Antipyretics for children are prescribed by a pediatrician. But there are emergency situations with fever when the child needs to be given medicine immediately. Then the parents take responsibility and use antipyretic drugs. What is allowed to be given to infants? How can you lower the temperature in older children? What medications are the safest?
QUESTIONS
1. Does a material point have mass? Does it have dimensions?
Under material point in physics we mean a body whose dimensions can be neglected in the conditions of a given problem. Material point has a certain mass, but has zero (very small) dimensions.
2. Is a material point a real object or an abstract concept?
Material point- an abstract concept, because In nature, all bodies have certain sizes.
3. For what purpose is the concept used? "material point"?
Concept material point used to simplify conditions and solutions to problems. If we neglect the dimensions of a real body, then there is no need to consider the movement of the body as it moves around its axis (a ball in flight) or the movement of some parts of the body (car wheels), if we are interested in how fast the body is moving.
4. In what cases is a moving body usually considered as a material point?
In this case, a moving body can be considered as a material point if its dimensions are much less than the distance over which it moves.
5. Give an example showing that the same body in one situation can be considered a material point, but not in another.
If we consider, for example, the movement of a car when it moves from city A to city B, then in this case, when determining the average speed of the car, it can be considered as a material point, but if we are interested in the movement of the car in more detail, it turns out that when movement of the car, for example, the front and rear wheels move differently (not synchronously) due to uneven roads.
6. In what motion of a body can it be considered as a material point even if the distances it travels are comparable to its dimensions?
If the body moves forward.
7. What is called a material point?
Material point- this is an abstract concept denoting a body, the dimensions of which do not play a role in the conditions of the problem under consideration.
8. In what case can the position of a moving body be specified using a single coordinate axis?
If the body moves in a straight line.
9. What is a frame of reference?
A reference system is a reference body, an associated coordinate system and a device for measuring time, in relation to which the movement of material points or bodies is considered.
EXERCISES
2. The plane flies from Moscow to Vladivostok. Can a controller observing its movement consider an airplane as a material point? passenger on this plane?
From the point of view of the dispatcher, if we consider only the route of the aircraft, then it is possible, but if there are other aircraft in the air or the aircraft is landing, then no. From the passenger's point of view, when flying en route, yes, but when moving a passenger inside the aircraft, no.
3. When talking about the speed of a car, train, etc. Vehicle, the body of reference is usually not indicated. What is meant in this case by reference body?
The body of reference, in this case, usually means the surface of the Earth.
4. The boy stood on the ground and watched his little sister ride on the carousel. After the ride, the girl told her brother that he, the houses, and the trees were quickly rushing past her. The boy began to claim that he, along with the houses and trees, was motionless, but his sister was moving. Relative to what reference bodies did the girl and boy consider the movement? Explain who is right in the dispute.
Both are right. The boy chose a frame of reference relative to himself (he was motionless), and the girl chose a frame relative to herself (she was on a swing).
5. Relative to what reference body is motion considered when they say:
a) wind speed is 5 m/s?
b) the log floats along the river, so its speed is zero;
c) the speed of a tree floating along a river is equal to the speed of water flow in the river;
d) any point on the wheel of a moving bicycle describes a circle;
e) The sun rises in the east in the morning, moves across the sky during the day, and sets in the west in the evening?
a) relative to the surface of the Earth; b) relative to flowing water; c) relative to the surface of the Earth; d) relative to the center (axis) of the wheel; e) relative to the surface of the Earth.
Material point
Material point(particle) - the simplest physical model in mechanics - an ideal body whose dimensions are equal to zero; the dimensions of the body can also be considered infinitesimal compared to other sizes or distances within the assumptions of the problem under study. The position of a material point in space is defined as the position of a geometric point.
In practice, a material point is understood as a body with mass, the size and shape of which can be neglected when solving this problem.
When a body moves in a straight line, one coordinate axis is sufficient to determine its position.
Peculiarities
The mass, position and speed of a material point at each specific moment in time completely determine its behavior and physical properties.
Consequences
Mechanical energy can be stored by a material point only in the form of the kinetic energy of its movement in space, and (or) the potential energy of interaction with the field. This automatically means that a material point is incapable of deformation (only an absolutely rigid body can be called a material point) and rotation around its own axis and changes in the direction of this axis in space. At the same time, the model of the motion of a body described by a material point, which consists in changing its distance from some instantaneous center of rotation and two Euler angles, which specify the direction of the line connecting this point to the center, is extremely widely used in many branches of mechanics.
