How does a body move if no other forces act on it? How does a body move if no other forces act on it? The body moves uniformly in a straight line. Does this change his speed? The body moves uniformly in a straight line. Does this change his speed? How is Newton's first law read? How is Newton's first law read? Is a reference frame moving with acceleration relative to an inertial frame inertial? Is a reference frame moving with acceleration relative to an inertial frame inertial? What is the reason for the accelerated movement of bodies What is the reason for the accelerated movement of bodies
How is Newton's second law read? How is Newton's second law read? How to read Newton's third law How to read Newton's third law What reference systems are called inertial? What reference systems are called inertial? What reference systems are called non-inertial? What reference systems are called non-inertial? Express the unit of force in terms of the unit of mass and acceleration. Express the unit of force in terms of the unit of mass and acceleration.
The story of how “The swan, the crayfish and the pike began to carry a load of luggage” is known to everyone. The story of how “The swan, the crayfish and the pike began to carry a load of luggage” is known to everyone. ...The swan rushes into the clouds, ...The swan rushes into the clouds, the crayfish moves back, the crayfish moves back, And the pike pulls into the water. And the pike pulls into the water. Justify the inconsistency of this statement from the point of view of classical mechanics. Justify the inconsistency of this statement from the point of view of classical mechanics.
Fill in the blanks: Fill in the blanks: By the action of a force, the body moves... By the action of a force, the body moves... If, with a constant mass of the body, the force is increased by 2 times, then the acceleration... by... times. If, with a constant body mass, the force is increased by 2 times, then the acceleration ... by ... times. If the mass of a body is reduced by 4 times, and the force acting on the body is increased by 2 times, then the acceleration ... by ... times. If the mass of a body is reduced by 4 times, and the force acting on the body is increased by 2 times, then the acceleration ... by ... times. If the force is increased by 3 times, and the mass ..., then the acceleration will remain unchanged. If the force is increased by 3 times, and the mass ..., then the acceleration will remain unchanged.
Graphs of the dependence of the projection of velocity and acceleration on time for rectilinear motion are given. Indicate in which areas the actions of surrounding bodies are compensated. What is the direction of the resultant force in relation to the direction of motion? Graphs of the dependence of the projection of velocity and acceleration on time for rectilinear motion are given. Indicate in which areas the actions of surrounding bodies are compensated. What is the direction of the resultant force in relation to the direction of motion? v a
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 travels equal distances in any equal intervals of time, its motion is considered uniform.
Uniform movement is very rare. The Earth moves almost uniformly around the Sun; every year the Earth makes one revolution around the Sun.
Almost never does a car driver manage to maintain uniform motion - for various reasons he has to either speed up or slow down. The movement of the clock hands (minute and hour) only seems uniform, which is easy to verify by observing 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. Gas molecules hitting each other stop for a while and then accelerate again. During subsequent collisions, with other molecules, they again slow down their movement in space.
These are all examples of uneven motion. This is how the train moves, leaving the station, passing larger and larger tracks in equal periods of time. A skier or skater covers equal distances in different times in competitions. This is how a plane takes off, a door opens, or a falling snowflake moves.
If a body travels different paths at equal intervals of time, then its motion is called uneven.
Uneven movement can be observed experimentally. The picture shows a cart with a dropper from which drops fall at regular intervals. When the cart moves under the influence of a load, we see that the distances between the traces of the drops are not the same. And this means that in the same periods of time the cart travels different paths.
Speed. Units of speed.
We often say that some bodies move faster, others slower. For example, a tourist is walking along the highway, a car is rushing, an airplane is flying in the air. Let us assume that they all move uniformly, nevertheless, the movement of these bodies will be different.
A car moves faster than a pedestrian, and an airplane moves faster than a car. In physics, the quantity that characterizes the speed of movement is called velocity.
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.
Velocity during uniform motion of a body shows how far the body has traveled per unit time.
Thus, using the concept of speed, we can now say that the tourist, the car and the plane are moving at different speeds.
With uniform motion, the speed of the body remains constant.
If a cyclist travels a distance of 25 m in 5 seconds, then his speed will be 25m/5s = 5m/s.
To determine the speed during uniform motion, the distance traveled by the body in a certain period of time must be divided by this period of time:
speed = path/time.
Speed is denoted by v, path by s, time by t. The formula for finding speed will look like this:
The speed of a body during uniform motion is a quantity equal to the ratio of the path to the time during which this path is covered.
In the International System (SI), speed is measured in meters per second (m/s).
This means that the unit of speed is taken to be the speed of such uniform motion that in one second the body travels a distance of 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, that is, we’ll convert kilometers into meters, and hours into seconds:
54 km/h = 54000 m/ 3600 s = 15 m/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 its numerical value, has a direction.
For example, if you need to indicate where a plane departing from Vladivostok will be in 2 hours, then you need to indicate not only the value of its speed, but also its destination, i.e. its direction. Quantities that, in addition to a numerical value (modulus), also have a direction, are called vector.
Speed is a vector physical quantity.
All vector quantities are designated by the corresponding letters with an arrow. For example, speed is denoted by the symbol v with an arrow, and the velocity module is indicated 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, when a body moves, its speed changes from one section of the path to another, then such movement is uneven. To characterize the uneven movement of a body, the concept of average speed was introduced.
