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Observations show that bodies change their speed only in the presence of an uncompensated action. Since the rate of change in speed is characterized by the acceleration of a body, we can conclude that the cause of acceleration is the uncompensated action of one body on another. But one body cannot act on another without experiencing its effect on itself. Consequently, acceleration appears when bodies interact. Both interacting bodies acquire acceleration. Also, from observations, one more fact can be established: with the same action, different bodies acquire different accelerations.
Inertia is the property of a body to keep its speed constant (the same as inertia). It manifests itself in the fact that it takes some time to change the speed of the body. The process of changing the speed cannot be instantaneous.
For example A car moving along the road cannot stop instantly, it takes some time to reduce the speed, and during this time it manages to move a rather long distance (tens of meters). (Carefully cross the road !!!)
The measure of inertia is inert mass.
Mass (inert) is a measure of the inertness of a body.
The more inert the body, the greater its mass. The more inertia, the less acceleration. Consequently, the greater the mass of the body, the less its acceleration: a ∼ 1 m \ boxed (a \ sim \ frac 1m).
This dependence is written in the only correct way, because. form m ∼ 1 a m \ sim \ frac 1ais not correct. Mass cannot depend on acceleration, it is a property of the body, and acceleration is a characteristic of the state of motion of the body.
This dependence is confirmed by numerous experimental results.
Rice. 2 Measurement of mass by the method of interaction of bodies.
Two bodies, fastened together by a compressed spring, after burning through the thread holding the spring, begin to move for some time with acceleration (Fig. 1). Experience shows that for any interactions of these two bodies, the ratio of the accelerations of the bodies is equal to the inverse ratio of their masses:
\ [\ frac (a_1) (a_2) = \ frac (m_2) (m_1); \]
if we take the first mass as the reference one (m 1 = m floor m_1 = m_ \ mathrm (floor)), then m 2 = m floor a floor a 2 m_2 = m_ \ mathrm (floor) \ frac (a_ \ mathrm (floor)) (a_2).
Weight, measured by interaction (measurement of acceleration) is calledinert .
Measurement of mass by weighing bodies.
The second way to measure masses is based on comparing the action of the Earth on different bodies. Such a comparison can be carried out either sequentially (first, the tension of the spring is determined under the action of the reference masses, and then under the action of the investigated body in the same conditions), or at the same time place the body under study on an equal-arm beam balance on one bowl and the reference masses on the other (Fig. 2).
Rice. 2
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The mass measured by weighing is called gravitational.
As a standard for both masses, the mass of a body made in the form of a cylinder 39 mm 39 \ \ mathrm (mm) high and 39 mm 39 \ mathrm (mm) in diameter, made of an alloy of 10% iridium and 90% platinum (Fig. . 3).
In 1971, our compatriots Braginsky and Panov invented and conducted an experiment comparing gravitational and inert masses. It turned out that these masses are equal to within 10 - 12 10 ^ (- 12)%.
The the fact was known earlier, and served as the basis for Einstein's formulation of the principle of equivalence.
Equivalence principle States that
1) acceleration due to gravitational interaction in a small region of space, and for a short time interval, indistinguishable from an accelerated moving frame of reference.
2) an accelerated body is equivalent to a stationary body in a gravitational field.
Example 1.
Two bodies weighing 400 g 400 \ \ mathrm (g) and 600 g 600 \ \ mathrm (g) moved towards each other and stopped after impact. What is the speed of the second body if the first was moving at a speed of 3 m / s 3 \ \ mathrm (m) / \ mathrm (s)?
Mechanical motion Relativity of motion, Reference system, Material point, Trajectory. Path and movement. Instant speed. Acceleration. Uniform and uniformly accelerated movement
Mechanical movement is called a change in the position of the body (or its parts) relative to other bodies. For example, a person riding an escalator in a subway is at rest relative to the escalator itself and moves relative to the walls of the tunnel; the body, relative to which the motion is considered, it is called reference body. The coordinate system, the reference body with which it is associated, and the chosen way of measuring time form frame of reference. the size of the body in comparison with the distance to it can be neglected, in these cases the body is considered a material point. The line along which a material point moves is called a trajectory. The length of the part of the path between the start and end position of a point is called a path (L). The unit of measure for the path is 1m.
Mechanical movement is characterized by three physical quantities: displacement, speed and acceleration.
