat away from him, then an interaction occurs. Both boats are moving.
If a person jumps from the boat to the shore, then the boat moves in the direction opposite to the jump. The man affected the boat. In turn, the boat acts on a person. It acquires a speed that is directed towards the shore.
So, as a result of the interaction, both bodies can change their speed.
Body mass. Mass unit.
When two bodies interact, the speeds of the first and second bodies always change.
Experience with carts. One is bigger than the other.
One body after the interaction acquires a speed that can differ significantly from the speed of another body. For example, after firing a bow, the speed of the arrow is much greater than the speed that the bow string acquires after interaction.
Why is this happening? Let's carry out the experiment described in paragraph 18. Only now, let's take carts of different sizes. After the thread has been burned out, the bogies move at different speeds. A cart that moves more slowly after an interaction is called more massive. She has more weight. The cart, which after the interaction moves at a higher speed, has a smaller mass. This means that the carts have different masses.
The speeds that the carts acquired as a result of the interaction can be measured. These speeds are used to compare the masses of the interacting carts.
Example. The velocities of the carts before the interaction are equal to zero. After the interaction, the speed of one cart became equal to 10 m/s, and the speed of the other 20 m/s. Since the speed acquired by the second cart, 2 times the speed of the first, then its mass is 2 times less than the mass of the first cart.
If, after the interaction, the speeds of the initially resting carts are the same, then their masses are the same. So, in the experiment shown in Figure 42, after the interaction, the carts move apart with equal speeds. Therefore, their masses were the same. If after the interaction the bodies acquired different speeds, then their masses are different.
International standard of the kilogram. In the picture: the kilogram standard in the USA.
How many times the speed of the first body is greater (less) than the speed of the second body, so many times the mass of the first body is less (greater) than the mass of the second.
How less change in body speed when interacting, the greater the mass it has. Such a body is called more inert.
And vice versa than more body speed changes when interacting, the less mass it has, the less it inertly.
This means that all bodies are characterized by the property of changing their speed in different ways during interaction. This property is called inertia.
The mass of a body is a physical quantity that characterizes its inertia.
You should know that any body: the Earth, a person, a book, etc. - has mass.
Mass is denoted by the letter m. The SI unit of mass is the kilogram ( 1 kg).
Kilogram is the mass of the standard. The standard is made of an alloy of two metals: platinum and iridium. The international standard of the kilogram is kept in Sevres (near Paris). More than 40 exact copies were made from the international standard and sent to different countries. One of the copies of the international standard is in our country, at the Institute of Metrology. D. I. Mendeleev in St. Petersburg.
In practice, other units of mass are also used: ton (T), gram (G), milligram (mg).
| 1 t | = 1000 kg (10 3 kg) | 1 g | = 0.001 kg (10 -3 kg) |
| 1 kg | = 1000 g (10 3 g) | 1 mg | = 0.001 g (10 -3 g) |
| 1 kg | = 1,000,000 mg (10 6 mg) | 1 mg | = 0.000001 kg (10 -6 kg) |
In the future, when studying physics, the concept of mass will be revealed more deeply.
Measurement of body weight on the scales.
In order to measure body weight, the method described in paragraph 19 can be used.
Educational scales.
Comparing the speeds acquired by the bodies during the interaction, determine how many times the mass of one body is greater (or less) than the mass of another. It is possible to measure the mass of a body in this way if the mass of one of the interacting bodies is known. In this way masses are defined in science celestial bodies as well as molecules and atoms.
In practice, body weight can be measured using scales. Scales are of various types: educational, medical, analytical, pharmaceutical, electronic, etc.
Special set of weights.
Consider training scales. The main part of such scales is the rocker. An arrow is attached to the middle of the rocker - a pointer that moves to the right or left. Cups are suspended from the ends of the rocker. Under what condition will the scales be in equilibrium?
Let us place the trolleys used in the experiment on the balance pans (see § 18). since during the interaction the carts acquired the same speeds, we found out that their masses are the same. Therefore, the scales will be in balance. This means that the masses of the bodies lying on the scales are equal to each other.
Now on one pan of scales, we place the body, the mass of which must be found. We will put weights on the other, the masses of which are known, until the scales are in equilibrium. Therefore, the mass of the weighed body will be equal to the total mass of the weights.
When weighing, a special set of weights is used.
Various scales are designed to weigh different bodies, both very heavy and very light. So, for example, with the help of wagon scales, it is possible to determine the mass of a wagon from 50 tons to 150 tons. The mass of a mosquito, equal to 1 mg, can be found using an analytical balance.
The density of matter.
Weigh two cylinders of equal volume. One is aluminum and the other is lead.
The bodies that surround us are made up of various substances: wood, iron, rubber, and so on.
The mass of any body depends not only on its size, but also on what substance it consists of. Therefore, bodies having the same volumes, but consisting of different substances, have different masses.
Let's do this experiment. Weigh two cylinders of the same volume, but consisting of different substances. For example, one is aluminum, the other is lead. Experience shows that the mass of aluminum is less than lead, that is, aluminum is lighter than lead.
At the same time, bodies with the same masses, consisting of different substances, have different volumes.
An iron beam weighing 1 ton occupies 0.13 cubic meters. And ice weighing 1 ton has a volume of 1.1 cubic meters.
So, an iron bar with a mass of 1 t occupies a volume of 0.13 m 3, and ice with the same mass of 1 t - a volume of 1.1 m 3. The volume of ice is almost 9 times the volume of an iron bar. This is because different substances can have different densities.
It follows that bodies with a volume of, for example, 1 m 3 each, consisting of different substances, have different masses. Let's take an example. Aluminum with a volume of 1 m 3 has a mass of 2700 kg, lead of the same volume has a mass of 11,300 kg. That is, with the same volume (1 m 3), lead has a mass that exceeds the mass of aluminum by about 4 times.
Density shows what the mass of a substance is, taken in a certain volume.
How can you find the density of a substance?
Example. The marble slab has a volume of 2m 3 and its mass is 5400 kg. It is necessary to determine the density of marble.
So, we know that marble with a volume of 2 m 3 has a mass of 5400 kg. This means that 1 m 3 of marble will have a mass 2 times less. In our case - 2700 kg (5400: 2 = 2700). Thus, the density of marble will be equal to 2700 kg per 1 m 3.
So, if the mass of the body and its volume are known, the density can be determined.
To find the density of a substance, it is necessary to divide the mass of the body by its volume.
Density is a physical quantity that is equal to the ratio of the mass of a body to its volume:
density = mass/volume.
We denote the quantities included in this expression by letters: the density of the substance - ρ (Greek letter "ro"), the mass of the body - m, its volume - V. Then we get the formula for calculating the density:
The SI unit for the density of matter is the kilogram per cubic meter(1kg / m 3).
The density of a substance is often expressed in grams per cubic centimeter (1g/cm3).
If the density of a substance is expressed in kg / m 3, then it can be converted to g / cm 3 as follows.
