Depends not only on its size, but also on the substance of which the body is composed. So, bodies of the same volume, made of different substances, have different masses, and vice versa: bodies with the same masses, made of different substances, have different volumes.

Body density - dependence of mass and volume

For example, an iron cube with an edge of 10 cm has a mass of 7.8 kg, an aluminum cube of the same dimensions has a mass of 2.7 kg, and the mass of the same cube of ice is 0.9 kg. The quantity characterizing the mass per unit volume of a given substance is called density. The density is equal to the quotient of the body weight and its volume, i.e.

ρ = m / V, where ρ (read "ro") is the density of the body, m is its mass, V is the volume.

In SI units, density is measured in kilograms per cubic meter (kg / m3); off-system units are also often used, such as grams per cubic centimeter (g / cm3). Obviously, 1 kg / m3 = 0.001 g / cm3. Note that when substances are heated, their density decreases or (less often) increases, but this change is so insignificant that it is neglected in calculations.

Let us make a reservation that the density of gases is not constant; when we talk about the density of a gas, we usually mean its density at 0 degrees Celsius and normal atmospheric pressure(760 millimeters of mercury).

Calculation of body weight and volume

V Everyday life we are often faced with the need to calculate the masses and volumes of different bodies. It is convenient to do this by applying density.

The densities of various substances are determined from tables, for example, the density of water is 1000 kg / m3, the density of ethyl alcohol is 800 kg / m3.

From the definition of density it follows that the mass of a body is equal to the product of its density and volume. The volume of the body is equal to the quotient of the mass and density. This is used in calculations:

m = ρ * V; or V = m / p;

gdn m is the mass of a given body, ρ is its density, V is the volume of the body.

Consider an example of such a calculation

An empty glass has a mass of m1 = 200 g. If you pour water into it, its mass will be m2 = 400 g. What mass will this glass have if you pour the same amount (by volume) of mercury?

Solution. Let's find a lot of poured water. It will be equal to the difference between the mass of a glass of water and the mass of an empty glass:

mwater = m2- m1 = 400 g 200 g = 200 g

Let's find the volume of this water:

V = m / ρw = 200 g / 1 g / cm3 = 200 cm3 (pw water density).

Let's find the mass of mercury in this volume:

mрт = ρртV = 13.6 g / cm3 * * 200 cm3 = 2720 g.

Let's find the required mass:

m = mrt + m1 = 2720 g + 200 g = 2920 g.

Answer: the mass of a glass with mercury is 2920 grams.

Let's consider a more complex calculation example

An ingot of two metals with densities ρ1 and ρ2, has mass m and volume V. Determine the volume of these metals in the ingot.

Solution. Let V1 be the volume of the first metal, V2 the volume of the second metal. Then V1 + V2 = V; V1 = V V2; ρ1V1 + p2V2 = ρ1V1 + ρ2 (V V1) = m

Instructions

To find mass, knowing the density, divide the volume of a body or substance by its density. That is, use the formula: m = V / ρ, where: V - volume,
ρ is the density,
V - volume. Before calculating the mass, bring all units of measurement into one system, for example, into the international system of measurement (SI). To do this, convert the volume (m³), and the density - in (kg / m³). In this case, the weight will be in kilograms.

If the density and volume are specified in the same system of units, then it is not necessary to produce a preliminary one in SI. In this case, the mass of a body or substance will be measured in the unit indicated in the numerator of the density unit (the volume units will be reduced in the calculation).
So, for example, if the volume is specified in liters and the density is in grams per liter, then the calculated mass will be in grams.

If the volume of a body (substance) is unknown or is not explicitly specified in the conditions of the problem, then try to measure, calculate, or find out using indirect (additional) data.
If the substance is free-flowing or liquid, then it is usually located in a container, which usually has a standard volume. So, for example, the volume of a barrel is usually 200 liters, the volume of a bucket is 10 liters, the volume of a glass is 200 milliliters (0.2 liters), the volume of a tablespoon is 20 ml, and the volume of a teaspoon is 5 ml. The volume of three-liter and one-liter cans is easy to guess from their names.
If the liquid does not occupy the entire container or the container is non-standard, then pour it into another container, the volume of which is known.
If there is no suitable container, pour the liquid using a measuring cup (cans, bottles). In the process of scooping out the liquid, simply count the number of such mugs and multiply by the volume of the measured container.