A directed segment of a straight line drawn from the starting position of a moving point to its final position is called displacement(s), Displacement - vector value. Displacement unit is 1m.
Speed- vector physical quantity characterizing the speed of movement of the body, numerically equal to the ratio of displacement over a short period of time to the value of this interval. The defining formula for the velocity is v= s / t. The unit of measurement for speed is m / s. In practice, the unit of measurement for speed is km / h (36 km / h = 10 m / s). Measure the speed with a speedometer.
Acceleration- vector physical quantity characterizing the rate of change in speed, numerically equal to the ratio of change in speed to the time interval during which this change occurred. acceleration can be calculated using the formula a= (v - v 0) / t. Acceleration unit - m / s 2.
The characteristics of mechanical motion are related to each other by the basic kinematic equations.
s = v 0 t + at 2/2;
v = v 0 + at.
The movement in which the speed of the body does not change, that is, the body moves by the same amount for any equal intervals of time, is called uniform rectilinear movement.
the speed changes in the same way for any equal time intervals. This kind of movement is called uniformly accelerated.
When braking a car, the speed decreases equally for any equal periods of time. Such movement is called uniformly slowed down.
All physical quantities characterizing the movement of a body (speed, acceleration, displacement), as well as the type of trajectory, can change when passing from one system to another, i.e., the nature of the movement depends on the choice of the frame of reference, and this is what manifests itself relativity of motion.
Ticket №2
The interaction of bodies. Force. Newton's second law
the quantitative characteristic of the interaction is strength. Force is the reason for the acceleration of bodies in relation to the inertial frame of reference or their deformation. Force is a vector physical quantity that is a measure of the acceleration acquired by bodies during interaction. Strength is characterized by: a) module; b) the point of application; c) direction.
The unit of measure for force is newton. 1 Newton is a force that gives a body with a mass of 1 kg an acceleration of 1 m / s in the direction of the action of this force, if other bodies do not act on it. The effect of several forces is called a force, the action of which is equivalent to the action of the forces that it replaces. The resultant is the vector sum of all forces applied to the body.
R = F1 + F2 + ... + Fn ,.
Based on experimental data, Newton's laws were formulated. Newton's second law. The acceleration with which the body moves is directly proportional to the resultant of all forces acting on the body, inversely proportional to its mass and is directed in the same way as the resultant force: a = F / m.
To solve problems, the law is often written in the form: F = ta.
The third law is a generalization and sounds like this: Bodies act on each other with forces equal in magnitude and opposite in direction.
The first law: there are such frames of reference, relative to which a body in translation keeps its speed constant, if other bodies do not act on it (or the action of other bodies is compensated).
In the course of this lesson, you will get acquainted in more detail with the interaction of bodies, learn about such a property of bodies as inertia and about a physical quantity that quantitatively describes the inertia of bodies, or, as they say, is a measure of inertia - about mass.
Topic: Body Interaction
Lesson:The interaction of bodies. Weight
In the last lesson, we realized that you can change the speed of a body only by acting on it with another body. But if one body acts on another, then the other body necessarily acts on the first. We say that there is an interaction of bodies. That is, it is an action that is mutual.
Since bodies can only mutually act, then in the course of interaction the velocities of both bodies will necessarily change.
Imagine two balls moving towards each other: a table tennis ball and a steel ball of about the same size.
Rice. 1. Collision - an example of the interaction of bodies
When these balls collide (that is, during their interaction), the speed of the steel ball will change slightly, and the speed of the table tennis ball will change significantly (it will even change direction). Physicists say that a steel ball is more inert than a tennis ball.
Inertia is a property of a body in that it takes some time to change its speed.
Since in the example considered, the balls acted on each other for the same time, and the speed of the steel ball changed less, this means that its inertness is greater than the inertia of a tennis ball.
Let's complicate the experience discussed above. We place between two stationary balls a compressed spring tied with a thread that prevents the spring from straightening. Gently pinch the thread. The spring will begin to straighten, resting its ends on the balls. We can say that the balls will begin to interact by means of a spring and, as a result of this interaction, they will acquire some speed.
Let's say, for example, that a steel ball has acquired a speed of 2 cm / s, and a tennis one - 1 m / s. That is, the speed of the steel ball changed 50 times less than the speed of the tennis ball. We can say that the inertness of a steel ball is 50 times that of a tennis ball. This means that the inertia of bodies can be compared!