Example. The density of silver is 10,500 kg/m 3 . Express it in g / cm 3.
10,500 kg \u003d 10,500,000 g (or 10.5 * 10 6 g),
1m3 \u003d 1,000,000 cm 3 (or 10 6 cm 3).
Then ρ \u003d 10,500 kg / m 3 \u003d 10.5 * 10 6 / 10 6 g / cm 3 \u003d 10.5 g / cm 3.
It should be remembered that the density of the same substance in solid, liquid and gaseous states is different. So, the density of ice is 900 kg / m 3, water 1000 kg / m 3, and water vapor - 0.590 kg / m 3. Although all these are states of the same substance - water.
Below are tables of densities of some solids, liquids and gases.
table 2
Densities of some solids (at standard atm. pressure, t = 20 °C)
| Solid | ρ, kg / m 3 | ρ, g/cm 3 | Solid | ρ, kg / m 3 | ρ, g/cm 3 |
|---|---|---|---|---|---|
| Osmium | 22 600 | 22,6 | Marble | 2700 | 2,7 |
| Iridium | 22 400 | 22,4 | Window glass | 2500 | 2,5 |
| Platinum | 21 500 | 21,5 | Porcelain | 2300 | 2,3 |
| Gold | 19 300 | 19,3 | Concrete | 2300 | 2,3 |
| Lead | 11 300 | 11,3 | Brick | 1800 | 1,8 |
| Silver | 10 500 | 10,5 | Rafinated sugar | 1600 | 1,6 |
| Copper | 8900 | 8,9 | plexiglass | 1200 | 1,2 |
| Brass | 8500 | 8,5 | Kapron | 1100 | 1,1 |
| Steel, iron | 7800 | 7,8 | Polyethylene | 920 | 0,92 |
| Tin | 7300 | 7,3 | Paraffin | 900 | 0,90 |
| Zinc | 7100 | 7,2 | Ice | 900 | 0,90 |
| Cast iron | 7000 | 7 | Oak (dry) | 700 | 0,70 |
| Corundum | 4000 | 4 | Pine (dry) | 400 | 0,40 |
| Aluminum | 2700 | 2,7 | Cork | 240 | 0,24 |
Table 3
Densities of some liquids (at standard atm. pressure t=20 °C)
Table 4
Densities of some gases (at standard atm. pressure t=20 °C)
Calculation of mass and volume by its density.
Knowing the density of substances is very important for various practical purposes. When designing a machine, an engineer can calculate in advance the mass of the future machine based on the density and volume of the material. The builder can determine what will be the mass of the building under construction.
Therefore, knowing the density of a substance and the volume of a body, one can always determine its mass.
Since the density of a substance can be found by the formula ρ = m/V, then from here you can find the mass i.e.
m = ρV.
To calculate the mass of a body, if its volume and density are known, it is necessary to multiply the density by the volume.
Example. Determine the mass of the steel part, the volume is 120 cm 3.
According to table 2, we find that the density of steel is 7.8 g/cm 3 . Let's write down the condition of the problem and solve it.
Given:
V \u003d 120 cm 3;
ρ \u003d 7.8 g / cm 3;
Solution:
m \u003d 120 cm 3 7.8 g / cm 3 \u003d 936 g.
Answer: m= 936
If the mass of the body and its density are known, then the volume of the body can be expressed from the formula m = ρV, i.e. body volume will be:
V = m/ρ.
To calculate the volume of a body, if its mass and density are known, it is necessary to divide the mass by the density.
Example. The mass of sunflower oil filling the bottle is 930 g. Determine the volume of the bottle.
According to table 3, we find that the density of sunflower oil is 0.93 g/cm 3 .
Let's write down the condition of the problem and solve it.
Given:
ρ \u003d 0.93 g / cm 3
Solution:
V \u003d 930 / 0.93 g / cm 3 \u003d 1000 cm 3 \u003d 1l.
Answer: V= 1 l.
To determine the volume, a formula is used, as a rule, in cases where the volume is difficult to find using simple measurements.
Force.
Each of us constantly meets with various cases of the action of bodies on each other. As a result of the interaction, the speed of movement of a body changes. You already know that the speed of a body changes the more, the less its mass. Let's look at some examples to prove this.
By pushing the trolley with our hands, we can set it in motion. The speed of the trolley changes under the action of the human hand.
A piece of iron lying on a cork dipped in water is attracted by a magnet. A piece of iron and a cork change their speed under the influence of a magnet.
Acting on the spring with your hand, you can compress it. First, the end of the spring comes into motion. Then the movement is transferred to the rest of its parts. A compressed spring, when straightened, can, for example, set a ball in motion.
When the spring is compressed, the human hand was the acting body. When the spring is extended, the acting body is the spring itself. It sets the ball in motion.
With a racket or a hand, you can stop or change the direction of a flying ball.
In all the examples given, one body under the action of another body starts moving, stops, or changes the direction of its movement.
Thus, The speed of a body changes when it interacts with other bodies.
Often it is not indicated which body and how it acted on this body. It just says that a force acting on or applied to a body. So the force can be considered as the reason for the change in speed.
By pushing the trolley with our hands, we can set it in motion. |
Experiment with a piece of iron and a magnet. |
Spring experience. We set the ball in motion. |
Experience with a racket and a flying ball. |
The force acting on the body can not only change the speed of its body, but also of its individual parts.
A board lying on supports sags if a person sits on it.
For example, if you press your fingers on an eraser or a piece of plasticine, it will shrink and change its shape. It is called deformation.
Deformation is any change in the shape and size of the body.
Let's take another example. A board lying on supports sags if a person sits on it, or any other load. The middle of the board moves a greater distance than the edges.
Under the action of a force, the speed of different bodies in the same time can change in the same way. To do this, it is necessary to apply different forces to these bodies.
So, to set in motion a truck, more power is needed than for a car. This means that the numerical value of the force can be different: greater or less. What is strength?
Force is a measure of the interaction of bodies.
Force is a physical quantity, which means it can be measured.
In the drawing, the force is displayed as a straight line segment with an arrow at the end.
Strength, like speed, is vector quantity . It is characterized not only by numerical value, but also by direction. The force is denoted by the letter F with an arrow (as we remember, the arrow indicates the direction), and its modulus is also the letter F, but without the arrow.
When talking about force, it is important to indicate to which point of the body the acting force is applied.
In the drawing, the force is depicted as a straight line segment with an arrow at the end. The beginning of the segment - point A is the point of application of force. The length of the segment conditionally denotes the modulus of force on a certain scale.
So, The result of a force acting on a body depends on its modulus, direction, and point of application.
The phenomenon of attraction. Gravity.
Let's release the stone from our hands - it will fall to the ground.
If you release a stone from your hands, it will fall to the ground. The same will happen with any other body. If the ball is thrown in a horizontal direction, it does not fly straight and evenly. Its trajectory will be a curved line.
The stone flies in a curved line.
An artificial Earth satellite also does not fly in a straight line, it flies around the Earth.
An artificial satellite is moving around the earth.