Restrictions
The limited application of the concept of a material point is visible from the following example: in a rarefied gas at high temperature the size of each molecule is very small compared to the typical distance between molecules. It would seem that they can be neglected and the molecule can be considered a material point. However, this is not always the case: vibrations and rotations of a molecule are an important reservoir of the “internal energy” of the molecule, the “capacity” of which is determined by the size of the molecule, its structure and chemical properties. To a good approximation, a monatomic molecule (inert gases, metal vapors, etc.) can sometimes be considered as a material point, but even in such molecules, at a sufficiently high temperature, excitation of electron shells is observed due to collisions of molecules, followed by emission.
Notes
Wikimedia Foundation. 2010.
- Mechanical movement
- Absolutely solid body
See what a “material point” is in other dictionaries:
MATERIAL POINT- a point with mass. In mechanics, the concept of a material point is used in cases where the size and shape of a body do not play a role in the study of its motion, and only mass is important. Almost any body can be considered as a material point if... ... Big Encyclopedic Dictionary
MATERIAL POINT- a concept introduced in mechanics to designate an object, which is considered as a point with mass. The position of the M. t. in law is defined as the position of the geom. points, which greatly simplifies the solution of mechanics problems. Practically, the body can be considered... ... Physical encyclopedia
material point- A point with mass. [Collection of recommended terms. Issue 102. Theoretical mechanics. Academy of Sciences of the USSR. Committee of Scientific and Technical Terminology. 1984] Topics theoretical mechanics EN particle DE materialle Punkt FR point matériel ... Technical Translator's Guide
MATERIAL POINT Modern encyclopedia
MATERIAL POINT- In mechanics: an infinitesimal body. Dictionary of foreign words included in the Russian language. Chudinov A.N., 1910 ... Dictionary of foreign words of the Russian language
Material point- MATERIAL POINT, a concept introduced in mechanics to designate a body whose dimensions and shape can be neglected. The position of a material point in space is defined as the position of a geometric point. The body can be considered material... ... Illustrated Encyclopedic Dictionary
material point- a concept introduced in mechanics for an object of infinitesimal size that has mass. The position of a material point in space is defined as the position of a geometric point, which simplifies the solution of mechanics problems. Almost any body can... ... encyclopedic Dictionary
Material point- a geometric point with mass; material point is an abstract image of a material body that has mass and has no dimensions... The beginnings of modern natural science
material point- materialusis taškas statusas T sritis fizika atitikmenys: engl. mass point; material point vok. Massenpunkt, m; materieller Punkt, m rus. material point, f; point mass, f pranc. point mass, m; point matériel, m … Fizikos terminų žodynas
material point- A point with mass... Polytechnic terminological explanatory dictionary
Books
- Set of tables. Physics. 9th grade (20 tables), . Educational album of 20 sheets. Material point. Coordinates of a moving body. Acceleration. Newton's laws. The law of universal gravitation. Rectilinear and curvilinear movement. Body movement along...
To describe the movement of a body, you need to know how its various points move. However, in the case of translational motion, all points of the body move equally. Therefore, to describe the translational motion of a body, it is enough to describe the movement of one of its points.
Also, in many mechanics problems there is no need to indicate the positions of individual parts of the body. If the dimensions of a body are small compared to the distances to other bodies, then this body can be described as a point.
DEFINITION
Material point is a body whose dimensions can be neglected under given conditions.
The word “material” here emphasizes the difference between this point and the geometric one. A geometric point does not have any physical properties. A material point may have mass, electric charge and other physical characteristics.
The same body can be considered a material point under some conditions, but not under others. So, for example, considering the movement of a ship from one seaport to another, the ship can be considered a material point. However, when studying the motion of a ball rolling along the deck of a ship, the ship cannot be considered a material point. The movement of a hare running through the forest from a wolf can be described by taking the hare as a material point. But the hare cannot be considered a material point when describing its attempts to hide in a hole. When studying the movement of planets around the Sun, they can be described by material points, but with the daily rotation of planets around their axis, such a model is not applicable.
It is important to understand that material points do not exist in nature. A material point is an abstraction, a model for describing movement.
Examples of solving problems on the topic “Material point”
EXAMPLE 1
EXAMPLE 2
| Exercise | Indicate in which of the following cases the body under study can be taken as a material point: a) calculate the pressure of the tractor on the ground; b) calculate the height to which the rocket rose; c) calculate the work when lifting in horizontal position floor slabs of known mass to a given height; d) determine the volume of a steel ball using a measuring cylinder (beaker). |
| Answer | a) when calculating the pressure of a tractor on the ground, the tractor cannot be taken as a material point, since in this case it is important to know the surface area of the tracks; b) when calculating the lifting height of a rocket, the rocket can be considered a material point, since the rocket moves translationally and the distance traveled by the rocket. much larger than its size; c) in this case, the floor slab can be considered a material point. since it performs translational motion and to solve the problem it is enough to know the movement of its center of mass; d) when determining the volume of a ball. the ball cannot be considered a material point, because in this problem the dimensions of the ball are essential. |
EXAMPLE 3
| Exercise | Is it possible to take the Earth as a material point when calculating: a) the distance from the Earth to the Sun; b) the path traveled by the Earth in its orbit around the Sun; c) the length of the Earth's equator; d) the speed of movement of the equator point during the daily rotation of the Earth around its axis; e) the speed of the Earth's orbit around the Sun? |
| Answer | a) under these conditions, the Earth can be taken as a material point, since its dimensions are much less than the distance from it to the Sun; e) in this case, the Earth can be taken as a material point, since the dimensions of the orbit are much greater than the dimensions of the Earth. |
From the seventh grade physics course we remember that the mechanical motion of a body is its movement in time relative to other bodies. Based on such information, we can assume the necessary set of tools for calculating body movement.
