Physical quantities. Unified State Examination in Physics: reviewing assignments with the teacher Units of measurement of physical quantities

Example. The following table is presented in the directory of physical properties of various materials.

Table

1) With equal dimensions, an aluminum conductor will have greater mass and lower electrical resistance compared to a copper conductor.

2) Conductors made of nickel and constantan with the same dimensions will have the same electrical resistance.

3) Conductors made of brass and copper with the same dimensions will have different masses.

4) When replacing the Constantine spiral of an electric stove with a nichrome one of the same size, the electrical resistance of the spiral will decrease.

5) With an equal cross-sectional area, a constantan conductor 10 m long will have an electrical resistance almost 10 times greater than a brass conductor 8 m long.

This task requires very careful analysis of the tables. In order to cope with the task, you should:

1. Determine the values of which physical quantities are given in the tables.

2. Write down on a draft the formulas that include these quantities.

4. Choose the correct statements.

5. Be sure to carry out a self-test and then write down the numbers of the correct answers.

Tasks for independent work

159. The student conducted an experiment to study the force of sliding friction, moving a block with weights evenly along horizontal surfaces using a dynamometer (see figure).

The results of experimental measurements of the mass of the block with loads m, the area of contact between the block and the surface S and the applied force F are presented in the table.

Which statements correspond to the results of the experimental measurements?

From the proposed list of statements, select two correct ones. Indicate their numbers.

1) The sliding friction coefficients in the second and third experiments are equal

2) The sliding friction coefficient between the block and the wooden slats is greater than the sliding friction coefficient between the block and the plastic slats

3) The sliding friction force depends on the area of contact between the block and the surface

4) As the mass of the block with loads increases, the sliding friction force increases

5) The sliding friction force depends on the type of contacting surfaces

160. The electrical circuit contains a current source, conductor AB, a switch and a rheostat. The conductor AB is placed between the poles of a permanent magnet (see figure).

Using the picture, select two true statements from the list provided. Indicate their numbers.

1) When you move the rheostat slider to the right, the Ampere force acting on conductor AB will decrease.

2) When the key is closed, the conductor will be pushed out of the magnet area to the right.

3) When the key is closed, the electric current in the conductor is directed from point A to point B.

4) The magnetic field lines of the permanent magnet in the area where the conductor AB is located are directed vertically upward.

5) Electric current flowing in conductor AB creates a uniform magnetic field.

161. The teacher conducted the following experiment. A hot plate (1) was placed opposite a hollow cylindrical closed box (2), connected by a rubber tube to the elbow of a U-shaped pressure gauge (3). Initially, the fluid in the knees was at the same level. After some time, the fluid levels in the pressure gauge changed (see figure).

Select two statements from the proposed list that correspond to the results of the experimental observations. Indicate their numbers.

1) The transfer of energy from the tile to the box was carried out mainly due to radiation.

2) The transfer of energy from the tile to the box was carried out mainly due to convection.

3) During the process of energy transfer, the air pressure in the box increased.

4) Matte black surfaces absorb energy better than light shiny surfaces.

5) The difference in liquid levels in the pressure gauge elbows depends on the temperature of the tile.

162. The figure shows a graph of temperature t versus time τ during continuous heating and subsequent continuous cooling of a substance initially in a solid state.

1) The BV section of the graph corresponds to the process of melting of the substance.

2) The section of the HD graph corresponds to the cooling of the substance in the solid state.

3) During the transition of a substance from state A to state B, the internal energy of the substance does not change.

4) In the state corresponding to point E on the graph, the substance is entirely in a liquid state.

5) During the transition of a substance from state D to state F, the internal energy of the substance decreases.

163. The figure shows graphs of the dependence of displacement x on time t during oscillations of two mathematical pendulums. From the proposed list of statements, select two correct ones. Indicate their numbers.

1) When pendulum 2 moves from the position corresponding to point A to the position corresponding to point B, the kinetic energy of the pendulum increases.