What is the reason for the observed phenomena? And here's what. A force acts on these bodies - the force of attraction to the Earth. Due to attraction to the Earth, bodies fall, raised above the Earth, and then lowered. And also, because of this attraction, we walk on the Earth, and do not fly away into the endless Space, where there is no air to breathe.
The leaves of the trees fall to the ground because the ground pulls them. Due to attraction to the Earth, water flows in rivers.
The Earth attracts any bodies to itself: houses, people, the Moon, the Sun, water in the seas and oceans, etc. In turn, the Earth is attracted to all these bodies.
Attraction exists not only between the Earth and the listed bodies. All bodies are attracted to each other. The moon and earth are attracted to each other. The attraction of the Earth to the Moon causes the ebb and flow of water. Huge masses of water rise in the oceans and seas twice a day for many meters. You are well aware that the Earth and other planets move around the Sun, being attracted to it and to each other.
The attraction of all bodies of the universe to each other is called universal gravitation.
The English scientist Isaac Newton was the first to prove and establish the law of universal gravitation.
According to this law, the force of attraction between bodies is greater, the greater the mass of these bodies. The forces of attraction between bodies decrease as the distance between them increases.
For all living on Earth, one of the most important values is the force of attraction to the Earth.
The force with which the Earth pulls a body towards itself is called gravity.
The force of gravity is denoted by the letter F with the index: Ftyazh. It always points vertically down.
The globe is slightly flattened at the poles, so the bodies at the poles are located a little closer to the center of the Earth. Therefore, gravity at the pole is slightly greater than at the equator, or at other latitudes. The force of gravity at the top of the mountain is somewhat less than at its foot.
The force of gravity is directly proportional to the mass of a given body.
If we compare two bodies with different masses, then the body with a larger mass is heavier. A body with less mass is lighter.
How many times the mass of one body is greater than the mass of another body, the same number of times the force of gravity acting on the first body is greater than the force of gravity acting on the second. When the masses of bodies are the same, then the forces of gravity acting on them are the same.
Elastic force. Hooke's law.
You already know that all bodies on Earth are affected by gravity.
A book lying on a table is also affected by gravity, but it does not fall through the table, but is at rest. Let's hang the body on a thread. It won't fall.
Hooke's law. Experience.
Why do bodies rest on a support or suspended on a thread? Apparently, the force of gravity is balanced by some other force. What is this power and where does it come from?
Let's do an experiment. In the middle of a horizontally located board, located on supports, we put a weight. Under the influence of gravity, the weight will begin to move down and bend the board, i.e. board is deformed. In this case, a force arises with which the board acts on the body located on it. From this experience, we can conclude that, in addition to the force of gravity directed vertically downwards, another force acts on the weight. This force is directed vertically upwards. She balanced the force of gravity. This force is called elasticity force.
So, the force that arises in the body as a result of its deformation and tends to return the body to its original position is called the elastic force.
The elastic force is denoted by the letter F with the index Fupr.
The stronger the support (board) bends, the greater the elastic force. If the elastic force becomes equal to the force of gravity acting on the body, then the support and the body stop.
Now let's hang the body on the thread. The thread (suspension) is stretched. In the thread (suspension), as well as in the support, an elastic force arises. When the suspension is stretched, the elastic force will be equal to the force of gravity, then the stretching stops. The elastic force arises only when the bodies are deformed. If the deformation of the body disappears, then the elastic force also disappears.
Experiment with a body suspended by a thread.
Deformations happen different types: tension, compression, shear, bending and torsion.
We have already met two types of deformation - compression and bending. You will study these and other types of deformation in more detail in high school.
Now let's try to find out what the elastic force depends on.
English scientist Robert Hooke , a contemporary of Newton, established how the elastic force depends on deformation.
Consider experience. Take a rubber cord. We fix one end of it in a tripod. The original length of the cord was l 0 . If you hang a cup with a weight to the free end of the cord, the cord will lengthen. Its length will become equal to l. Cord extension can be found like this:
If you change the weights on the cup, then the length of the cord will also change, which means its elongation Δl.
Experience has shown that the modulus of elastic force in tension (or compression) of the body is directly proportional to the change in the length of the body.
This is Hooke's law. Hooke's law is written as follows:
Fcontrol \u003d -kΔl,
The weight of a body is the force with which a body, due to attraction to the Earth, acts on a support or suspension.
where Δl is the elongation of the body (change in its length), k is the coefficient of proportionality, which is called rigidity.
The rigidity of a body depends on its shape and dimensions, as well as on the material from which it is made.
Hooke's law is valid only for elastic deformation. If, after the cessation of the forces that deform the body, it returns to its original position, then the deformation is elastic.
You will learn more about Hooke's law and types of deformations in high school.
Body weight.
IN Everyday life very often used the concept of "weight". Let's try to find out what this value is. In experiments, when the body was placed on a support, not only the support was compressed, but also the body attracted by the Earth.
A deformed, compressed body presses on a support with a force called body weight . If the body is suspended on a thread, then not only the thread is stretched, but the body itself.
The weight of a body is the force with which a body, due to attraction to the Earth, acts on a support or suspension.
Body weight is a vector physical quantity and it is denoted by the letter P with an arrow above this letter, pointing to the right.
However, it should be remembered that the force of gravity is applied to the body, and the weight is applied to the support or suspension.
If the body and the support are motionless or move uniformly and rectilinearly, then the weight of the body in terms of its numerical value equal to strength gravity, i.e.
P = Ft.
It should be remembered that gravity is the result of the interaction of the body and the Earth.
So, the weight of the body is the result of the interaction of the body and the support (suspension). The support (suspension) and the body are thus deformed, which leads to the appearance of an elastic force.
Units of power. Relationship between gravity and body mass.
You already know that force is a physical quantity. In addition to the numerical value (modulo), it has a direction, that is, it is a vector quantity.
Force, like any physical quantity, can be measured, compared with the force taken as a unit.
Units physical quantities always choose conditionally. Thus, any force can be taken as a unit of force. For example, you can take as units of force the elastic force of a spring stretched to a certain length. The unit of force is the force of gravity acting on a body.
Do you know that force causes a change in the speed of the body. That is why A unit of force is a force that changes the velocity of a 1 kg body by 1 m/s in 1 s.
In honor of the English physicist Newton, this unit is named newton (1 N). Other units are often used kilonewtons (kN), millinewtons (mN):
1kN=1000 N, 1N=0.001 kN.
Let's try to determine the magnitude of the force in 1 N. It is established that 1 N is approximately equal to the force of gravity that acts on a body with a mass of 1/10 kg, or more precisely 1/9.8 kg (i.e., about 102 g).
It must be remembered that the force of gravity acting on a body depends on the geographical latitude at which the body is located. The force of gravity changes as the height above the Earth's surface changes.
If it is known that the unit of force is 1 N, then how to calculate the force of gravity that acts on a body of any mass?