For example, a train from Moscow to St. Petersburg travels at a speed of 80 km/h. What speed do they 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 is moving unevenly, which means that the speed of 80 km/h is the average speed of the train.
It is determined in almost the same way as speed during uniform motion.
To determine the average speed of a body during uneven movement, the entire distance traveled must be divided by the entire time of movement:
It should be recalled that only with uniform motion will the s/t ratio be constant over any period of time.
With uneven movement of a body, 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 points in time during this period.
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 route and time of movement.
If the speed of a body and time during uniform motion are known, then the distance traveled by it can be found.
Since v = s/t, the path is determined by the formula
To determine the distance traveled by a body during uniform motion, the speed of the body must be multiplied 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 time during uneven motion, the distance traveled by the body must be divided by the speed of its movement.
If a body moves unevenly, then, knowing its average speed of movement and the time during which this movement occurs, find the path:
Using this formula, you can determine the time when the body moves unevenly:
Inertia.
Observations and experiments show that the speed of a body by itself cannot change.
Experience with trolleys. Inertia.
A soccer ball lies on the field. With a kick, the football player sets it in motion. But the ball itself will not change its speed and will not begin to move 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 the powder gases.
Thus, both the ball and the bullet do not have their own speed until they are acted upon by other bodies.
A soccer ball rolling on the ground stops due to friction with the ground.
A body reduces its speed and stops not by itself, but under the influence of other bodies. Under the influence of another body, the direction of speed also changes.
A tennis ball changes direction after hitting the racket. After hitting the hockey player’s stick, the puck also changes its direction of movement. The direction of movement of a gas molecule changes when it hits another molecule or the walls of a container.
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 place the board at an angle on the table. Place a pile of sand on the table, a short distance from the end of the board. Place the cart on the inclined board. The cart, having rolled down the inclined board, quickly stops, hitting the sand. The speed of the cart decreases very quickly. Its movement is uneven.
Let's level the sand and release the cart again from the previous height. The cart will now travel a greater distance across the table before it stops. Its speed changes more slowly, and its movement becomes closer to uniform.
If you completely remove sand from the path of the cart, then the only obstacle to its movement will be friction on the table. The cart gets to the stop even slower, and it will travel further than the first and second time.
So, the less the effect of another body on the cart, the longer the speed of its motion 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 established experimentally? Thorough experiments to study the motion of bodies were first carried out by G. Galileo. They made it possible to establish that if a body is not acted upon by other bodies, 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 the action of other bodies 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 movement by inertia.
For example, a bullet fired from a gun would still fly, maintaining its speed, if it were not 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 stops pedaling and continues moving. He would be able to maintain the speed of his movement if the force of friction did not act on him.
So, If the body is not acted upon by other bodies, then it moves at a constant speed.
Interaction of bodies.
You already know that when moving unevenly, the speed of a body changes over time. A change in the speed of a body occurs under the influence of another body.
Experience with trolleys. The carts move relative to the table.
Let's do an experiment. We will attach an elastic plate to the cart. Then we bend it and tie it with thread. The cart is at rest relative to the table. Will the cart move if the elastic plate straightens?
To do this, we will cut the thread. The plate will straighten out. The cart will remain in the same place.
Then we will place another similar cart close to the bent plate. Let's burn the thread again. After this, both carts begin to move 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 begin to move.
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 considered the simplest case of interaction of two bodies. Before the interaction, both bodies (carts) were at rest relative to each other and relative to the table.
Boat experience. The boat moves away 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 a shot), the bullet and the gun move in different directions. The result is a phenomenon of recoil.
If a person sitting in a boat pushes another boat away from him, then interaction occurs. Both boats begin to move.
If a person jumps from a boat to the shore, then the boat moves in the direction opposite to the jump. The man acted on the boat. In turn, the boat also affects the person. It acquires a speed that is directed toward the shore.
So, As a result of interaction, both bodies can change their speed.
Body mass. Unit of mass.
When two bodies interact, the velocities of the first and second bodies always change.
Experience with trolleys. One is bigger than the other.
After interaction, one body acquires a speed that can differ significantly from the speed of another body. For example, after shooting from a bow, the speed of the arrow is much greater than the speed that the bow string acquires after the 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, the carts move away at different speeds. A cart that moves slower after interaction is called more massive. She has more weight. A cart that moves at a higher speed after the interaction has less mass. This means that the carts have different masses.
The speeds acquired by the carts as a result of the interaction can be measured. These speeds are used to compare the masses of interacting carts.
Example. The speeds of the carts before interaction are zero. After the interaction, the speed of one cart became 10 m/s, and the speed of the other 20 m/s. Since the speed acquired by the second cart If the speed of the first one is 2 times greater, then its mass is 2 times less than the mass of the first cart.
If, after interaction, the velocities of the initially stationary carts are the same, then their masses are the same. Thus, in the experiment depicted in Figure 42, after the interaction the carts move apart at equal speeds. Therefore, their masses were the same. If after interaction the bodies acquire different speeds, then their masses are different.
International standard kilogram. In the picture: the US kilogram standard.
How many times the speed of the first body is greater (less than) the speed of the second body, how many times the mass of the first body is less (greater) than the mass of the second.
How body speed changes less when interacting, the more mass it has. Such a body is called more inert.