First, we need something against which we will make our calculations. Next, we will need to agree on how we will determine the position of the body relative to this “something”. And finally, you will need to somehow record the time. Thus, in order to calculate where the body will be at a particular moment, we need a frame of reference.
Frame of reference in physics
A reference system in physics is the combination of a reference body, a coordinate system associated with the reference body, and a clock or other device for keeping time. It should always be remembered that any reference system is conditional and relative. You can always adopt a different reference system, relative to which any movement will have completely different characteristics.
Relativity is generally an important aspect that should be taken into account in almost any calculation in physics. For example, in many cases we cannot determine the exact coordinates of a moving body at any time.
In particular, we cannot place observers with watches every hundred meters along the railway track from Moscow to Vladivostok. In this case, we calculate the speed and location of the body approximately over a certain period of time.
Accuracy of up to one meter is not important to us when determining the location of a train on a route of several hundred or thousand kilometers. There are approximations for this in physics. One of these approximations is the concept of “material point”.
Material point in physics
In physics, a material point denotes a body in cases where its size and shape can be neglected. In this case, it is assumed that the material point has the mass of the original body.
For example, when calculating the time it will take an airplane to fly from Novosibirsk to Novopolotsk, the size and shape of the airplane are not important to us. It is enough to know what speed it develops and the distance between cities. In the case when we need to calculate wind resistance at a certain altitude and at a certain speed, then we certainly cannot do without accurate knowledge of the shape and dimensions of the same aircraft.
Almost any body can be considered a material point either when the distance covered by the body is large in comparison with its size, or when all points of the body move equally. For example, a car traveling a few meters from the store to the intersection is quite comparable to this distance. But even in such a situation, it can be considered a material point, because all parts of the car moved equally and at an equal distance.
But in the case when we need to place the same car in the garage, it can no longer be considered a material point. You will have to take into account its size and shape. These are also examples when it is necessary to take into account relativity, that is, in relation to what we make specific calculations.
In the world around us, everything is in constant motion. Movement in the general sense of the word means any changes occurring in nature. The simplest type of movement is mechanical movement.
From the 7th grade physics course, you know that the mechanical motion of a body is the change in its position in space relative to other bodies that occurs over time.
When solving various scientific and practical problems related to the mechanical movement of bodies, you need to be able to describe this movement, that is, determine the trajectory, speed, distance traveled, position of the body and some other characteristics of movement for any moment in time.
For example, when launching an aircraft from Earth to another planet, scientists must first calculate where this planet is located relative to the Earth at the moment the device lands on it. And to do this, it is necessary to find out how the direction and magnitude of the velocity of this planet change over time and along what trajectory it moves.
From a mathematics course, you know that the position of a point can be specified using a coordinate line or a rectangular coordinate system (Fig. 1). But how to set the position of a body that has dimensions? After all, each point of this body will have its own coordinate.
Rice. 1. The position of a point can be specified using a coordinate line or a rectangular coordinate system
When describing the motion of a body that has dimensions, other questions arise. For example, what should be understood by the speed of a body if, while moving in space, it simultaneously rotates around its own axis? After all, the speed of different points of this body will be different both in magnitude and in direction. For example, during the daily rotation of the Earth, its diametrically opposite points move in opposite directions, and the closer to the axis the point is located, the lower its speed.
How can you set the coordinates, speed and other characteristics of the movement of a body that has dimensions? It turns out that in many cases, instead of the movement of a real body, one can consider the movement of a so-called material point, that is, a point that has the mass of this body.
For a material point, it is possible to unambiguously determine the coordinates, speed and other physical quantities, since it has no dimensions and cannot rotate around its own axis.
There are no material points in nature. A material point is a concept, the use of which simplifies the solution of many problems and at the same time allows one to obtain fairly accurate results.
- A material point is a concept introduced in mechanics to designate a body that is considered as a point having mass
Almost any body can be considered as a material point in cases where the distances traveled by the points of the body are very large compared to its size.