If the body has a simple shape, then calculate its volume using the appropriate geometric formulas. So, for example, if the body has the shape rectangular parallelepiped, then its volume will be equal to the product of the lengths of its edges. That is: Vpr. Par. = a * b * c, where: Vpr. par. Is the volume of a rectangular parallelepiped, and
a, b, c - values ​​of its length, width and height (thickness), respectively.

If the body has a complex geometric shape, then try (conditionally!) to split it into several simple parts, find the volume of each of them separately and then add the obtained values.

If the body cannot be divided into more simple shapes(for example, a figurine), then use the Archimedes technique. Submerge the body in water and measure the volume of the displaced liquid. If the body does not sink, then "drown" it with a thin stick (wire).
If it is problematic to calculate the volume of water displaced by the body, then weigh the spilled water, or find the difference between the initial and remaining mass of water. At the same time, the number of kilograms of water will be equal to the number of liters, the number of grams - to the number of milliliters, and the number of tons - to the number of cubic meters.

In actual problems in physics and mathematics, such quantities as volume, mass and density... Knowing the density and volume of a body or substance, it is absolutely permissible to detect it mass .

You will need

• - computer or calculator;
• - roulette;
• - measuring capacity;
• - ruler.

Instructions

1. As is known, objects with the same volume, but made of different materials, will have different masses (wood and metal, glass and plastic). The masses of bodies made of the same substance (without voids) are directly proportional to the volume of the objects in question. On the contrary, a continuous quantity is the ratio of the mass of an object to its volume. This value is called “density of matter. In the future, we will denote it by the letter d.

2. Based on the definition, d = m / V, where m is the mass of an object (kg), V is its volume (m3). As can be seen from the formula, the density of a substance is the mass of a unit of its volume.

3. It is allowed to find out the density of the substance from which the object is made from the density table in the appendix to the physics textbook or on the website http://www.kristallikov.net/page15.html, where the densities of virtually all existing substances are given.

5. If it is not possible to accurately measure the geometric dimensions of the body, use Archimedes' law. To do this, take a vessel that has a scale (or divisions) for measuring the volume of a liquid, lower the object into water (in the vessel itself, equipped with divisions). The volume for the one that increases the contents of the vessel is the volume of the body immersed in it.

6. If the density d and volume V of an object are known, it is invariably allowed to detect its mass using the formula: m = V * d. Before calculating the mass, bring all units of measurement into one system, say, the international system of measurement SI.

7. The result from the above formulas is further: in order to get the desired value of mass, knowing the density and volume, you need to multiply the value of the volume of the body by the value of the density of the substance from which it is made.

Mass body traditionally determined experimentally. To do this, take the load, put it on the scales and get the result of the measurement. But when solving physical problems given in textbooks, the measurement of mass for objective reasons is unrealistic, but there are some data about the body. Knowing these data, it is allowed to determine the mass body implicitly by calculation.

Instructions

1. V school courses physics, chemistry, astronomy, it is allowed to meet the representation of mass. By mass body find the reciprocal values ​​- volume, density, force. Mass is a quantitative indicator of a substance; therefore, in problems in chemistry, the number of a substance is found based on the mass. Mass depends on the properties of the substance of which the body is composed, as well as on the number of this substance. There are several basic methods for calculating mass. They are chosen depending on what other physical quantities are specified in the problem. Let's consider each case separately.

2. The most common method for finding mass body Is its calculation based on volume and density. True, in a number of tasks, before determining the mass, it is necessary to calculate the volume itself, guided by other geometric collations body... Say, for a cylinder with a famous base area and height, made of a substance with a known density, the mass will be: m =? * V =? * S * h, where Vcyl. = S * h,? Is the density, S is the area of ​​the base of the cylinder, h is the height of the cylinder. If the volume is indicated in the problem directly, to find its mass it is rather primitive to multiply it by the density: m =? * V

3. Another branch of physics, where it is possible to calculate the mass - dynamics. Traditionally, it studies the interaction between body mi, action external forces on body, the state of bodies in uniform motion. Any body by force F gains acceleration when interacting with another body. Moreover, it is a certain mass m. The mass is related to the force by a further ratio: F = m * a, where a is the acceleration of a given body; m -mass body From here it is allowed to know the mass body: m = F / a