2) In the position corresponding to point B on the graph, both pendulums have maximum kinetic energy.

3) The periods of oscillation of the pendulums coincide.

4) In the position corresponding to point D on the graph, pendulum 1 has maximum speed.

5) Both pendulums perform damped oscillations.

165. The figure shows graphs of coordinates versus time for two bodies moving along the Ox axis.

Using the graph data, select two true statements from the list provided. Indicate their numbers.

1) At time t 1, body (2) was moving with a greater absolute speed.

2) At time t 2 bodies had identical velocities.

3) In the time interval from t 1 to t 2, both bodies moved in the same direction.

4) In the time interval from 0 to t 1, both bodies moved uniformly.

5) By time t 1, body (1) has traveled a greater distance.

166. The figure shows a graph of the temperature versus the amount of heat received for two substances of the same mass. Initially, each of the substances was in a solid state.

Using the graph data, select two true statements from the list provided. Indicate their numbers.

1) The specific heat capacity of the first substance in the solid state is less than the specific heat capacity of the second substance in the solid state.

2) In the process of melting the first substance, more heat was consumed than in the process of melting the second substance.

3) The presented graphs do not allow us to compare the boiling points of two substances.

4) The melting point of the second substance is higher.

5) The specific heat of fusion of the second substance is greater.

167. In Fig. 1 shows the ranges of audible sounds for humans and various animals, and Fig. 2 - ranges corresponding to infrasound, sound and ultrasound.

Using the data in the drawings, select two correct ones from the proposed list of statements. Indicate their numbers.

1) The wavelength of ultrasound is greater than the wavelength of infrasound.

2) Of the animals presented, the budgerigar has the widest range of audible sounds.

3) The range of audible sounds in a cat is shifted to the ultrasound region compared to the human range.

4) Sounds with a frequency of 10 kHz belong to the infrasonic range.

5) A sound signal having a wavelength of 3 cm in the air will be heard by all represented animals and humans. (The speed of sound in air is 340 m/s.)

Using the data in the table, select two correct statements from the list provided. Indicate their numbers.

1) With equal dimensions, an aluminum conductor will have less mass and greater electrical resistance compared to a copper conductor.

2) Conductors made of nichrome and brass with the same dimensions will have the same electrical resistance.

3) Conductors made of constantan and nickel with the same dimensions will have different masses.

4) When replacing the nickel spiral of an electric stove with a nichrome one of the same size, the electrical resistance of the spiral will decrease.

5) Given the same cross-sectional area, a constantan conductor 4 m long will have the same electrical resistance as a nickel conductor 5 m long.

Using the data in the table, select two correct statements from the list provided. Indicate their numbers.

1) Copper wire will begin to melt if it is placed in a bath of molten aluminum at its melting temperature.

2) The density of lead is almost 4 times less than the density of aluminum.

3) During the crystallization of 3 kg of zinc taken at its melting point, the same amount of heat will be released as during the crystallization of 2 kg of copper at its melting temperature.

4) The tin soldier will drown in molten lead.

5) A zinc ingot will float in molten tin almost completely submerged.

Using the data in the table, select two correct statements from the list provided. Indicate their numbers.

1) With the same mass, a body made of copper will have a smaller volume compared to a body made of lead and will give off approximately 3 times more heat when cooled by the same number of degrees.

2) Bodies made of zinc and silver with the same volume will have the same mass

3) With the same dimensions, the mass of a platinum body is approximately 2 times greater than the mass of a silver body

4) The temperature of bodies of equal volume made of tin and zinc will change by the same number of degrees when the same amount of heat is imparted to them

5) With equal mass, a body made of platinum must be given the same amount of heat to be heated by 30 °C as a body made of zinc to be heated by 10 °C.

From the statements below, choose the correct ones and write down their numbers.