And vice versa than body speed changes more during interaction, the less mass it has, the more less it inert.
This means that all bodies have the characteristic property of changing their speed differently when interacting. This property is called inertia.
Body mass is a physical quantity that characterizes its inertia.
You should know that any body: Earth, man, book, etc. - has mass.
Mass is designated by the letter m. The SI unit of mass is the kilogram ( 1 kg).
Kilogram- this is the mass of the standard. The standard is made of an alloy of two metals: platinum and iridium. The international standard kilogram is stored 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 located in our country, at the Institute of Metrology named after. D.I. Mendeleev in St. Petersburg.
In practice, other units of mass are 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.
Measuring body weight on scales.
To measure body weight, you can use the method described in paragraph 19.
Training scales.
By comparing the velocities acquired by bodies during interaction, they determine how many times the mass of one body is greater (or less) than the mass of the other. 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, the masses of celestial bodies, as well as molecules and atoms, are determined in science.
In practice, body weight can be found using scales. There are various types of scales: educational, medical, analytical, pharmaceutical, electronic, etc.
Special set of weights.
Let's consider training scales. The main part of such scales is the rocker arm. 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 carts that were used in the experiment on the scales (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 bodies lying on the scales are equal to each other.
Now, on one pan of the scale, we place the body whose mass we need to find out. We will place weights whose masses are known on the other until the scales are in equilibrium. Consequently, the mass of the body being weighed will be equal to the total mass of the weights.
When weighing, a special set of weights is used.
Different scales are designed to weigh different bodies, both very heavy and very light. So, for example, using carriage scales, you can determine the mass of a carriage from 50 tons to 150 tons. The mass of a mosquito, equal to 1 mg, can be determined using analytical balances.
Density of matter.
We weigh two cylinders of equal volume. One is aluminum and the other is lead.
The bodies around us consist of various substances: wood, iron, rubber, etc.
The mass of any body depends not only on its size, but also on what substance it consists of. Therefore, bodies that have the same volumes, but consist of different substances, have different masses.
Let's do this experiment. Let's weigh two cylinders of the same volume, but consisting of different substances. For example, one is made of aluminum, the other is made of 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.
Thus, an iron bar weighing 1 ton occupies a volume of 0.13 m 3, and ice with the same mass of 1 ton occupies a volume of 1.1 m 3. The volume of ice is almost 9 times the volume of the 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 give an example. Aluminum with a volume of 1 m3 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 m3), lead has a mass that is approximately 4 times greater than the mass of aluminum.
Density shows the mass of a substance taken in a certain volume.
How can you find the density of a substance?
Example. A marble slab has a volume of 2 m 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 2m3 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 2700 kg per 1 m 3.
This means that if the mass of a body and its volume are known, the density can be determined.
To find the density of a substance, you need 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.
Let us denote the quantities included in this expression by letters: the density of the substance is ρ (Greek letter “rho”), the mass of the body is m, its volume is V. Then we obtain a formula for calculating density:
The SI unit of density of a substance is kilogram per cubic meter (1kg/m3).
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/m3, then it can be converted to g/cm3 as follows.
Example. The density of silver is 10,500 kg/m3. Express it in g/cm3.
10,500 kg = 10,500,000 g (or 10.5 * 10 6 g),
1m3 = 1,000,000 cm3 (or 10 6 cm3).
Then ρ = 10,500 kg/m 3 = 10.5 * 10 6 / 10 6 g/cm 3 = 10.5 g/cm 3.
It should be remembered that the density of the same substance in solid, liquid and gaseous states is different. Thus, the density of ice is 900 kg/m3, water is 1000 kg/m3, and water vapor is 0.590 kg/m3. 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 normal atmospheric 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 | Plexiglas | 1200 | 1,2 |
| Brass | 8500 | 8,5 | Capron | 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 normal atmospheric pressure t=20 °C)
Table 4
Densities of some gases (at normal atmospheric pressure t=20 °C)
Calculation of mass and volume based on its density.
Knowing the density of substances is very important for various practical purposes. An engineer, when designing a machine, can calculate the mass of the future machine in advance based on the density and volume of the material. The builder can determine what the mass of the building under construction will be.
Therefore, knowing the density of a substance and the volume of a body, it is always possible to determine its mass.
Since the density of a substance can be found using 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, the density must be multiplied by the volume.
Example. Determine the mass of a steel part with a volume of 120 cm3.
From Table 2 we find that the density of steel is 7.8 g/cm 3 . Let's write down the conditions of the problem and solve it.
Given:
V = 120 cm 3;
ρ = 7.8 g/cm3;
Solution:
m = 120 cm 3 7.8 g/cm 3 = 936 g.
Answer: m= 936 g
If the mass of a body and its density are known, then the volume of the body can be expressed from the formula m = ρV, i.e. the volume of the body will be equal to:
V = m/ρ.
To calculate the volume of a body if its mass and density are known, the mass must be divided 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 conditions of the problem and solve it.
Given:
ρ = 0.93 g/cm 3
Solution:
V = 930/0.93 g/cm 3 = 1000 cm 3 = 1 l.
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 encounters various cases of the action of bodies on each other. As a result of interaction, the speed of movement of a body changes. You already know that the speed of a body changes the more, the smaller its mass. Let's look at some examples that prove this.