4. In chemistry textbooks, we find representations of the number of matter and molar mass. It is also possible to express the mass of a substance through these two quantities. Since the number of a substance is a physical quantity proportional to the number of particles that make up a substance, and the molar mass is the mass of one mole of a substance, it is allowed to calculate the mass of a given number of this substance in the following way: mw = Mw * nw, where Mw is the molar mass, nb is the number of substance

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Helpful advice
An example of the problem of finding the mass of a body. Perhaps a small steel ball with a radius of R = 5 cm is given. Determine the mass of the ball, if it is known that p des. = 7.8 mg / m ^ 3. Initially, find the volume of the ball. It is equal to: V = 4? R ^ 2 = 4 * 3.14 * 25 = 314 cm ^ 3 The mass is calculated in the following way: m = p * V = 7.8 * 314 = 24.492 g

Density is the ratio of mass to the volume occupied by it - for solids, and the ratio of molar mass to molar volume - for gases. In its most general form, volume (or molar volume) will be the ratio of mass (or molar mass) to its density. Density is known. What to do? First, determine the mass, then calculate the volume, and then make the necessary corrections.

Instructions

1. The volume of a gas is equal to the ratio of the product of the number of a substance multiplied by its molar mass- to a more closely known density. In other words, even knowing the density, you need to know the molar mass of the gas and the number of the substance, that is, how much mole of gas you have. In the thesis, knowing how many moles of gas you have, it is allowed to calculate its volume without even knowing the density - according to Avogadro's law, one mole of any gas occupies a volume of 22.4 liters. If, however, it is imperative to calculate the volume through density, then you will need to find out the mass of gas in a volume unknown so far.

2. The volume of a solid can be determined, even without knowing the density, by easily measuring it, and in the case of a difficult and hefty irregular shape, the volume is determined, say, by the volume of the liquid displaced by the solid. However, if it is necessary to calculate the volume precisely through the density, then the volume of a solid is the ratio of the body's mass to its density, and the mass is usually determined by simple weighing. If it is inconceivable to weigh the body for some reason (say, it is too huge or moves), then you will have to resort to rather difficult indirect calculations. For example, for a moving body, mass is the ratio of twice the kinetic energy to the square of its velocity, or the ratio of the force applied to the body to its acceleration. For a hefty large body at rest, you will have to resort to calculations in relation to the mass of the Earth, using the gravitational continuous and the moment of rotation. Or - through the calculation of the specific heat capacity of the substance; in any case, only density skills for calculating volume will be unsatisfactory.

3. Having calculated the mass of a solid, it is possible to calculate the volume - by simply dividing the mass by the density.

Note!
1. The above methods are more or less applicable only in the case of homogeneity of the substance of which the solid is composed2. The above methods are more or less applicable in a relatively close temperature range - from minus 25 to plus 25 degrees Celsius. When it changes aggregate state substance density can change abruptly; in this case, the formulas and methods of calculations will be completely different.

Mass as a physical quantity is a parameter that characterizes the force of the body's action on gravity. To calculate body weight in physics it is required to know two of its values: the density of the body material and its volume.

Instructions

1. Let a certain body be given with a volume V and a density of its substance p. Then his mass calculated as follows: m = p * V. For clarity, an example is given: Let an aluminum bar with a volume of 5 cubic meters be given. meters. The density of aluminum is 2700 kg / cu. meter. In this case, the mass of the bar will be: m = 2700/5 = 540 kg.

Note!
The representation of mass is often confused with another, no less rare, physical quantity - weight. Weight is measured in n / m? and characterizes the force that acts on the fulcrum. Mass, by its nature, does not have any point of support, and affects, as noted, only on the gravity of the Earth.

When solving some physical problems, it is required to detect density body... Occasionally, the density of a physical body must be determined in practice, say, in order to find out whether it will sink or not. By the way, the human body can also be attributed to physical bodies. Moreover, the representation of the "density" of the human body has long since come into common use. So a "firmly knocked down" person is traditionally called "dense", and the one who has the opposite body constitution is called "loose".

You will need

• calculator, scales, ruler, measuring cup, table of substance density.

Instructions

1. In order to detect the density of a physical body, determine what substance or material it consists of. After that, take the table of the density of substances and find the corresponding substance in it. So, say, if an object is made of aluminum, its density will be 2.7 g / cm ?.

2. If the body consists of several substances, then find in the appropriate tables the density of all of them. In order to find the density of the body in the aggregate, determine the contribution of all matter to the formation of the density of the object. To do this, determine the volume or mass of the entire homogeneous part, and then calculate the mass and volume of each body.