Body mass is a physical quantity that is a measure of the body's inertia.
The greater the body mass, the greater its inertia. In our example, the mass of a steel ball is 50 times the mass of a table tennis ball.
Any body - a person, a table, the planet Earth, a drop of water - has mass.
At the very beginning of the physics course, we said that measurement is a comparison of a physical quantity with a homogeneous quantity taken as a unit. This means that now it is necessary to set the unit of measurement of mass and indicate which body's mass is equal to this unit (choose a standard of mass).
Mass in physics is denoted by the letter m and in the SI system is measured in kilograms (kg):
There are other units of mass: ton (t), gram (g), milligram (mg).
1 t = 1000 kg; 1 g = 0.001 kg;
1 kg = 1000 g; 1 mg = 0.001 g;
1 kg = 1,000,000 mg; 1 mg = 0.000001 kg.
1 kilogram is the mass of the standard. The international standard of mass is kept in France in the city of Sevres, in the Chamber of Weights and Measures.
Rice. 2. Place of storage of the International Kilogram Standard
The standard for the kilogram is a platinum-iridium alloy cylinder. Its diameter and height are about 39 mm.
Rice. 3. The standard of the kilogram
Rice. 4. Container for storing the standard kilogram
Copies of the mass standard are stored in 40 countries around the world. For example, in Russia there is a copy of the standard - sample №12.
The process of measuring mass is called weighing, and a mass measuring device is called a balance. The image of the scales has been found since the days of Ancient Egypt.
Rice. 5. Egyptian scales
By the way, correct weighing and careful attitude to scales have always been taken very seriously. For example, one of the ancient Russian letters of the XII century contains the following lines:
"For improper use of measures and weights, one should execute close to death, and divide the property into three parts: part of the St. Sophia Church, part of the Ivanovo Church, and part of the Sotsky Church and the city of Novgorod."
Modern scale designs are very diverse. For example, cars, wagons can be weighed on the so-called transport scales. They allow you to measure weights up to 200 tons.
Rice. 6. Transport scales
Bodies, the mass of which does not exceed hundreds of grams, but the measurement accuracy must be very high, are weighed on an analytical balance. Such scales allow weighing with an accuracy of tenths of a milligram.
Rice. 7. Analytical balance
In school physics and chemistry classrooms, educational scales are used. The upper limit of measurement of such a balance is 200 g.
2. Unified collection of Digital Educational Resources ().
Homework
Lukashik V.I., Ivanova E.V. Collection of problems in physics for grades 7 - 9 № 205-213.
What is the reason for the movement of bodies? The answer to this question is given by a section of mechanics called dynamics.
How can you change the speed of the body, make it move faster or slower? Only when interacting with other bodies. When interacting, bodies can change not only their speed, but also the direction of movement and deform, changing their shape and volume. In dynamics, a quantity called force is introduced for a quantitative measure of the interaction of bodies against each other. And the change in speed during the action of the force is characterized by acceleration. Strength is the cause of acceleration.
Force concept
Force is a vector physical quantity that characterizes the action of one body on another, manifested in the deformation of the body or a change in its movement relative to other bodies.
The force is denoted by the letter F. The unit of measurement in the SI system is Newton (N), which is equal to the force under which a body weighing one kilogram receives an acceleration of one meter per second squared. The force F is fully defined if its modulus, direction in space and point of application are given.
A special device called a dynamometer is used to measure forces.
How many forces are there in nature?
Forces can be divided into two types:
- They act in direct interaction, contact (elastic forces, friction forces);
- They act at a distance, long-range (gravity, gravity, magnetic, electrical).
In direct interaction, for example a shot from a toy gun, the bodies experience a change in shape and volume compared to the initial state, that is, compression, stretching, bending deformation. The pistol spring is compressed before firing, the bullet is deformed when it hits the spring. In this case, the forces act at the moment of deformation and disappear with it. Such forces are called elastic. Friction forces arise from the direct interaction of bodies, when they roll, slide relative to each other.
An example of forces acting at a distance is a stone thrown upwards, due to attraction it will fall to the Earth, the ebbs and flows that occur on the ocean coasts. With increasing distance, such forces decrease.
Depending on the physical nature of the interaction, forces can be divided into four groups:
- weak;
- strong;
- gravitational;
- electromagnetic.