It is known that how many times the mass of one body is greater than the mass of another body, the same number of times the force of gravity acting on the first body is greater than the force of gravity acting on the second body. Thus, if a body of mass 1/9.8 kg is acted upon by a force of gravity equal to 1 N, then a body of 2/9.8 kg will be acted upon by a force of gravity equal to 2 N.
On a body weighing 5 / 9.8 kg - gravity equal to - 5 N, 5.5 / 9.8 kg - 5.5 N, etc. On a body weighing 9.8 / 9.8 kg - 9, 8 N.
Since 9.8 / 9.8 kg \u003d 1 kg, then a body with a mass of 1 kg will be acted upon by a force of gravity equal to 9.8 N. The value of the force of gravity acting on a body with a mass of 1 kg can be written as follows: 9.8 N/kg.
So, if a force equal to 9.8 N acts on a body with a mass of 1 kg, then a force 2 times greater will act on a body with a mass of 2 kg. It will be equal to 19.6 N, and so on.
Thus, to determine the force of gravity acting on a body of any mass, it is necessary to multiply 9.8 N / kg by the mass of this body.
Body weight is expressed in kilograms. Then we get that:
Ft = 9.8 N/kg m.
The value of 9.8 N / kg is denoted by the letter g, and the formula for gravity will be:
where m is mass, g is called free fall acceleration. (The concept of free fall acceleration will be given in grade 9.)
When solving problems where great accuracy is not required, g \u003d 9.8 N / kg is rounded up to 10 N / kg.
You already know that P = Fstrand if the body and the support are stationary or move uniformly and in a straight line. Therefore, body weight can be determined by the formula:
Example. There is a teapot with water weighing 1.5 kg on the table. Determine the force of gravity and the weight of the kettle. Show these forces in figure 68.
Given:
g ≈ 10 N/kg
Solution:
Ftight \u003d P ≈ 10 N / kg 1.5 kg \u003d 15 N.
Answer: Fstrand = P = 15 N.
Now let's represent the forces graphically. Let's choose the scale. Let 3 N be equal to a segment 0.3 cm long. Then a force of 15 N. must be drawn with a segment 1.5 cm long.
It should be borne in mind that gravity acts on the body, and therefore is applied to the body itself. The weight acts on the support or suspension, that is, it is applied to the support, in our case, to the table.
Dynamometer.
The simplest dynamometer.
In practice, it is often necessary to measure the force with which one body acts on another. An instrument used to measure force is called dynamometer (from Greek. dynamis- force, metreo- measure).
Dynamometers come in a variety of devices. Their main part is a steel spring, which is given a different shape depending on the purpose of the device. The device of the simplest dynamometer is based on a comparison of any force with the elastic force of a spring.
The simplest dynamometer can be made from a spring with two hooks mounted on a plank. A pointer is attached to the lower end of the spring, and a strip of paper is glued onto the board.
Mark on the paper with a dash the position of the pointer when the spring is not stretched. This mark will be the zero division.
Hand dynamometer - power meter.
Then we will hang a weight of 1/9.8 kg, i.e. 102 g, from the hook. A gravity force of 1 N will act on this load. Under the action of this force (1 N), the spring will stretch, the pointer will go down. We mark its new position on paper and put the number 1. After that, we hang the load with a mass of 204 g and set the mark 2. This means that in this position the elastic force of the spring is 2 N. Having suspended the load with a mass of 306 g, we mark 3, and t d.
In order to apply tenths of a newton, it is necessary to apply divisions - 0.1; 0.2; 0.3; 0.4, etc. For this, the distances between each integer marks are divided by ten equal parts. This can be done, given that the elastic force of the spring Fupr increases as many times as its elongation Δl increases. This follows from Hooke's law: Fupr \u003d kΔl, i.e. the force of elasticity of the body during tension is directly proportional to the change in the length of the body.
Traction dynamometer.
A graduated spring will be the simplest dynamometer.
With the help of a dynamometer, not only gravity is measured, but also other forces, such as elastic force, friction force, etc.
So, for example, to measure the strength of various human muscle groups, medical dynamometers.
To measure the muscular strength of the hand when squeezing the hand into a fist, a manual dynamometer - power meter .
Mercury, hydraulic, electric and other dynamometers are also used.
Recently, electric dynamometers have been widely used. They have a sensor that converts the deformation into an electrical signal.
To measure large forces, such as, for example, the traction forces of tractors, tractors, locomotives, sea and river tugs, special traction dynamometers . They can measure forces up to several tens of thousands of newtons.
In each such case, it is possible to replace several forces actually applied to the body by one force, equivalent in its effect to these forces.
A force that produces the same effect on a body as several at the same time active forces, is called the resultant of these forces.
Find the resultant of these two forces acting on the body in one straight line in one direction.
Let's turn to experience. To the spring, one below the other, we will hang two weights with a mass of 102 g and 204 g, i.e., weighing 1 N and 2 N. Note the length over which the spring is stretched. Let's remove these weights and replace them with one weight, which stretches the spring to the same length. The weight of this load is 3 N.
Experience shows that: the resultant of forces directed along one straight line in the same direction, and its module is equal to the sum of the modules of the component forces.
In the figure, the resultant of the forces acting on the body is denoted by the letter R, and the terms of the force are denoted by the letters F 1 and F 2. In this case
Let us now find out how to find the resultant of two forces acting on the body along one straight line in different directions. The body is a dynamometer table. Let's put a 5 N weight on the table, i.e. act on it with a force of 5 N directed downwards. We tie a thread to the table and act on it with a force equal to 2 N directed upwards. Then the dynamometer will show a force of 3 N. This force is the resultant of two forces: 5 N and 2N.
So, resultant of two forces acting in the same straight line opposite sides, is directed towards the greater force in absolute value, and its module is equal to the difference between the modules of the component forces(rice.):
If two equal and opposite forces are applied to a body, then the resultant of these forces is zero. For example, if in our experiment the end is pulled with a force of 5 N, then the dynamometer needle will be set to zero. The resultant of the two forces in this case is zero:
The sleigh rolled down the mountain soon stops.
The sleigh, having rolled down the mountain, moves unevenly along a horizontal path, their speed gradually decreases, and after a while they stop. A man, having run up, slides on his skate on the ice, but, no matter how smooth the ice, the man still stops. The bicycle also stops when the cyclist stops pedaling. We know that force is the cause of such phenomena. In this case, it is the force of friction.
When one body comes into contact with another, an interaction is obtained that prevents their relative motion, which is called friction. And the force that characterizes this interaction is called friction force.
Friction force- this is another type of force that differs from the previously considered gravity and elastic forces.
Another reason for friction is mutual attraction of molecules of contacting bodies.
The emergence of the friction force is mainly due to the first reason, when the surfaces of the bodies are rough. But if the surfaces are well polished, then when they come into contact, some of their molecules are located very close to each other. In this case, the attraction between the molecules of the contacting bodies begins to noticeably manifest itself.
Experience with a bar and a dynamometer. We measure the force of friction.