3. Let, say, the body consists of 2 parts with mass m1 and m2, respectively. The density of the entire part is? 1 and? 2. In order to find the average body density, find the total volume: V = V1 + V2 = m1 *? 1 + m2 *? 2, and then divide by the total body weight (m = m1 + m2):? = V / m = (m1 *? 1 + m2 *? 2) / (m1 + m2), where: V is the total volume of the body; V1 and V2 are the volume of the first and second parts of the body, respectively; m is the total mass of the body ; m1 and m2 are the mass of the first and second parts of the body, respectively ;? - the average density of the body;? 1 and? 2 - the density of the first and second parts of the body, respectively.

4. If the volumes (V1 and V2) of the entire body part, as well as their density, are famous, use a similar formula to calculate the density of the body :? = V / m = (V1 + V2) / (m1 + m2) = (V1 + V2) / (V1 /? 1 + V2 /? 2). The parameter designations are the same as in the previous formula.

5. If the material (substance) that makes up the body is unknown or has a variable density (say, wood, the density of which depends on moisture), in order to detect its density, determine its volume and divide by mass. That is, use the formula: = V / m. For this, finally, you will have to calculate or measure the volume and mass of the body, but this method will give the most accurate result. If the body has a primitive shape geometric shape, calculate its volume using the appropriate stereometry formulas. Determine the volume of difficult bodies through the volume of liquid displaced by them. Find body weight with weighing support.

Tip 6: How to detect mass when volume and density are famous

The mass of a body is its most important physical collation. In the current physical science there is a distinction between the concept of "mass": gravitational mass (as the degree of influence of a body on the earth's gravity) and inertial mass (what effort is needed to bring the body out of the state of inertia). Find out anyway mass hefty easy if famous density and body volume.

Instructions

1. In the event that the body has such famous indicators as its volume (V) and density(p), then to calculate body weight you will need to use the formula: m = p * V.

2. For clarity, it is allowed to give an example. It is required to discover mass concrete slab, whose volume is 15 m? Solution: to find the mass of a concrete slab, you only need to know it density... In order to find out this information, one must use the table of densities of different substances.

3. According to this table density concrete is 2300 kg / m2. Then in order to discover mass concrete slab, you will need to perform a primitive algebraic action: m = 15 * 2300 = 34500 kg, or 34.5 tons. Result: The mass of the concrete slab is 34.5 tons.

4. The measurement of mass by the traditional method takes place using one of the oldest devices in society - with the support of scales. This is due to the comparison of the body weight with the help of the reference weight of the load - weights.

Note!
When calculating according to the above formula, you need to comprehend that in this way the rest mass of a given body is recognized. It is fascinating that many elementary particles have an oscillating mass, which depends on the speed of their movement. If an elementary particle moves with the speed of a body, then this particle is massless (say, a photon). If the speed of the particle is lower than the speed of light, then such a particle is called bulky.

Helpful advice
When measuring mass, it is never possible to forget in which system the final result will be given. It means that in the SI system, mass is measured in kilograms, while in the CGS system, mass is measured in grams. Also, mass is measured in tons, centners, carats, pounds, ounces, poods, as well as in many other units depending on the country and culture. In our country, for example, the mass has long been measured in poods, berkovtsy, zolotniks.

You have a two-hundred-liter barrel. You plan to fill it entirely with diesel fuel, which you use to heat your mini-boiler room. And how much will it weigh, filled with solarium? Now let's calculate.

You will need

• - table of specific gravity of substances;
• - knowledge to make the simplest mathematical calculations.

Instructions

1. In order to find the mass of a substance by its volume, use the formula for the specific density of the substance. P = m / v here p is the specific density of the substance; m is its mass; v is the occupied volume. We will consider the mass in grams, kilograms and tons. Volumes in cubic centimeters, decimeters and measures. And the specific density, respectively, in g / cm3, kg / dm3, kg / m3, t / m3.

2. It turns out, according to the terms of the problem, you have a two-hundred-liter barrel. This means: a barrel with a capacity of 2 m3. It is called two-hundred-liter, since water, with its specific gravity equal to one, contains 200 liters in such a barrel. You care about the mass. Consequently, bring it to the first place in the presented formula m = p * v On the right side of the formula, the value of p is unknown - the specific gravity of diesel fuel. Find it in the directory. It is even easier to enter a search query on the Internet “specific gravity of diesel fuel”.