1) The speed of a whale is equal to the speed of a fox

2) The speed of a shark is less than the speed of a beetle

3) The speed of a dolphin is greater than the speed of a starling

4) The speed of a crow is greater than the speed of an elephant

5) The speed of a giraffe is greater than the speed of a crow

172. A solution of copper sulfate (blue solution) was poured into two identical vessels, and water was poured on top (Fig. 1). One of the vessels was left at room temperature, and the second was placed in the refrigerator. A few days later, the solutions were compared and it was noted that the boundary of the two liquids was much more noticeably blurred in the vessel, which was at room temperature (Fig. 2 and 3).


Figure 1. Liquid boundary in the initial state	Figure 2. Mixing liquids in a vessel at room temperature	Figure 3. Mixing liquids in a vessel located in the refrigerator

Using the data in the table, select two correct statements from the list provided. Indicate their numbers.

1) The process of diffusion can be observed in liquids.

2) The rate of diffusion depends on the temperature of the substance.

3) The rate of diffusion depends on the state of aggregation of the substance.

4) The rate of diffusion depends on the type of liquid.

5) In solids, the diffusion rate is the lowest.

All objects of the material world have a number of properties that allow us to distinguish one object from another.

Property an object is an objective feature that manifests itself during its creation, operation and consumption.

The property of an object can be expressed qualitatively - in the form of a verbal description, and quantitatively - in the form of graphs, figures, diagrams, tables.

Metrological science deals with measuring the quantitative characteristics of material objects - physical quantities.

Physical quantity- this is a property that is qualitatively inherent in many objects, and quantitatively inherent to each of them.

For example, mass have all material objects, but each of them mass value individual.

Physical quantities are divided into measurable And assessed.

Measurable physical quantities can be expressed quantitatively in the form of a certain number of established units of measurement.

For example, the network voltage value is 220 IN.

Physical quantities that do not have a unit of measurement can only be estimated. For example, smell, taste. Their assessment is carried out by tasting.

Some quantities can be estimated on a scale. For example: material hardness - on the Vickers, Brinell, Rockwell scale, earthquake strength - on the Richter scale, temperature - on the Celsius (Kelvin) scale.

Physical quantities can be qualified by metrological criteria.

By types of phenomena they are divided into

A) real, describing the physical and physico-chemical properties of substances, materials and products made from them.

For example, mass, density, electrical resistance (to measure the resistance of a conductor, current must pass through it, this measurement is called passive).

b) energy, describing the characteristics of the processes of transformation, transmission and use of energy.

These include: current, voltage, power, energy. These physical quantities are called active. They do not require an auxiliary energy source.

There is a group of physical quantities that characterize the course of processes over time, for example, spectral characteristics, correlation functions.

By accessories to various groups of physical processes, the values can be

· spatio-temporal,

· mechanical,

· electrical,

· magnetic,

· thermal,

· acoustic,

· light,

· physical and chemical,

· ionizing radiation, atomic and nuclear physics.

By degrees of conditional independence physical quantities are divided into

· basic (independent),

· derivatives (dependent),

· additional.

By presence of dimension physical quantities are divided into dimensional and dimensionless.

Example dimensional magnitude is force, dimensionless- level sound power.

To quantify a physical quantity, the concept is introduced size physical quantity.

Size of physical quantity- this is the quantitative determination of a physical quantity inherent in a specific material object, system, process or phenomenon.

For example, each body has a certain mass, therefore, they can be distinguished by mass, i.e. by physical size.

The expression of the size of a physical quantity in the form of a certain number of units accepted for it is defined as the value of a physical quantity.

The value of a physical quantity is This is an expression of a physical quantity in the form of a certain number of units of measurement accepted for it.

The measurement process is a procedure for comparing an unknown quantity with a known physical quantity (compared) and in this regard the concept is introduced true meaning physical quantity.

True value of a physical quantity is the value of a physical quantity that ideally characterizes the corresponding physical quantity in qualitative and quantitative terms.

The true value of independent physical quantities is reproduced in their standards.

The true meaning is rarely used, more used real value physical quantity.

Real value of a physical quantity is a value obtained experimentally and somewhat close to the true value.