The friction force can be reduced many times over if a lubricant is introduced between the rubbing surfaces. A layer of lubricant separates the surfaces of rubbing bodies. In this case, it is not the surfaces of the bodies that are in contact, but the layers of lubricant. Lubrication, in most cases, is liquid, and the friction of liquid layers is less than that of solid surfaces. For example, on skates, the low friction when sliding on ice is also explained by the action of the lubricant. A thin layer of water forms between the skates and the ice. Various oils are widely used in engineering as lubricants.
At sliding one body on the surface of another, friction will arise, which is called sliding friction. For example, such friction will occur when sleds and skis move on snow.
If one body does not slide, but rolls on the surface of another, then the friction that occurs in this case is called rolling friction . So, when the wheels of a wagon, a car move, when logs or barrels roll on the ground, rolling friction appears.
The force of friction can be measured. For example, to measure the sliding friction force of a wooden block on a board or table, you need to attach a dynamometer to it. Then evenly move the block along the board, keeping the dynamometer horizontal. What will the dynamometer show? Two forces act on the block in the horizontal direction. One force is the elastic force of the dynamometer spring directed in the direction of motion. The second force is the force of friction directed against the motion. Since the block moves uniformly, this means that the resultant of these two forces is zero. Therefore, these forces are equal in modulus, but opposite in direction. The dynamometer shows the elastic force (traction force), equal in modulus to the friction force.
Thus, by measuring the force with which the dynamometer acts on the body during its uniform motion, we measure the force of friction.
If a weight, for example, a weight, is placed on a bar and the friction force is measured using the method described above, then it will be greater than the friction force measured without a load.
The greater the force that presses the body to the surface, the greater the resulting friction force.By placing a block of wood on round sticks, the rolling friction force can be measured. It turns out to be less than the sliding friction force.
Thus, for equal loads, the rolling friction force is always less than the sliding friction force . That is why, in ancient times, people used rollers to drag large loads, and later they began to use the wheel.
Friction of rest.
Friction of rest.
We got acquainted with the force of friction arising from the movement of one body on the surface of another. But is it possible to talk about the force of friction between solid bodies in contact if they are at rest?
When a body is at rest on an inclined plane, it is held on it by friction. Indeed, if there were no friction, then the body would slide down the inclined plane under the influence of gravity. Consider the case when the body is at rest on a horizontal plane. For example, there is a wardrobe on the floor. Let's try to move it. If the cabinet is pressed lightly, then it will not move from its place. Why? The acting force in this case is balanced by the force of friction between the floor and the legs of the cabinet. Since this force exists between bodies at rest relative to each other, this force is called the static friction force.
In nature and technology, friction has great importance. Friction can be beneficial and harmful. When it is useful, they try to increase it, when it is harmful - to reduce it.
Without rest friction, neither people nor animals would be able to walk on the ground, since when walking we push off from the ground. When the friction between the sole of the shoe and the ground (or ice) is small, for example, in icy conditions, it is very difficult to push off the ground, the legs slip. So that the feet do not slip, the sidewalks are sprinkled with sand. This increases the frictional force between the sole of the shoe and the ice.
If there were no friction, objects would slip out of the hands.
The force of friction stops the car when braking, but without friction it could not stand still, it skidded. To increase friction, the surface of the tires on the car are made with ribbed protrusions. In winter, when the road is especially slippery, it is sprinkled with sand and cleared of ice.
Many plants and animals have various organs that serve for grasping (the antennae of plants, the elephant's trunk, the tenacious tails of climbing animals). All of them have a rough surface to increase friction.
Insert . Inserts are made of hard metals - bronze, cast iron or steel. Their inner surface is covered with special materials, most often babbit (it is an alloy of lead or tin with other metals), and lubricated. Bearings in which the shaft slides over the surface of the bushing during rotation are called plain bearings.
We know that the force of rolling friction under the same load is much less than the force of sliding friction. This phenomenon is based on the use of ball and roller bearings. In such bearings, the rotating shaft does not slide over the fixed bearing shell, but rolls along it on steel balls or rollers.
The device of the simplest ball and roller bearings is shown in the figure. The bearing inner ring, made of hard steel, is mounted on the shaft. The outer ring is fixed in the machine body. As the shaft rotates, the inner ring rolls on balls or rollers between the rings. Replacing plain bearings in the machine with ball or roller bearings can reduce the friction force by 20-30 times.
Ball and roller bearings are used in a variety of machines: cars, lathes, electric motors, bicycles, etc. Without bearings (they use friction), it is impossible to imagine modern industry and transportation.
195. There is a book on the table. What bodies does it interact with? Why is the book at rest?
The book lying on the table interacts with the Earth and with the table. It is at rest because these interactions are balanced.
196. Interaction of what bodies determines the movement of clouds; an arrow fired from a bow; projectile inside the gun barrel when fired; rotating the wings of a wind turbine?
The interaction of water droplets entering the cloud with air currents and the Earth.
Interaction with the bowstring, Earth and air.
Interaction with the gases formed as a result of the explosion of gunpowder, the barrel of the gun, its bed and the Earth.
The interaction of the wings of the mill with the oncoming air flow.
197. Give 3-5 names of bodies, as a result of interaction with which the ball can move (or change the direction of its movement).
Footballer's leg, tennis racket, golf club, baseball bat, airflow.
198. What will happen to a spring suspended on threads if the thread AB, which compresses it, is burned with a match (Fig. 38)?
The action of the thread A B on the spring will stop, and it will open and begin to move.
199. Why is it difficult for a firefighter to hold a hose from which water is beating?
Because of the phenomenon of rebound.
200. Why does the tube deviate when water flows out of it (Fig. 39)?
As a result of the interaction of the flowing water and the tube, the latter will begin to move.
201. Why does the tube not deviate if, in the path of the water flowing out of it (see problem 200), a cardboard is placed on the tube, as shown in Figure 40?
The interaction between the tube and water is balanced by the interaction between the cardboard and the tube, and so the tube remains at rest.
202. Why does a vessel suspended on a thread rotate when water flows out (Fig. 41)?
The flow of water flowing from the tubes acts on the walls of the tubes. As a result, the vessel rotates.
203. The flask is suspended on a thread (Fig. 42). Will the flask remain at rest when the water in it boils strongly? Explain the phenomenon.
No. see #202.
204. In some parks, children's playgrounds are equipped with wooden cylinders (drums) rotating on a horizontal axis. In what direction and when is the child running along it?
The child pushes away from the cylinder, which moves in the opposite direction.
205. A fish can move forward by throwing streams of water with its gills. Explain this phenomenon.
This principle of movement is called reactive. The water thrown off by the gills of the fish acts on the fish, which due to this comes into motion.
206. What is the purpose of the webbed feet in waterfowl?
Webbed feet allow increased interaction between water and birds.
207. Why should the butt of a rifle be pressed tightly against the shoulder when firing?
A loose buttstock due to recoil can injure the shoulder.
208. Why do projectiles and guns get different speeds when fired?
The mass of the gun is many times greater than the mass of the projectile, and, accordingly, the speed of the gun will be many times less than the speed of the projectile.