3. Found: the density of summer diesel fuel at t = +200 C - 860 kg / m3. Substitute the values ​​in the formula: m = 860 * 2 = 1720 (kg) 1 ton and 720 kg - this is how much 200 liters of summer diesel fuel weigh. Having hung the barrel in advance, it is allowed to calculate the total weight and estimate the capacity of the rack under the barrel with solarium.

4. In rural areas, it can be useful to calculate in advance the mass of firewood needed by cubic capacity in order to determine the carrying capacity of the transport on which this firewood will be delivered. For example, you need at least 15 cubic meters for the winter. meters of birch firewood. Look in the reference books for the density of birch firewood. This is: 650 kg / m3. Calculate the mass by substituting the values ​​into the same formula for specific gravity m = 650 * 15 = 9750 (kg) Now, based on the carrying capacity and capacity of the body, you can determine the type vehicle and the number of trips.

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Note!
Older people are more familiar with the concept of specific gravity. Specific gravity of a substance is the same as specific gravity.

There are situations when you need to calculate mass liquids contained in a container. This can be during a training session in the laboratory, and in the course of solving a household problem, say, during repair or painting.

Instructions

1. The easiest way is to weigh yourself. First, weigh the container together with the liquid, then pour the liquid into another container of suitable size and weigh the empty container. And after that, all that remains is to subtract the smaller value from the larger value, and you will get the result. Of course, it is allowed to resort to this method only when dealing with non-viscous liquids, which after overflow do not actually remain on the walls and bottom of the first container. That is, some number will remain then, but it will be so small that it is allowed to neglect it, this will not approximately affect the accuracy of the calculations.

2. And if the liquid is viscous, say, glycerin? How then to define it mass? In this case, you need to know its density (?) And occupied volume (V). And then everything is more elementary. Mass (M) is calculated by the formula M =? V. Of course, before calculating, you need to translate the factors into an integral system of units.

3. Density liquids allowed to be found in a physical or chemical reference book. But it's better to use a measuring device - a density meter (densitometer). And the volume can be calculated, knowing the shape and dimensions of the container (if it has the correct geometric shape). Say, if the same glycerin is in a cylindrical barrel with a base diameter d and a height h, then the barrel volume is calculated by the formula:? D ^ 2h / 4.

4. Let's imagine you are given the following task. In the course of a laboratory experiment, a liquid of mass m, located in the calorimeter vessel and having a heat capacity c, was heated from the initial temperature t1 to the final temperature t2. A number of heat equal to Q was spent on this heating. What is the mass of this liquids ?

5. All quantities, besides m, are famous; heat losses during the experiment can be neglected. There is certainly nothing difficult about calculating. You just need to remember the formula that unites the number of heat, mass liquids, its heat capacity and temperature difference. It is as follows: Q = mc (t2-t1). Consequently, the mass liquids calculated by the formula: m = Q / c (t2-t1). Substituting the quantities you know into the formula, you can easily calculate mass liquids m.

The value of the Planck continuous, denoted by the letter h, was determined experimentally in laboratory conditions with an accuracy of ten decimal places. It is also allowed to put a skill by its definition in a physical office, but the accuracy will be much less.

You will need

• - photocell with external photoelectric effect;
• - a light source with a monochromator;
• - continuously adjustable 12 V power supply;
• - voltmeter;
• - microammeter;
• - lamp 12 V, 0.1 A;
• - a calculator that works with numbers presented in exponential form.

Instructions

1. Use a photocell with external photoelectric effect for the skill. An element with an internal photoelectric effect (i.e., not a vacuum, but a semiconductor) will not work. Test it for suitability for the skill, for which connect to the microammeter lightly, observing the polarity. Direct light on it - the arrow should deviate. If this does not happen, use a different type of photocell.

2. Without changing the polarity of connecting either the photocell or the microammeter, break the circuit and turn on an adjustable power supply in its open circuit, the output voltage of which can be smoothly changed from 0 to 12 V (with two knobs for bold and precise adjustment). Attention: this source should be turned on not in direct, but in reverse polarity, so that it does not increase with its voltage, but reduces the current through the element. Connect a voltmeter parallel to it - this time in the polarity corresponding to the designations on the source. It is permissible not to do this if the unit has a built-in voltmeter. Also connect a load in parallel with the output, say, in the form of a 12 V, 0.1 A lamp, in case the internal resistance of the source is large. The light of the lamp should not fall on the photocell.