Previously, there was the concept of “measurable parameters”; now, according to the regulatory document RMG 29-99, the concept of “measurable quantities” is recommended.

There are many physical quantities and they are systematized. A system of physical quantities is a set of physical quantities formed in accordance with accepted rules, when some quantities are taken as independent, while others are defined as functions of independent quantities.

In the name of a system of physical quantities, symbols of quantities accepted as basic ones are used.

For example, in mechanics, where lengths are taken as basic - L , weight - m and time - t , the name of the system accordingly is Lm t .

The system of basic quantities corresponding to the international system of SI units is expressed by symbols LmtIKNJ , i.e. symbols of basic quantities are used: length - L , weight - M , time - t , current strength - I , temperature - K, the amount of substance - N , the power of light - J .

Basic physical quantities do not depend on the values of other quantities of this system.

Derived physical quantity is a physical quantity included in a system of quantities and determined through the basic quantities of this system. For example, force is defined as mass times acceleration.

3. Units of measurement of physical quantities.

A unit of measurement of a physical quantity is a quantity that, by definition, is assigned a numerical value equal to 1 and which is used for the quantitative expression of physical quantities homogeneous with it.

Units of physical quantities are combined into a system. The first system was proposed by Gauss K (millimeter, milligram, second). Now the SI system is in force; previously there was a standard of the CMEA countries.

Units of measurement are divided into basic, additional, derivative and non-systemic.

In the SI system seven basic units:

· length (meter),

· weight (kilogram),

· time (second),

· thermodynamic temperature (kelvin),

· amount of substance (mol),

· electric current strength (ampere),

· luminous intensity (candela).

Table 1

Designation of SI base units

9. Give examples of physical quantities known to you.
Joule, meter, newton, second, energy, temperature - ˚С or Kelvin

10. Enter in the appropriate columns of Table 3 the name, value, numerical value and unit of physical quantity for the following cases: air temperature 25˚С; path traveled by a pedestrian, 4000 m; runner's movement time is 15 s; cargo weight 30 kg; car speed is 60 km/h.

Table 3

11. Fill out table 4.

Table 4

12. Express the values of physical quantities in appropriate units.

13. The radius of the Earth is 6400 km. Express the radius of the Earth in meters.
64 m

14. The height of Mont Blanc is 4807 m. Express this height in kilometers.
4,807 km.

15. A high-speed train covers the distance from Moscow to St. Petersburg in 4 hours 20 minutes. Express this time in minutes; in seconds.
260 m, 15600 s.

16. The area of Great Britain is 230,000. Express this area in square meters.
23·

17. The volume of a drop of water is 8. Express this volume in cubic centimeters; in cubic meters.
8·

Preparation for the OGE and the Unified State Exam

Secondary general education

Line UMK N. S. Purysheva. Physics (10-11) (BU)

Line UMK G. Ya. Myakisheva, M.A. Petrova. Physics (10-11) (B)

Line UMK L. S. Khizhnyakova. Physics (10-11) (basic, advanced)

The figure shows a graph of the speed modulus versus time t. Determine from the graph the distance traveled by the car in the time interval from 10 to 30 s.

Answer: ____________________ m.

Solution

The path traveled by a car in a time interval from 10 to 30 s is most easily defined as the area of a rectangle whose sides are, the time interval (30 – 10) = 20 s and the speed v = 10 m/s, i.e. S= 20 · 10 m/s = 200 m.

Answer: 200 m.

The graph shows the dependence of the sliding friction force modulus on the normal pressure force modulus. What is the coefficient of friction?

Answer: _________________

Solution

Let us recall the relationship between two quantities, the modulus of the friction force and the modulus of the normal pressure force: F tr = μ N(1) , where μ is the friction coefficient. Let us express from formula (1)

Answer: 0.125.

The body moves along the axis OH under force F= 2 N, directed along this axis. The figure shows a graph of the dependence of the body velocity modulus on time. What power does this force develop at a moment in time? t= 3 s?