We meet all types of these forces in nature.
Gravitational or gravitational forces are the most universal, anything that has mass is capable of experiencing these interactions. They are omnipresent and pervasive, but very weak, so we do not notice them, especially at great distances. Long-range gravitational forces bind all bodies in the Universe.
Electromagnetic interactions arise between charged bodies or particles through the action of an electromagnetic field. Electromagnetic forces allow us to see objects, since light is one of the forms of electromagnetic interactions.
Weak and strong interactions became known through the study of the structure of the atom and atomic nucleus. Strong interactions arise between particles in nuclei. Weak ones characterize the mutual transformations of elementary particles into each other, act in thermonuclear fusion reactions and radioactive decays of nuclei.
If several forces act on the body?
When several forces act on a body, this action is simultaneously replaced with one force equal to their geometric sum. The force obtained in this case is called the resultant. It imparts to the body the same acceleration as the forces simultaneously acting on the body. This is the so-called principle of superposition of forces.
You already know that bodies, if they were not acted upon by other bodies, friction and air resistance, would constantly move or be at rest.
Let's make an experiment.
Bend the plate attached to the cart and tie it with a thread. If you set fire to the thread, the plate will unbend, but the cart will be in the same place.
Let's repeat this experience with two identical carts. Attach another similar cart to the bent plate. After the thread burns out and the plate straightens, the carts will move a certain distance from each other. When one body acted on another, their speed changed.
Thus, bodies change their speed only during interaction, that is, when one body acts on another.
Watch a game of billiards or curling. When one body acts on another, that is, when they interact, the speed changes for both bodies.
Remember the famous cartoon "The Adventures of Captain Vrungel". With the help of bottles of champagne, he was able to continue his journey on the yacht "Trouble". During the interaction of the champagne cork and the bottle itself, both of these bodies moved in opposite directions, thereby giving the yacht movement forward.
Let's do another experiment with carts. Now we will put an additional load on one of the trolleys. Let's see how the trolley speeds change under such conditions.
Many of you, using your life experience, have already guessed what will happen.
After the thread burns out, the carts will move a certain distance. Of course, a cart with an additional load will change its speed less than without a load. Comparing the change in speeds after interaction, we can judge their masses: if the speed of one cart is three times higher, then its mass, respectively, will be three times less.
Let's look at some examples.
Two cars are moving along the road at the same speed. One car is a truck, the other is a passenger car. Which one will take longer to stop?
Obviously, the truck will need more time to stop.
Which cart is more difficult to move, empty or fully loaded? It is harder to move a loaded cart.
Let's conclude: a body with a larger mass is more inert, that is, it “tries” to keep its speed unchanged longer. A body with a smaller mass is less inert, since its speed changes more.
Thus, the mass of the body is a measure of the inertia of bodies.
Body mass is a physical quantity that is a measure of the body's inertia.
The mass of a body can be found not only by comparing the change in the velocities of bodies during their interaction, but also by weighing.
The mass is denoted by the letter m "uh".
In the international system of units, SI, one kilogram is taken as a unit of mass.
A kilogram is the mass of the standard. The international standard for the kilogram is kept in France. In accordance with the standard, 40 exact copies were made, one of which is kept in Russia, namely in St. Petersburg at the Institute of Metrology.
Other units are also used to measure mass: ton, gram, milligram.
1t = 1000kg
1 kg = 1,000g
1kg = 1,000,000mg
1g = 0.001kg
1 mg = 0.000001kg
Body weight can be determined using scales. In life, you have come across various types of scales:
-lever,
-spring,
-electronic.
We will be using a laboratory balance. They are also called beam scales. The principle of weighing on a beam scale is balancing. A body is placed on one side of the scale, the mass of which must be determined. On the other side of the scale, weights are placed, the mass of which is known to us.
In a state of equilibrium, the total mass of the weights will be equal to the mass of the weighed body.
When weighing, certain rules must be followed:
1. Check the scales before starting weighing: they must be in balance.
2. Place the body to be weighed on the left side of the balance and the weights on the right.
3. With both bowls balanced, calculate the total weight of the weights you need.
Remember that when two bodies interact, their speeds change. The speed changes more for the body whose mass is less and vice versa. By measuring the velocities, we can calculate the mass of the body. We can also determine body weight using weights.