209. A boy jumps from a loaded barge to the shore. Why is the movement of the barge in the direction opposite to the jump imperceptible?
The mass of the barge is much greater than the mass of the boy, and as a result, the speed of the gun is practically zero.
210. At the same distance from the shore there is a boat with cargo and the same boat without cargo. Which boat is easier to jump ashore? Why?
It is easier to jump from a loaded boat because it has more mass.
211. a) In a compressed state, the spring on the stand is held with a thread (Fig. 43, a). If the thread is burned at point A, the spring will take off. Indicate the interaction of which bodies causes the movement of the spring.
b) If, for example, a ball is first placed on the spring, then it will also begin to move. The interaction of which bodies will cause the ball to move?
c) On the left cart there is a cube made of iron, on the right - made of wood (Fig. 43, b). A spring compressed with a thread is placed between the carts. If the thread is burned, then the carts will move. Which cart will get the most speed? Why?
a) The interaction of the spring, support and thread.
b) The interaction of the spring, thread, ball and support.
c) m1v1 = m2v2. This means that a trolley with a wooden block will acquire a greater speed, since it has a smaller mass.
212. The left cart (see problem 211, c) acquired a speed of 4 cm / s, the right - 60 cm / s. Which cart has more mass and by how much?
213. What is the mass of the left cart (see problem 212) if the mass of the right cart is 50 g?
214. A 90 kg pedestrian is moving at a speed of 3.6 km/h, and a 7.5 kg dog is running at a speed of 12 m/s. Find the ratio of the impulses of the pedestrian and the dog.
215. a) A steel plate is attached to the end of the spring (Fig. 44). The spring in the compressed state is held by the thread. If you burn the thread, the spring straightens and the steel plate simultaneously hits the balls that lie on the table. The masses of the balls are equal, but they are made of different metals (aluminum, lead, steel). What metal are ball 1, ball 2 and ball 3 made of? (In the figure, the position of each ball after impact is indicated by a dotted line.)
b) A spring compressed with a thread is placed between the carts (see Fig. 43, b). If the thread is burned, then as a result of interaction with the spring, the carts will begin to move. How will the speeds acquired by the carts differ if the mass of the left cart is 7.5 kg and that of the right cart is 1.5 kg?
216. A spring, the ends of which are pulled together by a thread, is placed between the carts as shown in Figure 45. There are vessels with sand on the carts. When the thread was burned out, the right cart acquired a greater speed than the left one. How can this be explained?
The left cart is heavier than the right one.
217. What is the mass of the right cart (see problem 216), if it has acquired 0.5 times more speed than the left cart, whose mass with a load is 450 g?
218. The boy chooses a rope, and the boats approach in the lake (Fig. 46). Which of the two identical boats acquires greater speed by the time of approach? Why?
The left boat has the highest speed, because it is lighter than the right one, in which the child is sitting.
219. During the interaction of two carts, their speeds changed by 20 and 60 cm / s. The mass of the larger trolley is 0.6 kg. What is the mass of the smaller cart?
220. The same forces were applied to the balls lying on the table during the same period of time. In this case, a ball with a mass of 3 kg acquired a speed of 15 cm / s. What is the speed of a 1 kg ball?
221. A boy weighing 45 kg jumped ashore from a stationary inflatable boat weighing 30 kg. In this case, the boat acquired a speed of 1.5 m/s relative to the shore. What is the boy's speed relative to the boat?
222. A boy, whose mass is 46 kg, jumped onto the shore at a speed of 1.5 m / s from a stationary raft weighing 1 ton. What speed did the raft acquire relative to the shore?
223. Can two initially immobile bodies, as a result of interaction with each other, acquire speeds that are identical in numerical value?
They can, provided that their masses are equal.
224. The air under the pump piston is compressed. Has the mass of air changed?
The mass of air has not changed.
225. A weight was lowered into a vessel with water. Has the weight of the weight changed?
The mass of the kettlebell has not changed.
226. Competing in pulling, two boys pull the rope in different directions, applying forces to it of 500 N each. Will a rope break if it can withstand only 800 N of tension?
It will not break, since a force of only 500 N acts on it.
227. Will the mass of water change when part of it turns into ice or steam?
Its mass will change by an amount equal to the mass of ice or steam.
>> Interaction of bodies
- Why does the moon move around the earth instead of flying into outer space? What body is called charged? How do charged bodies interact with each other? How often do we encounter electromagnetic interaction? These are just a few of the questions that we have to deal with in this section. Let's get started!
1. We make sure that the bodies interact
In everyday life, we constantly meet with various types of influences of some bodies on others. To open the door, you need to “act” on it with your hand, from the impact of your foot the ball flies into the goal, even sitting down on a chair, you act on it (Fig. 1.35, p. 38).
At the same time, when we open the door, we feel its effect on our hand, the effect of the ball on the foot is especially noticeable if you play football with bare feet, and the effect of the chair does not allow us to fall to the floor. That is, an action is always an interaction: if one body acts on another, then the other body also acts on the first.
Rice. 1.35. Examples of body interaction
You can clearly see that the action is not one-sided. Carry out a simple experiment: standing on skates, lightly push your friend. As a result, not only your friend will start moving, but also you yourself.
These examples confirm the conclusion of scientists that in nature we are always dealing with interaction, and not with one-way action.
Let us consider in more detail some types of interactions.
2. Recall the gravitational interaction
Why does any object, be it a pencil released from the hand, a leaf of a tree or a drop of rain, fall, move down (Fig. 1.36)? Why does an arrow shot from a bow not fly straight, but eventually fall to the ground? Why does the moon move around the earth? The reason for all these phenomena is that the Earth attracts other bodies to itself, and these bodies also attract the Earth to themselves. For example, the attraction of the Moon causes tides on the Earth (Fig. 1.37). Our planet and all other planets in the solar system are attracted to the Sun and to each other.
Rice. 1.36. Raindrops fall down under the gravity of the Earth
In 1687, the outstanding English physicist Isaac Newton (Fig. 1.38) formulated the law according to which there is mutual attraction between all bodies in the Universe.
Rice. 1.37. Tides are caused by the pull of the moon.
Such mutual attraction of material objects is called gravitational interaction. Based on experiments and mathematical calculations, Newton found that the intensity of gravitational interaction increases with increasing masses of interacting bodies. That is why it is easy to make sure that the Earth attracts us, but we do not feel the attraction of our neighbor on the desk at all.
3. Get acquainted with the macromagnetic interaction
There are other types of interactions as well. For example, if you rub a balloon with a piece of silk, it will begin to attract various light objects to itself: villi, rice grains, pieces of paper (Fig. 1.39). They say about such a ball that it is electrified, or charged.
Charged bodies interact with each other, but the nature of their interaction can be different: they either attract or repel each other (Fig. 1.40).
Rice. 1.38. Famous English scientist Isaac Newton (1643-1727)
For the first time, serious studies of this phenomenon were carried out by the English scientist William Gilbert (1544-1603) at the end of the 16th century.