Solution

To determine the power of the force from the graph, we determine what the velocity module is equal to at the moment of time 3 s. The speed is 8 m/s. We use the formula to calculate power at a given time: N = F · v(1), let's substitute the numerical values. N= 2 N · 8 m/s = 16 W.

Answer: 16 W.

Task 4

A wooden ball (ρ w = 600 kg/m3) floats in vegetable oil (ρ m = 900 kg/m3). How will the buoyancy force acting on the ball and the volume of the part of the ball immersed in liquid change if the oil is replaced with water (ρ in = 1000 kg/m 3)

Increased;
Decreased;
Hasn't changed.

Write it down to the table

Solution

Since the density of the ball material (ρ w = 600 kg/m 3) is less than the density of oil (ρ m = 900 kg/m 3) and less than the density of water (ρ h = 1000 kg/m 3), the ball floats in both oil and in water. The condition for a body to float in a liquid is that the buoyant force Fa balances the force of gravity, that is F a = F t. Since the gravity of the ball did not change when replacing oil with water, then The buoyant force did not change either.

The buoyancy force can be calculated using the formula:

Fa = V pcht · ρ f · g(1),

Where V pt is the volume of the immersed part of the body, ρ liquid is the density of the liquid, g – acceleration of gravity.

The buoyancy forces in water and oil are equal.

F am = F aw, that's why V pcht · ρ m · g = V vpcht · ρ in · g;

V mpcht ρ m = V vpcht ρ in (2)

The density of oil is less than the density of water, therefore, for equality (2) to hold, it is necessary that the volume of the part of the ball immersed in oil V mpcht, was greater than the volume of the part of the ball immersed in water V vpcht. This means that when replacing oil with water, the volume of the part of the ball immersed in water decreases.

The ball is thrown vertically upward with an initial speed (see figure). Establish a correspondence between the graphs and physical quantities, the dependence of which on time these graphs can represent ( t 0 – flight time). For each position in the first column, select the corresponding position in the second and write down to the table selected numbers under the corresponding letters.

GRAPHICS

PHYSICAL QUANTITIES

Solution

Based on the conditions of the problem, we determine the nature of the motion of the ball. Considering that the ball moves with free fall acceleration, the vector of which is directed opposite to the chosen axis, the equation for the dependence of the velocity projection on time will have the form: v 1y = v y – GT (1) The speed of the ball decreases, and at the highest point of rise it is zero. After which the ball will begin to fall until the moment t 0 – total flight time. The speed of the ball at the moment of falling will be equal to v, but the projection of the velocity vector will be negative, since the direction of the y-axis and the velocity vector are opposite. Therefore, the graph with the letter A corresponds to the dependence of number 2) of the projection of speed on time. The graph under letter B) corresponds to the dependence under number 3) projection of the acceleration of the ball. Since the acceleration of gravity at the surface of the Earth can be considered constant, the graph will be a straight line parallel to the time axis. Since the acceleration vector and direction do not coincide in direction, the projection of the acceleration vector is negative.

It is useful to exclude incorrect answers. If the motion is uniformly variable, then the graph of the coordinates versus time should be a parabola. There is no such schedule. The modulus of gravity, this dependence must correspond to a graph located above the time axis.

The load of the spring pendulum shown in the figure performs harmonic oscillations between points 1 and 3. How does the kinetic energy of the pendulum weight, the speed of the load and the spring stiffness change when the pendulum weight moves from point 2 to point 1

For each quantity, determine the corresponding nature of the change:

Increased;
Decreased;
Hasn't changed.

Write it down to the table selected numbers for each physical quantity. The numbers in the answer may be repeated.

Kinetic energy of cargo	Load speed	Spring stiffness

Solution

The load on the spring performs harmonic oscillations between points 1 and 3. Point 2 corresponds to the equilibrium position. According to the law of conservation and transformation of mechanical energy, when a load moves from point 2 to point 1, the energy does not disappear, it transforms from one type to another. Total energy is conserved. In our case, the deformation of the spring increases, the resulting elastic force will be directed towards the equilibrium position. Since the elastic force is directed against the speed of movement of the body, it slows down its movement. Consequently, the speed of the ball decreases. Kinetic energy decreases. Potential energy increases. The stiffness of the spring does not change during the movement of the body.