For example, the Earth and other planets are considered material points when studying their movement around the Sun. In this case, differences in the movement of different points of any planet, caused by its daily rotation, do not affect the quantities describing the annual movement.
Planets are considered material points when studying their movement around the Sun
But when solving problems related to the daily rotation of planets (for example, when determining the time of sunrise in different places on the surface of the globe), it makes no sense to consider the planet a material point, since the result of the problem depends on the size of this planet and the speed of movement of points on its surface. So, for example, in the Vladimir time zone the sun will rise 1 hour later, in Irkutsk - 2 hours later, and in Moscow - 8 hours later than in Magadan.
It is legitimate to take an airplane as a material point if it is necessary, for example, to determine the average speed of its movement on the way from Moscow to Novosibirsk. But when calculating the air resistance force acting on a flying airplane, it cannot be considered a material point, since the resistance force depends on the shape and speed of the airplane.
An airplane flying from one city to another can be taken as a material point.
A body moving translationally 1 can be taken as a material point even if its dimensions are commensurate with the distances it travels. For example, a person standing on the step of a moving escalator moves forward (Fig. 2, a). At any given time, all points of the human body move equally. Therefore, if we want to describe the movement of a person (i.e., determine how his speed, path, etc. changes over time), then it is enough to consider the movement of only one of his points. In this case, solving the problem is significantly simplified.
When a body moves in a straight line, one coordinate axis is sufficient to determine its position.
For example, the position of a cart with a dropper (Fig. 2, b), moving along the table rectilinearly and translationally, at any time can be determined using a ruler located along the trajectory of movement (the cart with a dropper is taken as a material point). In this experiment, it is convenient to take the ruler as a body of reference, and its scale can serve as a coordinate axis. (Recall that the body of reference is the body relative to which the change in the position of other bodies in space is considered.) The position of the cart with the dropper will be determined relative to the zero division of the ruler.
Rice. 2. When a body moves forward, all its points move equally
But if it is necessary to determine, for example, the path that a cart has traveled in a certain period of time, or the speed of its movement, then in addition to a ruler, you will need a device for measuring time - a watch.
In this case, the role of such a device is played by a dropper, from which drops fall at regular intervals. By turning the tap, you can ensure that the drops fall at intervals of, for example, 1 second. By counting the number of intervals between the traces of drops on the ruler, you can determine the corresponding period of time.
From the above examples it is clear that in order to determine the position of a moving body at any time, the type of movement, the speed of the body and some other characteristics of movement, a reference body, an associated coordinate system (or one coordinate axis if the body is moving along a straight line) and a device for time measurements.
- The coordinate system, the reference body with which it is associated, and the device for measuring time form a reference system relative to which the movement of the body is considered
Of course, in many cases it is impossible to directly measure the coordinates of a moving body at any time. We have no real opportunity, for example, to place a measuring tape and place observers with watches along the many-kilometer path of a moving car, a liner sailing on the ocean, a flying airplane, a shell fired from an artillery gun, various celestial bodies whose movement we observe, etc. .
Nevertheless, knowledge of the laws of physics allows us to determine the coordinates of bodies moving in various systems reference, in particular in the reference frame associated with the Earth.
Questions
- What is a material point called?
- For what purpose is the concept of “material point” used?
- In what cases is a moving body usually considered as a material point?
- Give an example showing that the same body in one situation can be considered a material point, but not in another.
- In what case can the position of a moving body be specified using a single coordinate axis?
- What is a frame of reference?
Exercise 1
- Can a car be considered a material point when determining the distance it travels in 2 hours, moving at an average speed of 80 km/h; when overtaking another car?
- The plane flies from Moscow to Vladivostok. Can a controller observing its movement consider an airplane as a material point? passenger on this plane?
- When talking about the speed of a car, train and other vehicles, the body of reference is usually not indicated. What is meant in this case by reference body?
- The boy stood on the ground and watched his little sister ride on the carousel. After the ride, the girl told her brother that he, the houses, and the trees were quickly rushing past her. The boy began to claim that he, along with the houses and trees, was motionless, but his sister was moving. Relative to what reference bodies did the girl and boy consider the movement? Explain who is right in the dispute.
- Relative to what body of reference is motion considered when they say: a) the wind speed is 5 m/s; b) the log floats along the river, so its speed is zero; c) the speed of a tree floating along a river is equal to the speed of water flow in the river; d) any point on the wheel of a moving bicycle describes a circle; e) the sun rises in the east in the morning, moves across the sky during the day, and sets in the west in the evening?
1 Translational motion is the movement of a body in which a straight line connecting any two points of this body moves, remaining at all times parallel to its original direction. Translational motion can be either rectilinear or curvilinear motion. For example, the cabin of a Ferris wheel moves forward.