Rice. 1.39. An electrified ball attracts a piece of paper
Rice. 1.40. Two charged balls interact with each other: a - attract; b - repel
Gilbert called the interaction between charged bodies electric (from the Greek word elektron - amber), since the ancient Greeks noticed that amber, if rubbed, begins to attract small objects to itself.
You well know that the compass needle, if allowed to rotate freely, always stops so that one end points north and the other south (Fig. 1.41). This is due to the fact that the compass needle is a magnet, our planet Earth is also a magnet, and a huge one, and two magnets always interact with each other. Take any two magnets, and as soon as you try to bring them closer to each other, you will immediately feel attraction or repulsion. This interaction is called magnetic.
Physicists have established that the laws describing electrical and magnetic interactions are the same. Therefore, in science it is customary to talk about a single electromagnetic interaction.
We encounter electromagnetic interactions literally at every step - after all, when walking, we interact with the road surface (we push off), and the nature of this interaction is electromagnetic. Thanks to electromagnetic interactions, we move, sit, write. We see, hear, smell and touch we also with the help of electromagnetic interaction (Fig. 1.42). The action of most modern appliances and household appliances is based on electromagnetic interaction.
Let's say more: the existence of physical bodies, including us, would be impossible without electromagnetic interaction. Ho how is the interaction of charged balls and magnets related to all this? - you ask. Do not hurry: studying physics, you will definitely make sure that this connection exists.
4. Facing Unresolved Problems
Our description will be incomplete if we do not mention two more types of interactions that were discovered only in the middle of the last century.
Rice. 1.41 The compass needle is always oriented to the north
Rice. 1.42 We see, we hear, we understand thanks to the electromagnetic interaction
They are called strong and weak interactions and act only within the microcosm. Thus there are four different kind interactions. Is there a lot? Of course, it would be much more convenient to deal with a single universal view interactions. Moreover, there is already an example of combining various interactions - electric and magnetic - into a single electromagnetic one.
For many decades, scientists have been trying to create a theory of such unification. Some steps have already been taken. In the 60s of the XX century, it was possible to create a theory of the so-called electroweak interaction, within which the electromagnetic and weak interactions were combined. But the complete ("great") unification of all types of interaction is still far away. Therefore, each of you has a chance to make a scientific discovery of world significance!
- Summing up
Interaction in physics is the action of bodies or particles on each other. We have briefly characterized two of the four types of interaction known to science: gravitational and electromagnetic.
The attraction of bodies to the Earth, planets to the Sun and vice versa - these are examples of the manifestation of gravitational interaction.
An example of an electrical interaction is the interaction of an electrified balloon with pieces of paper. An example of magnetic interaction is the interaction of a compass needle with the Earth, which is also a magnet, as a result of which one end of the needle always points north and the other end south.
Electric and magnetic interactions are manifestations of a single electromagnetic interaction.
- Control questions
1. Give examples of the interaction of bodies.
2. What types of interactions exist in nature?
3. Give examples of gravitational interaction.
4. Who discovered the law according to which there is a mutual attraction between all bodies in the Universe?
5. Give examples of electromagnetic interaction.
- Exercise
Write a short essay on the topic “My experience confirming the interaction of bodies” (it can even be poetry!).
- Physics and technology in Ukraine
A significant part of its short life Lev Vasilyevich Shubnikov (1901-1945) lived in Kharkov, where he headed the laboratory of low temperatures. The level of accuracy of many measurements in the laboratory was not inferior to the modern one. In the laboratory in the 1930s, oxygen, nitrogen and other gases were obtained in a liquid state. Shubnikov was the founder of the study of metals in the so-called superconducting state, when the electrical resistance of the material is zero. The highest award for a scientist is when the name of the scientist himself is used instead of a technical term to name the phenomenon he discovered. "Shubnikov-de Haas effect"; "Shubnikov's phase"; "Obreimov-Shubnikov method" - these are just a few examples of the contribution of the famous Ukrainian scientist to the construction of modern physics.
Physics. Grade 7: Textbook / F. Ya. Bozhinova, N. M. Kiryukhin, E. A. Kiryukhina. - X .: Publishing house "Ranok", 2007. - 192 p.: ill.
Phone interaction.
In the absence of interaction, the bodies move uniformly in inertial frames of reference. Only the action of one body on another leads to a change in the speed of its movement, to the appearance of acceleration. Therefore, the acceleration of the body serves as an indicator that the body has been affected by other bodies. However, the acceleration itself cannot serve as a measure of the interaction of bodies, since it depends not only on the characteristics of the interaction, but also on the properties of the body itself. Therefore, we need to determine on what characteristics of the body and on what characteristics of interaction the magnitude of acceleration depends.
When bodies (or systems of bodies) approach each other, the nature of their behavior changes. Since these changes are mutual, the bodies are said to interact with each other. When the bodies are separated over very large distances (to infinity), all currently known interactions disappear.
External and internal forces
Forces are a measure of the mechanical interaction of bodies. If the structure is considered in isolation from the surrounding bodies, then the action of the latter on it is replaced by forces that are called external. External forces acting on a body can be divided into active (independent) and reactive. Reactive forces arise in the bonds imposed on the body and are determined by the active forces acting on the body.
By way of application external forces divided into volume and surface.
Body forces are distributed over the entire volume of the body under consideration and are applied to each of its particles. In particular, body forces include the own weight of a structure, magnetic attraction, or inertial forces. The unit of measurement of body forces is the force related to the volume unit - kN/m 3 .
Surface forces are applied to surface areas and are the result of direct contact interaction of the object under consideration with the surrounding bodies. Depending on the ratio of the area of application of the load and the total surface area of the body under consideration, surface loads are divided into pump-concentrated and distributed. The former include loads, the real area of application of which is disproportionately smaller full area surface of the body (for example, the impact of columns on a foundation slab of sufficiently large dimensions can be considered as the action of concentrated forces on it). If the area of application of the load is comparable to the surface area of the body, then such a load is considered as distributed. Concentrated forces are measured in kN, and distributed forces - kN / m 2.
The interaction between the parts of the body under consideration is characterized by internal forces that arise inside the body under the action of external loads and are determined by the forces of intermolecular action.
The external forces acting on the structure are divided into active forces (load) and support reactions. By the nature of the action, there are concentrated forces measured in newtons (N, kN), a distributed load measured in newtons per meters (N / m, kN / m), if the load is distributed along the line, or in newtons per square meter (N / m 2, kN / m 2), if the load is distributed over the surface, the concentrated moment, measured in newtonometers (Nm, kNm) (Fig. 1.2). Support reactions are calculated through active forces by methods of theoretical mechanics.