By pushing the trolley with our hands, we can set it in motion. The speed of the trolley changes under the influence of the human hand.
A piece of iron lying on a plug lowered into water is attracted by a magnet. A piece of iron and a cork change their speed under the influence of a magnet.
By acting on the spring with your hand, you can compress it. First, the end of the spring moves. 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 was compressed, the acting body was the human hand. When a spring straightens, the acting body is the spring itself. She sets the ball in motion.
You can use your racket or hand to stop or change the direction of movement of a flying ball.
In all the examples given, one body, under the influence of another body, begins to move, 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 simply says that a force acts on a body or a force is applied to it. This means that force can be considered as the reason for the change in speed.
By pushing the trolley with our hands, we can put it into action. |
Experiment with a piece of iron and a magnet. |
Spring experiment. We set the ball in motion. |
Experience with a racket and a flying ball. |
A force acting on a body can not only change the speed of its body, but also its individual parts.
A board lying on supports bends when 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 give another example. A board lying on supports bends if a person or any other load sits on it. The middle of the board moves a greater distance than the edges.
Under the influence of a force, the speed of different bodies at the same time can change equally. To do this, it is necessary to apply different forces to these bodies.
So, to move a truck, more force 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 shown as a straight line segment with an arrow at the end.
Force, 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 denotes the direction), and its module is also denoted by the letter F, but without the arrow.
When talking about force, it is important to indicate to which point of the body the force is applied.
In the drawing, 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 conventionally 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 gravity. Gravity.
Let's release the stone from our hands - it will fall to the ground.
If you let go of a stone from your hands, it will fall to the ground. The same thing will happen with any other body. If a ball is thrown horizontally, it does not travel straight and evenly. Its trajectory will be a curved line.
The stone flies along a curved line.
The artificial Earth satellite also does not fly in a straight line, it flies around the Earth.
An artificial satellite moves around the Earth.
What is the reason for the observed phenomena? Here's the thing. These bodies are acted upon by a force - the force of gravity towards the Earth. Due to gravity towards the Earth, bodies raised above the Earth and then lowered fall. And also, because of this attraction, we walk on the Earth, and do not fly into endless Space, where there is no air to breathe.
The leaves of the trees fall to the Earth because the Earth attracts them. Due to gravity towards 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 attract 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 by many meters. You are well aware that the Earth and other planets move around the Sun, attracted to it and to each other.
The attraction of all bodies in the Universe to each other is called universal gravity.
The English scientist Isaac Newton was the first to prove and establish the law of universal gravitation.
According to this law, The greater the mass of these bodies, the greater the force of attraction between bodies. The forces of attraction between bodies decrease if the distance between them increases.
For everyone living on Earth, one of the most important values is the force of gravity towards the Earth.
The force with which the Earth attracts a body towards itself is called gravity.
Gravity is denoted by the letter F with the index: Fgravity. It is always directed vertically downwards.
The globe is slightly flattened at the poles, so bodies located 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 a mountain is slightly 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 also the same.
Elastic force. Hooke's law.
You already know that all bodies on Earth are affected by gravity.
A book lying on the 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 lying on a support or suspended on a thread rest? Apparently, gravity is balanced by some other force. What kind of power is this and where does it come from?
Let's conduct an experiment. Place a weight in the middle of a horizontal board, placed on supports. Under the influence of gravity, the weight will begin to move down and bend the board, i.e. the board is deformed. In this case, a force arises with which the board acts on the body located on it. From this experiment we can conclude that, in addition to the force of gravity directed vertically downward, another force acts on the weight. This force is directed vertically upward. She balanced the force of gravity. This force is called elastic force.
So, the force that arises in a 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 Fup.
The more 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 a thread. The thread (suspension) stretches. An elastic force arises in the thread (suspension), as well as in the support. When the suspension is stretched, the elastic force is equal to the force of gravity, then the stretching stops. Elastic force occurs only when bodies are deformed. If the deformation of the body disappears, then the elastic force also disappears.
Experience with a body suspended by a thread.
There are different types of deformations: tension, compression, shear, bending and torsion.
We have already become familiar with 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 force of elasticity depends on deformation.
Let's consider experience. Let's take a rubber cord. We will 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 on the free end of the cord, the cord will lengthen. Its length will become equal to l. The cord extension can be found like this:
If you change the weights on the cup, the length of the cord will also change, and therefore its elongation Δl.
Experience has shown that the modulus of the elastic force when stretching (or compressing) a 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 = -kΔl,
Body weight is the force with which the 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 proportionality coefficient, which is called rigidity.
The rigidity of a body depends on the shape and size, 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 deforming the body, it returns to its original position, then the deformation is elastic.
You will study Hooke's law and types of deformations in more detail in high school.
Body weight.
The concept of “weight” is used very often in everyday life. Let's try to find out what this value is. In experiments, when a 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 the support with a force called body weight . If a body is suspended by a thread, then not only the thread is stretched, but also the body itself.
Body weight is the force with which the body, due to attraction to the Earth, acts on a support or suspension.
Body weight is a vector physical quantity and is denoted by the letter P with an arrow above this letter, directed 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 stationary or moving uniformly and rectilinearly, then the weight of the body in its numerical value is equal to the force of gravity, i.e.
P = F heavy
It should be remembered that gravity is the result of the interaction between the body and the Earth.