Kinetic energy of cargo	Load speed	Spring stiffness

Answer: 223.

Task 7

Establish a correspondence between the dependence of the body’s coordinates on time (all quantities are expressed in SI) and the dependence of the velocity projection on time for the same body. For each position in the first column, select the corresponding position in the second and write down to the table selected numbers under the corresponding letters

COORDINATE

SPEED

Where X 0 – initial coordinate of the body; v x– projection of the velocity vector onto the selected axis; a x– projection of the acceleration vector onto the selected axis; t– movement time.

For body A we write: initial coordinate X 0 = 10 m; v x= –5 m/s; a x= 4 m/s 2. Then the equation for the projection of velocity versus time will be:

v x= v 0x + a x t (2)

For our case vx = 4t – 5.

For body B we write, taking into account formula (1): X 0 = 5 m; v x= 0 m/s; a x= –8 m/s 2 . Then we write the equation for the projection of velocity versus time for body B v x = –8t.

Where k – Boltzmann constant, T – gas temperature in Kelvin. From the formula it is clear that the dependence of the average kinetic energy on temperature is direct, that is, the number of times the temperature changes, the number of times the average kinetic energy of the thermal motion of molecules changes.

Answer: 4 times.

Task 9

In a certain process, the gas gave up an amount of heat of 35 J, and the internal energy of the gas in this process increased by 10 J. How much work was done on the gas by external forces?

Solution

The problem statement deals with the work of external forces on the gas. Therefore, it is better to write the first law of thermodynamics in the form:

∆U = Q + A v.s (1),

Where ∆ U= 10 J – change in the internal energy of the gas; Q= –35 J – the amount of heat given off by the gas, A v.s – work of external forces.

Let's substitute the numerical values into formula (1) 10 = –35 + A v.s; Therefore, the work done by external forces will be equal to 45 J.

Answer: 45 J.

The partial pressure of water vapor at 19° C was equal to 1.1 kPa. Find the relative humidity of the air if the saturated vapor pressure at this temperature is 2.2 kPa?

Solution

By definition of relative air humidity

φ – relative air humidity, in percent; P v.p – partial pressure of water vapor, P n.p. – saturated vapor pressure at a given temperature.

Let's substitute the numerical values into formula (1).

Answer: 50%.

The change in state of a fixed amount of monatomic ideal gas occurs according to the cycle shown in the figure.

Establish a correspondence between processes and physical quantities (∆ U– change in internal energy; A– gas work), which characterize them.

For each position from the first column, select the corresponding position from the second column and write the selected numbers in the table using the corresponding letters.

PROCESSES

PHYSICAL QUANTITIES

	transition 1 → 2
	transition 2 → 3

	Δ U > 0; A > 0
	Δ U < 0; A < 0
	Δ U < 0; A = 0
	Δ U > 0; A = 0

Solution

This graph can be rearranged in axes PV or deal with what is given. In section 1–2, isochoric process V= const; Pressure and temperature rise. Gas does not do work. That's why A= 0, The change in internal energy is greater than zero. Consequently, the physical quantities and their changes are correctly written under number 4) Δ U > 0; A= 0. Section 2–3: isobaric process, P= const; temperature increases and volume increases. The gas expands, gas work A>0. Therefore, transition 2–3 corresponds to entry number 1) Δ U > 0; A > 0.

An ideal monatomic gas located in a cylinder under a heavy piston (friction between the surface of the piston and the cylinder can be neglected) is slowly heated from 300 K to 400 K. The external pressure does not change. Then the same gas is heated again from 400 K to 500 K, but with the piston fixed (the piston does not move).

Compare the work done by the gas, the change in internal energy and the amount of heat received by the gas in the first and second processes.