3. Set the source voltage to zero. Direct a stream of light from a source with a monochromator into the photocell, setting a wavelength of about 650 nanometers. Smoothly increasing the voltage of the power source, achieve that the current through the microammeter becomes zero. Leave the slider in this position. Record the voltmeter and monochromator scale readings.

4. Set the wavelength on the monochromator to about 450 nanometers. Increase the output voltage of the power supply slightly so that the current through the photocell becomes zero again. Record the new voltmeter and monochromator scale readings.

5. Calculate the frequency of light in hertz for the first and second skills. To do this, divide the speed of light in a vacuum, equal to 299792458 m / s, by the wavelength, previously converted from nanometers to meters. For simplicity, consider the refractive index of air to be 1.

6. Subtract the higher voltage from the lower voltage. Multiply the total by the electron charge equal to 1.602176565 (35) 10 ^ (? 19) coulomb (C), and then divide by the total of subtracting the higher frequency from the lower one. The result is a continuous Planck expressed in joules multiplied by a second (J · s). If she gets close to official meaning equal to 6.62606957 (29) · 10 ^ (- 34) J · s, the skill can be considered set positively.

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Note!
Exercise caution when working with electrical equipment.

Class: 7

Lesson objectives.

1. Educational: to systematize the knowledge that students have about the concepts: “density”, “mass”, “volume”, to expand the area of ​​knowledge about these concepts, to develop the ability to apply the studied material to solve practical problems.

2. Developing: the formation of logical thinking, continue to develop the skill of solving physical problems.

3. Educational: instilling in students for friendly communication, mutual assistance.

Lesson type: combined.

Equipment: 15 sets of tables 1 and 2.

During the classes

1. Organizational stage.

2. Knowledge update.

Teacher activity	Student activities
- What is density?	A physical quantity that shows how much of a substance is contained in a unit of volume.
- What does it mean that the density of iron is 6800 kg / m 3? How can you find the density of a substance? What does body weight depend on?	This means that the mass of 1 m 3 of iron is 6800 kg. To find the density of a substance, you need to divide the mass by the volume.
- How to find body weight?	The mass of a body depends on its volume and the density of the substance that this body consists of.
- How to find the volume of a body, if you know its mass and the substance of which the body is composed?	To find the mass of the body, gently multiply its density by its volume. To find the volume of a body, you need to divide its mass by its density.

3. Solving problems
1. How will we give marks for work in the lesson on the principle of addition or subtraction?	By the principle of addition.
2. Table 1(Appendix # 1). There are loads in the warehouse: chalk, cork, birch, ice, steel. Each cargo is packed in containers of 2 m 3. five vehicles were called in to carry these goods. Your task is to distribute the goods among the vehicles.	Find the mass of loads.
- What needs to be done to distribute the goods among the vehicles?
- How to find the mass of a substance if its density and volume are known?	kg / m 3
- In what units is the density of a substance measured?	In kilograms
- In what units will the mass be calculated?	In tons and kilograms
- In what units is the carrying capacity of vehicles expressed?	In tons, and for a Muscovite in kilograms
- In what units do you need to get the mass of goods? Solve this problem and distribute the loads among the vehicles. The teacher checks the correctness of the completed assignment with the first student who solved it, and appoints him as his assistant. Records of the number of points scored are made in the cards (Appendix No. 3) of the students.	Students solve problems and distribute loads.
3. table 2(Appendix No. 2). There are five different fluids that have the same mass. These liquids must be poured into five different containers. What needs to be done to pour liquids into vessels?	Find the volume of liquids.
- How to find the volume if the mass of the substance and its density are known?
- In what units will the calculated volume be obtained?	in m 3.
- In what units is the volume of the vessels given?	In liters and milliliters
- In what units do you need to get the volume of liquids?	In liters and milliliters
Solve this problem and distribute the liquid through the vessels. The teacher checks the correctness of the completed assignment with the first student who decided, and appoints him as his assistant. Records of the number of points scored are made on the student cards.	The students solve the problem.
4. Reflection.
- What physical concepts did you use to complete the tasks? Compare number of points that you gave yourself, with the number of points that the reviewers gave you. What conclusion can you make for yourself? Are you ready for test work?	Mass, density, volume.

Homework: repeat 18-22.

Weight

Inert mass

Gravitational mass

Examples of problem solving

Solution.