So, body weight is the result of the interaction of the body and the support (suspension). The support (suspension) and the body are deformed, which leads to the appearance of an elastic force.
Units of force. The relationship between gravity and body weight.
You already know that force is a physical quantity. In addition to the numerical value (modulus), it has a direction, i.e. it is a vector quantity.
Force, like any physical quantity, can be measured and compared with force taken as a unit.
Units of physical quantities are always chosen arbitrarily. So, any force can be taken as a unit of force. For example, one can take the elastic force of a spring stretched to a certain length as a unit of force. The unit of force can also be taken as the force of gravity acting on a body.
Do you know that force causes a change in the speed of a body. That is why The unit of force is the force that changes the speed of a body weighing 1 kg by 1 m/s in 1 s.
This unit is named after the English physicist Newton. Newton (1 N). Other units are often used - kilonewtons (kN), millinewtons (mN):
1 kN = 1000 N, 1 N = 0.001 kN.
Let's try to determine the magnitude of the force in 1 N. It has been established that 1 N is approximately equal to the force of gravity, which acts on a body weighing 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 we know 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 weighing 1/9.8 kg is subject to a force of gravity equal to 1 N, then a body weighing 2/9.8 kg will be subject to a force of gravity equal to 2 N.
On a body weighing 5/9.8 kg - the force of gravity is 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 = 1 kg, then a force of gravity equal to 9.8 N will act on a body weighing 1 kg. The value of the force of gravity acting on a body weighing 1 kg can be written as follows: 9.8 N/kg.
This means that if a force equal to 9.8 N acts on a body weighing 1 kg, then a force equal to 2 times greater will act on a body weighing 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:
Ftie = 9.8 N/kg m.
The value 9.8 N/kg is denoted by the letter g, and the formula for gravity will be:
where m is mass, g is called acceleration of free fall. (The concept of acceleration due to gravity will be taught in 9th grade.)
When solving problems where great accuracy is not required, g = 9.8 N/kg is rounded to 10 N/kg.
You already know that P = Ftie, if the body and support are stationary or moving uniformly and rectilinearly. Therefore, body weight can be determined by the formula:
Example. There is a kettle with water weighing 1.5 kg on the table. Determine the force of gravity and the weight of the teapot. Show these forces in Figure 68.
Given:
g ≈ 10 N/kg
Solution:
Ftie = P ≈ 10 N/kg 1.5 kg = 15 N.
Answer: Ftie = P = 15 N.
Now let's depict the forces graphically. Let's choose a 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 taken into account that the force of 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. To measure force, a device called dynamometer (from Greek dynamis- force, metreo- I measure).
Dynamometers come in various designs. Their main part is a steel spring, which is given different shapes depending on the purpose of the device. The design of a simple dynamometer is based on comparing any force with the elastic force of a spring.
The simplest dynamometer can be made from a spring with two hooks mounted on a board. A pointer is attached to the lower end of the spring, and a strip of paper is glued to the board.
Mark on paper with a dash the position of the pointer when the spring is not tensioned. This mark will be the zero division.
Manual dynamometer - strength meter.
Then we will hang a load weighing 1/9.8 kg, i.e. 102 g, from the hook. A gravity force of 1 N will act on this load. Under the influence of this force (1 N), the spring will stretch and the pointer will move down. We mark its new position on paper and put the number 1. After that, we hang a load weighing 204 g and put a mark 2. This means that in this position the elastic force of the spring is 2 N. Having suspended a load weighing 306 g, we put a mark 3, and so on 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 whole mark are divided into ten equal parts. This can be done, taking into account that the elastic force of the spring Fupr increases as many times as its elongation Δl increases. This follows from Hooke's law: Fupr = kΔl, i.e. the elastic force of a body when stretched is directly proportional to the change in the length of the body.
Traction dynamometer.
A graduated spring will be the simplest dynamometer.
Using a dynamometer, not only gravity is measured, but also other forces, such as elastic force, friction force, etc.
For example, to measure the strength of various human muscle groups, it is used medical dynamometers.
To measure the muscular strength of the arm when clenching the hand into a fist, a manual dynamometer - strength meter .
Mercury, hydraulic, electric and other dynamometers are also used.
Recently, electric dynamometers have been widely used. They have a sensor that converts the strain into an electrical signal.
To measure large forces, such as, for example, traction forces of tractors, prime movers, 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 with one force equivalent in its effect to these forces.
A force that produces the same effect on a body as several simultaneously acting forces is called the resultant of these forces.
Let us find the resultant of these two forces acting on the body along one straight line in one direction.
Let's turn to experience. We hang two weights weighing 102 g and 204 g from the spring, one below the other, i.e., weighing 1 N and 2 N. Note the length to which the spring is stretched. Let's remove these weights and replace them with one weight, which the spring stretches to the same length. The weight of this load turns out to be 3 N.
From experience it follows 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 component forces 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 a body along one straight line in different directions. The body is a dynamometer table. Let's place a weight weighing 5 N on the table, i.e. Let's act on it with a force of 5 N directed downwards. Let's tie a thread to the table and act on it with a force equal to 2 N, directed upward. Then the dynamometer will show a force of 3 N. This force is the resultant of two forces: 5 N and 2 N.