Under the action of external forces, the rod is deformed, while additional interaction forces appear between the individual parts of the rod, called internal forces. If the rod is mentally cut by a plane perpendicular to the longitudinal axis of the rod Z, then internal forces will be transferred from one part of the rod to the other part over the entire cross-sectional area. Let's discard the right part of the rod. The internal forces transmitted from it to the left side (Fig. 1.3), in relation to the left side of the rod, become external forces and can be represented by the main vector and the main moment. The center of reference is the center of gravity of the cross section of the rod, through which the coordinate axes X,Y, lying in the plane of the section, and the Z axis, perpendicular to the plane of the cross section. The main vector is decomposed into forces N, Q x , Q y , and main point– for moments M x , M y , M z . These six quantities are called internal forces (internal force factors) of the rod. Each of them has its own name: N - longitudinal (normal) force, Q x and Q y - transverse (cutting) forces, M x and M y - bending moments, M z - torque.
Law of conservation of momentum.
When bodies interact, the momentum of one body can be partially or completely transferred to another body. If a system of bodies is not affected by external forces from other bodies, then such a system is called closed.
In a closed system, the vector sum of the impulses of all bodies included in the system remains constant for any interactions of the bodies of this system with each other.
This fundamental law of nature is called the law of conservation of momentum. It is a consequence of Newton's second and third laws.
Consider any two interacting bodies that are part of a closed system. The interaction forces between these bodies will be denoted by and According to Newton's third law If these bodies interact during time t, then the impulses of the interaction forces are identical in absolute value and directed in opposite directions: Let's apply Newton's second law to these bodies:
This equality means that as a result of the interaction of two bodies, their total momentum has not changed. Considering now all possible pair interactions of bodies included in a closed system, we can conclude that the internal forces of a closed system cannot change its total momentum, i.e., the vector sum of the momenta of all bodies included in this system.
The law of conservation of momentum in many cases makes it possible to find the velocities of interacting bodies even when the values of the acting forces are unknown. Jet propulsion is an example. Law of conservation of momentum (Law of conservation of momentum) asserts that the sum of the momenta of all bodies (or particles) of a closed system is a constant value.
IN classical mechanics the law of conservation of momentum is usually derived as a consequence of Newton's laws. From Newton's laws, it can be shown that when moving in empty space, momentum is conserved in time, and in the presence of interaction, the rate of its change is determined by the sum of the applied forces.
Like any of the fundamental laws of conservation, the law of conservation of momentum describes one of the fundamental symmetries - the homogeneity of space.
center of inertia. The theorem on the motion of the center of inertia. Examples.
Center of inertia
The momentum of a closed mechanical system has various meanings with respect to different inertial frames of reference. If the reference frame K "moves relative to the frame K with a speed V, then the particle velocities v" α and v α in these systems are related by the relation v α \u003d v " α + V. Therefore, the relationship between the values P and P" of the momentum in these systems is given by the formula :
(1.69)
(1.70)
It is always possible to choose such a frame of reference K" in which the total momentum vanishes. Putting P" = 0, we find that the speed of this frame of reference
. (1.71)
If the total momentum of a mechanical system is zero, then it is said to be at rest with respect to the corresponding coordinate system. The speed V has the meaning of the speed of movement of a mechanical system as a whole with a non-zero momentum. The relationship between the momentum P and the velocity V of the system as a whole is the same as it would be between the momentum and the velocity of one material point with a mass equal to the sum of the masses in the system, .
The right side of formula (1.71) can be represented as the total time derivative of the expression:
(1.72)
We can say that the speed V of the system as a whole is the speed of movement in space of a point whose radius vector is given by formula (1.72). Such a point is the center of inertia of the system.
The law of conservation of momentum of a closed system can be formulated as a statement that its center of inertia moves in a straight line and uniformly. This is a generalization of the law of inertia for a free material point.
The energy of a mechanical system at rest as a whole is usually called its internal energy E int. It consists of the kinetic energy of the motion of particles relative to each other and the potential energy of their interaction. The total energy of a system moving as a whole with a speed V,
(1.73
CENTER OF INERTIA
(center of mass) - geom. point, the position of which characterizes the distribution of masses in the body or mechanical. system. Coordinates of C. and. are defined by f-lams
or for the body continuous distribution masses
where m k - masses of material points that form the system; x k , y k , z k - coordinates of these points; M =Sm k - mass of the system; r(x, y, z) - density; V is the volume. The concept of C. and. differs from the concept of the center of gravity in that the latter makes sense only for solid body located in a uniform gravitational field; the concept of C. and. not associated with any force field and makes sense for any mechanical. systems. For a rigid body of the position C. and. and center of gravity are the same.
When moving mechanical systems of its C. and. moves as it would material point, which has a mass equal to the mass of the system, and is under the influence of all external. forces applied to the system. In addition, some-ryeur-niya movement of the mechanical. systems (bodies) in relation to the axes having the beginning in C. and. and moving along with C. and. translationally, retain the same form as for motion with respect to the inertial frame of reference. In view of these properties, the concept of C. and. plays important role in the dynamics of a system and a rigid body. S. M. Torg.
Push the wall. Right now, walk up and push the wall hard. Has anything happened? Hardly. Then push the wall not just hard, but with all your might. Did it happen this time? With a wall - hardly, but you, most likely, flew off the wall for some distance. How so?
After all, it was you who pushed the wall, but it turned out that it was the wall that pushed you. Another example is billiards. When we hit a ball with a cue and hit another ball, the second ball starts moving, but the first one also flies off into reverse side or sideways. The third example is a hammer. When a nail is struck with a hammer, not only is the nail hammered into the wall, but the hammer bounces back and can hit the unlucky craftsman in the forehead. In all these examples, we acted with one body on another, but it turned out that the other body also acted on the first. In physics, the action of two bodies on each other is called an interaction.
Interaction of bodies in physics
When two bodies interact, both bodies always feel the result. That is, by saying plain language, always when exposed to something, a return follows. Probably, all pugnacious boys know that during a fight, not only the enemy’s face suffers, but you can also beat your own fists. That is, while one bully attacks the other bully's nose with his fist, the nose at that time attacks the fist in response. However, the nose suffers much more. Well, everything is clear with the nose - it is softer and therefore more damaged, but why does the ball fly off much stronger when hit with a cue, whose cue at the same time? That is, the cue does not fly off, and we, along with it, a few meters from the table? And this is due to the fact that bodies are more inert and less inert.
Types of interaction of bodies and measure of interaction
About a body that changes its speed more slowly during interaction, they say that it is more inert and has a large mass. And a body that changes its speed faster, we call less inert, and we say that it has less mass. That is why we do not fly off the table when hitting the ball with a cue and, on the contrary, fly off the wall when we try to push the wall and, accordingly, the whole house to which it is attached. The mass of us with a cue is much greater than the mass of a billiard ball, but at the same time much less than the mass of a house, even if we pile a wife, three children, a bunch of bagels and a cat on our shoulders.
Acquaintance with the interaction of bodies is considered in the 7th grade physics course.
The measure of the interaction of bodies is force. There are 4 types of interactions that are not reducible to each other: gravitational, electromagnetic, strong and weak. But this topic is discussed in detail in the 10th grade course.