Exercise. What is the mass of 2m 3 of copper?

Answer.(kg)

Brief theory

Online calculators

Body mass formula

Definition and formula of body weight

In Newtonian mechanics, the mass of a body is called a scalar physical quantity, which is a measure of its inertial properties and a source of gravitational interaction. In classical physics, mass is always positive.

Weight- an additive value, which means: the mass of each set of material points (m) is equal to the sum of the masses of all separate parts of the system (m i):

In classical mechanics, it is considered:

• body weight is not dependent on body movement, on the impact of other bodies, body position;
• the law of conservation of mass is fulfilled: the mass of a closed mechanical system bodies are unchanged in time.

Inert mass

where mass determines the inert properties of a material point (inert mass).

Gravitational mass

The mass of a material point is included in the law of universal gravitation, while it determines the gravitational properties of a given point, while it is called gravitational (heavy) mass.

where g is the acceleration due to gravity. If we carry out observations at the same point, then the accelerations of gravity are the same.

Formula for calculating mass through body density

Body weight can be calculated as:

where is the density of the substance of the body, where the integration is carried out over the volume of the body. If the body is homogeneous (), then the mass can be calculated as:

Mass in special relativity

In SRT, mass is invariant, but not additive. It is defined here as:

where E - total energy free body, p is the momentum of the body, c is the speed of light.

The relativistic mass of a particle is determined by the formula:

where m 0 is the rest masses of the particle, v is the speed of the particle.

The basic SI unit of mass is: [m] = kg.

Examples of problem solving

Solution. With absolutely inelastic collision of particles, which before the impact had the same masses and velocities, one particle at rest is formed (Fig. 1), the rest energy of which is equal to:

In our case, the law of conservation of mechanical energy is fulfilled. The particles have only kinetic energy. By the condition of the problem, the speed of the particles is close to the speed of light, hence? we operate with the concepts of relativistic mechanics:

where E 1 is the energy of the first particle before impact, E 2 is the energy of the second particle before impact.

We write the law of conservation of energy in the form:

From expression (1.3) it follows that the mass of the particle obtained as a result of the fusion is equal to:

Exercise. What is the mass of 2m 3 of copper?

Moreover, if the substance (copper) is known, then using the reference book you can find its density. The density of copper will be considered equal to Cu = 8900 kg / m 3. All quantities are known for the calculation. Let's carry out the calculations:

Answer.(kg)

Brief theory

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How to find mass?

Many of us during school time asked the question: How to find body weight? Now we will try to answer this question.

Finding mass through its volume

It is quite easy to solve the problem of how to find the mass of a substance through its volume. To do this, apply the formula for the specific density of the substance

where p is the specific gravity of the substance;

v - occupied volume.

Grams, kilograms and tons will be used as a measure of mass. Volume measures: cubic centimeters, decimeters and meters. Specific gravity will be calculated in kg / dm, kg / m, g / cm, t / m.

Thus, in accordance with the conditions of the task, we have at our disposal a barrel with a volume of two hundred liters. This means that its volume is 2 m.

But you want to know how to find mass. From the above formula, it is derived as follows:

First, we need to find the value of p - the specific gravity of diesel fuel. Find given value it is possible using the reference book.

In the book we find that p = 860.0 kg / m.

Then we substitute the obtained values ​​into the formula:

m = 860 * 2 = 1720.0 (kg)

Finding mass through density and volume

Very often, in practical tasks in physics, you can find such quantities as mass, density and volume. In order to solve the problem of how to find the mass of a body, you need to know its volume and density.

Items that you will need:

2) Calculator (computer).

3) Capacity for measurement.

Now you need to solve the problem of how to find the mass in accordance with the formula d = m / V, where

m is the mass of the item (in kilograms),

V is its volume (in cubic meters).

Thus, the density of a substance is the mass of a unit of its volume.

If you need to find the density of the material from which the object is created, then you should use the density table, which can be found in a standard physics textbook.

The volume of the object is calculated by the formula V = h * S, where

H - object height (m),

S - the area of ​​the base of the object (m).

Knowing the volume V and the density d of an object, you can easily find its mass by the formula m = d * V. Before calculating the mass, you need to bring all measuring units into a single system, for example, the SI system, which is an international measuring system.

In accordance with the above formulas, the following conclusion can be drawn: to find the required mass with a known volume and known density, it is required to multiply the density value of the material from which the body is made by the volume of the body.

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