So, the resultant of two forces directed along one straight line in opposite directions is directed towards the larger force in magnitude, and its module is equal to the difference in the modules of the component forces(rice.):
If two equal and oppositely directed 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 sled has rolled down the mountain and soon stops.
The sled, having rolled down the mountain, moves unevenly along a horizontal path, its speed gradually decreases, and after a while it stops. The man, having taken a running start, slides on his skate across the ice, but no matter how smooth the ice is, the man still stops. The bicycle also stops when the cyclist stops pedaling. We know that the cause of such phenomena is force. In this case it is the friction force.
When one body comes into contact with another, an interaction occurs that prevents their relative motion, which is called friction. And the force characterizing this interaction is called friction force.
Friction force- this is another type of force, different from the previously discussed gravity and elastic force.
Another reason for friction is mutual attraction of molecules of contacting bodies.
The occurrence of friction force is mainly due to the first reason, when the surfaces of bodies are rough. But if the surfaces are well polished, then upon 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 manifest itself noticeably.
Experiment with a block and a dynamometer. We measure the friction force.
The friction force can be reduced many times if a lubricant is introduced between the rubbing surfaces. A layer of lubricant separates the surfaces of the rubbing bodies. In this case, it is not the surfaces of the bodies that come into contact, but the layers of lubricant. Lubrication is in most cases liquid, and the friction of liquid layers is less than that of solid surfaces. For example, on ice skates, the low friction when sliding on ice is also due to the effect of lubrication. A thin layer of water forms between the skates and the ice. In technology, various oils are widely used as lubricants.
At sliding one body on the surface of another will experience friction, 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 arises in this case is called rolling friction . Thus, when the wheels of a carriage or car move, or 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 move the block evenly along the board, holding the dynamometer horizontally. 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 movement. The second force is the frictional force directed against the movement. Since the block moves uniformly, this means that the resultant of these two forces is zero. Consequently, these forces are equal in magnitude, but opposite in direction. The dynamometer shows the elastic force (traction force), equal in magnitude to the friction force.
Thus, By measuring the force with which the dynamometer acts on a body during its uniform motion, we measure the friction force.
If you put a load on a block, for example a weight, and measure the friction force using the method described above, it will turn out to be greater than the friction force measured without the load.
The greater the force pressing the body to the surface, the greater the friction force that arises.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, under equal loads, the rolling friction force is always less than the sliding friction force . That is why, even in ancient times, people used rollers to drag large loads, and later they began to use a wheel.
Rest friction.
Rest friction.
We became acquainted with the frictional force that arises when one body moves along 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 the force of friction. Indeed, if there were no friction, the body would slide down the inclined plane under the influence of gravity. Let us consider the case when the body is at rest on a horizontal plane. For example, there is a closet on the floor. Let's try to move it. If you press the cabinet weakly, it will not budge. Why? The acting force in this case is balanced by the frictional force 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 is of great importance. Friction can be beneficial and harmful. When it is useful, they try to increase it, when it is harmful, they try to decrease it.
Without static friction, neither people nor animals would be able to walk on the ground, since when we walk we push off from the ground. When the friction between the sole of the shoe and the ground (or ice) is low, for example, in icy conditions, it is very difficult to push off from the ground, your feet slip. To prevent feet from slipping, the sidewalks are sprinkled with sand. This increases the friction force between the sole of the shoe and the ice.
Without friction, objects would slip out of your hands.
The force of friction stops the car when braking, but without friction it would not be able to stand still, it would skid. To increase friction, the surface of the car tires is 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 (plant antennae, elephant trunks, prehensile tails of climbing animals). They all 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 babbitt (an alloy of lead or tin with other metals), and lubricated. Bearings in which the shaft slides along the surface of the liner when rotating are called plain bearings.
We know that the rolling friction force under the same load is significantly less than the sliding friction force. The use of ball and roller bearings is based on this phenomenon. In such bearings, the rotating shaft does not slide on a stationary bearing shell, but rolls along it on steel balls or rollers.
The structure of the simplest ball and roller bearings is shown in the figure. The bearing inner ring, made of solid steel, is mounted on the shaft. The outer ring is fixed in the machine body. When the shaft rotates, the inner ring rolls on balls or rollers located between the rings. Replacing plain bearings in a 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 frictional force), it is impossible to imagine modern industry and transport.
Dynamics Basics
If kinematics is a branch of mechanics in which movements are described and studied without studying the causes that cause them, then dynamics considers movement from the other side.
Dynamics is a branch of mechanics in which the reasons why the nature of the motion of bodies can change are clarified.
Classical dynamics is based on Newton's three laws.
Any material body is influenced by the bodies surrounding it. At the same time, it itself influences the bodies around it. In other words, bodies interact between themselves.
The quantitative measure of interaction is force.
Force– vector quantity. To determine a force, you need to indicate its magnitude, direction of action, the body to which the force is applied and the point of application.
All bodies have the property of inertia.
Inertia consists in the ability of bodies to maintain a state of rest or uniform rectilinear motion (keep the speed they possess unchanged).
The inertia of different bodies is different.
A quantitative measure of inertia is body weight.
The unit of mass is kilogram. It is the basic unit represented by the mass of the international prototype of the kilogram (standard).
Observations and experience show that the speed of any body changes only when other bodies act on it (under the action of force). Constant speed is possible only if the acceleration is zero.
At the turn of the 16th-17th centuries, Galileo established the following law:
If no other bodies act on the body, then the body maintains a state of rest or rectilinear uniform motion.
At the end of the 17th century Newton included it in his laws of mechanics as first law by calling him law of inertia.
The law of inertia says:
If the body is not acted upon by other bodies, then it is in a state of rest or uniform linear motion, relative to the inertial frame of reference.
From this law it follows that the cause of the change in speed is force.
Newton's second law answers the question of how a body moves under the influence of force. Since speed can change only in the presence of acceleration, and the cause of the change is force, then force is the cause of acceleration.
The law states:
The acceleration acquired by a material point (body) in an inertial frame of reference is proportional to the force acting on the point, inversely proportional to the mass of the material point and coincides in direction with the force.
Unit of force – newton (H):
The first and second laws consider only one body. But forces arise only in the presence of two interacting bodies, and are a measure of this interaction.
Third Law considers both interacting bodies.
The law states:
The forces with which two bodies act on each other are equal in magnitude and directed in opposite directions along the straight line connecting these bodies.
in direct contact. In this case, it is accompanied by a change in the shape and volume of the interacting bodies - deformations. The forces that arise in this case are called elastic forces.
Interaction can be carried out on distance. In this case, they say there is force field. One of these fields is the gravitational field, and the forces arising in it are called forces of gravity.
When bodies come into direct contact, in addition to elastic forces, forces of another type arise, called friction forces. They are characterized by the fact that they prevent the movement of one rubbing body relative to another or prevent the very occurrence of this movement.
Gravity, the action of which we are accustomed to under terrestrial conditions, is due to the attraction (action of the gravitational field) of the Earth. It is quantitatively determined by the formula:
g - acceleration of gravity;
m– mass of the body under consideration;
The fact that for all bodies on which only gravity forces act, the resulting acceleration is the same and equal g , Galileo established.
The force of gravity is applied to the center of mass of the body and is directed downward along a plumb line.
Elastic forces arise as a result of the interaction of bodies that are deformed.
It has been established that the elastic force is proportional to the displacement of particles from the equilibrium position that occurs during deformation of the body, and is directed towards the equilibrium position.
This relationship was first established by Newton's contemporary Robert Hooke and is known in physics as Hooke's law.
X– the amount of elastic information;
k– body rigidity;
Stiffness has a dimension [N/m]. It depends not only on the material of the body, but also on the shape that this body has.
Sliding friction force prevents the movement of one rubbing body relative to another and acts when such movement (sliding) occurs. It is directed tangentially to the rubbing surfaces in the direction opposite to the movement of a given body relative to another and depends on the state of the rubbing surfaces and the pressing pressure.
– coefficient of sliding friction, depending on the nature and state of the contacting bodies, which has no dimension;
N– normal pressure force pressing the rubbing surfaces against each other;
Static friction force. In order for one rubbing body to begin to move relative to another, some force must be applied. If the force is less than required, the movement will not begin. This means that the applied force is compensated by some force. This static friction force.
The static friction force occurs when a force appears that tends to cause one body to slide over another.
The static friction force is equal in magnitude and opposite in direction to the external force.
The static friction force increases with increasing external force up to a certain limit, after which sliding begins.
The limiting force of static friction in many cases exceeds the force of sliding friction.
Rolling friction force. If a body has a shape that allows it to roll over the surface of another body, then a rolling friction force arises.
The rolling friction force is less than the sliding friction force.
The occurrence of rolling friction is caused by the deformation of the surfaces of both bodies, due to which the rolling body seems to roll up a hill. At the same time, the sections of one surface that were previously in contact are separated from the other.
This is the vector sum of all forces acting on the body.
The cyclist leans towards the turn. The force of gravity and the reaction force of the support from the earth provide a resultant force that imparts the centripetal acceleration necessary for motion in a circle
Relationship with Newton's second law
Let's remember Newton's law: 
The resultant force can be equal to zero in the case when one force is compensated by another, the same force, but opposite in direction. In this case, the body is at rest or moving uniformly.
If the resultant force is NOT zero, then the body moves with uniform acceleration. Actually, it is this force that causes the uneven movement. Direction of resultant force Always coincides in direction with the acceleration vector.
When it is necessary to depict the forces acting on a body, while the body moves with uniform acceleration, it means that in the direction of acceleration the acting force is longer than the opposite one. If the body moves uniformly or is at rest, the length of the force vectors is the same.
Finding the resultant force
In order to find the resultant force, it is necessary: firstly, to correctly designate all the forces acting on the body; then draw coordinate axes, select their directions; in the third step it is necessary to determine the projections of the vectors on the axes; write down the equations. Briefly: 1) identify the forces; 2) select the axes and their directions; 3) find the projections of forces on the axis; 4) write down the equations.
How to write equations? If in a certain direction the body moves uniformly or is at rest, then the algebraic sum (taking into account signs) of the projections of forces is equal to zero. If a body moves uniformly accelerated in a certain direction, then the algebraic sum of the projections of forces is equal to the product of mass and acceleration, according to Newton’s second law.
Examples
A body moving uniformly on a horizontal surface is subject to the force of gravity, the reaction force of the support, the force of friction and the force under which the body moves.
Let us denote the forces, choose the coordinate axes
Let's find the projections
Writing down the equations
A body that is pressed against a vertical wall moves downward with uniform acceleration. The body is acted upon by the force of gravity, the force of friction, the reaction of the support and the force with which the body is pressed. The acceleration vector is directed vertically downwards. The resultant force is directed vertically downwards.
The body moves uniformly along a wedge whose slope is alpha. The body is acted upon by the force of gravity, the reaction force of the support, and the force of friction.
The main thing to remember
1) If the body is at rest or moving uniformly, then the resultant force is zero and the acceleration is zero;
2) If the body moves uniformly accelerated, then the resultant force is not zero;
3) The direction of the resultant force vector always coincides with the direction of acceleration;
4) Be able to write equations of projections of forces acting on a body
A block is a mechanical device, a wheel that rotates around its axis. Blocks can be mobile And motionless.
Fixed block used only to change the direction of force.
Bodies connected by an inextensible thread have equal accelerations.
Movable block designed to change the amount of effort applied. If the ends of the rope clasping the block make equal angles with the horizon, then lifting the load will require a force half as much as the weight of the load. The force acting on a load is related to its weight as the radius of a block is to the chord of an arc encircled by a rope.
The acceleration of body A is half the acceleration of body B.
In fact, any block is lever arm, in the case of a fixed block - equal arms, in the case of a movable one - with a ratio of shoulders of 1 to 2. As for any other lever, the following rule applies to the block: the number of times we win in effort, the same number of times we lose in distance
A system consisting of a combination of several movable and fixed blocks is also used. This system is called a polyspast.
We feel it as if we are being “pressed” into the floor, or as if we are “hanging” in the air. This can best be felt when riding a roller coaster or in the elevators of high-rise buildings, which suddenly begin to rise and descend.
Example:
Examples of weight gain:
When the elevator suddenly begins to move upward, people in the elevator feel as if they are being “pressed” into the floor.
When the elevator sharply reduces its downward speed, then the people in the elevator, due to inertia, “press” their feet harder into the floor of the elevator.
When a roller coaster passes through the bottom of the roller coaster, the occupants of the cart experience a feeling of being “squeezed” into the seat.
Example:
Examples of weight loss:
When cycling fast on small hills, the cyclist at the top of the hill experiences a feeling of lightness.
When the elevator suddenly begins to move downward, people in the elevator feel that their pressure on the floor decreases, and a feeling of free fall occurs.
When a roller coaster passes through the highest point of the ride, the occupants of the cart experience the sensation of being “thrown” into the air.
When one swings to the highest point on a swing, one feels that for a short moment the body “hangs” in the air.
Weight change is associated with inertia - the body’s desire to maintain its initial state. Therefore, the change in weight is always opposite to the acceleration of movement. When the acceleration of movement is directed upward, the weight of the body increases. And if the acceleration of movement is directed downwards, the weight of the body decreases.
In the figure, blue arrows show the direction of acceleration of motion.
1) If the elevator is stationary or moving uniformly, then the acceleration is zero. In this case, the person’s weight is normal, it is equal to the force of gravity and is determined as follows: P = m ⋅ g.
2) If the elevator accelerates upward or decreases its speed when moving downward, then the acceleration is directed upward. In this case, the person’s weight increases and is determined as follows: P = m ⋅ g + a.
3) If the elevator accelerates downward or decreases its speed when moving up, then the acceleration is directed downward. In this case, the person’s weight decreases and is determined as follows: P = m ⋅ g − a.
4) If a person is in an object that is freely falling, then the acceleration of movement is directed downward and is the same as the acceleration of free fall: \( a = g\).
In this case, the person’s weight is zero: P = 0.
Example:
Given: human mass - \(80 kg\). A man enters an elevator to go up. The acceleration of the elevator is \(7\) m s 2 .
Each stage of movement, along with measurement readings, is shown in the figures below.
1) The elevator is stationary and the person’s weight is: P = m ⋅ g = 80 ⋅ 9.8 = 784 N.
2) The elevator begins to move upward with acceleration \(7\) m s 2, and the person’s weight increases: P = m ⋅ g a = 80 ⋅ 9.8 7 = 1334 N.
3) The elevator has picked up speed and is moving uniformly, while the person’s weight is: P = m ⋅ g = 80 ⋅ 9.8 = 784 N.
4) When moving upward, the elevator slows down with negative acceleration (deceleration) \(7\) m s 2, and the person’s weight decreases: P = m ⋅ g − a = 80 ⋅ 9.8 − 7 = 224 N.
5) The elevator has completely stopped, the person’s weight is: P = m ⋅ g = 80 ⋅ 9.8 = 784 N.
In addition to pictures and examples of the task, you can watch a video of an experiment conducted by schoolchildren, which shows how a person’s body weight changes in an elevator. During the experiment, schoolchildren use scales in which weight is immediately indicated in \(newtons, N\) instead of kilograms. http://www.youtube.com/watch?v=D-GzuZjawNI.
Example:
The state of weightlessness occurs in situations where a person is located in an object that is in free fall. There are special planes that are designed to create a state of weightlessness. They rise to a certain height, and after that the plane goes into free fall for about \(30 seconds\). During the free fall of an airplane, the people in it experience a state of weightlessness. This situation can be seen in this video.
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