For each quantity, determine the corresponding nature of the change:

Increased;
Decreased;
Hasn't changed.

Write it down to the table selected numbers for each physical quantity. The numbers in the answer may be repeated.

Solution

If a gas is slowly heated in a cylinder with a loose heavy piston, then at a constant external pressure the process can be considered isobaric (gas pressure does not change)

Therefore, the gas work can be calculated using the formula:

A = P · ( V 2 – V 1), (1)

Where A– gas work in an isobaric process; P– gas pressure; V 1 – volume of gas in the initial state; V 2 – volume of gas in the final state.

The change in internal energy of an ideal monatomic gas is calculated by the formula:

∆U =	3	v R∆t (2),
	2

Where v– amount of substance; R– universal gas constant; ∆ T– change in gas temperature.

∆T= T 2 – T 1 = 400 K – 300 K = 100 K.

According to the first law of thermodynamics, the amount of heat received by the gas is equal to

Q = ∆U + A (3)

Q = 150v R + P(V 2 – V 1) (4);

If a gas is heated in a cylinder with a fixed piston, then the process can be considered isochoric (the volume of the gas does not change). In an isochoric process, an ideal gas does not do any work (the piston does not move).

A z = 0 (5)

The change in internal energy is equal to:

Answer: 232.

An uncharged piece of dielectric was introduced into the electric field (see figure). It was then divided into two equal parts (dashed line) and then removed from the electric field. What charge will each part of the dielectric have?

The charge on both parts is zero;
The left side is positively charged, the right side is negatively charged;
The left side is negatively charged, the right side is positively charged;
Both parts are negatively charged;
Both parts are positively charged.

Solution

If you introduce a dielectric (a substance in which there are no free electric charges) into an electric field under normal conditions, then the phenomenon of polarization is observed. In dielectrics, charged particles are not able to move throughout the entire volume, but can only move short distances relative to their constant positions, the electric charges in dielectrics are bound. If the dielectric is removed from the field, then the charge on both parts is zero.

The oscillatory circuit consists of a capacitor with a capacity C and inductor coils L. How will the frequency and wavelength of the oscillating circuit change if the area of the capacitor plates is halved? For each quantity, determine the corresponding nature of the change:

Increased;
Decreased;
Hasn't changed.

Write it down to the table selected numbers for each physical quantity. The numbers in the answer may be repeated.

Solution

The problem talks about an oscillatory circuit. By determining the period of oscillations occurring in the circuit , wavelength is related to frequency

Where v– oscillation frequency. By determining the capacitance of a capacitor

C = ε 0 ε S/d (3),

where ε 0 is the electrical constant, ε is the dielectric constant of the medium. According to the conditions of the problem, the area of the plates is reduced. Consequently, the capacitance of the capacitor decreases. From formula (1) we see that the period of electromagnetic oscillations arising in the circuit will decrease. Knowing the relationship between the period and frequency of oscillations

The graph shows how the magnetic field induction changes over time in a conducting circuit. In what period of time will an induced current appear in the circuit?

Solution

By definition, an induced current in a conducting closed circuit occurs under the condition of a change in the magnetic flux passing through this circuit.

Ɛ =	–	∆Φ	(1)
		∆t

Law of electromagnetic induction, where Ɛ – induced emf, ∆Φ – change in magnetic flux, ∆ t the period of time during which changes occur.

According to the conditions of the problem, the magnetic flux will change if the magnetic field induction changes. This occurs in a time interval from 1 s to 3 s. The contour area does not change. Therefore, the induced current occurs in the case

By the time t= 1 s change in magnetic flux through the circuit is greater than zero.
The induced current in the circuit occurs in the range from ( t= 1 s to t= 3 s)
The module of the inductive emf arising in the circuit is 10 mV.
change in magnetic flux through the circuit from t = 3 s to t = 4 s less than zero.
The induction current is zero at intervals from ( t= 0 s to t= 1 s) and from ( t= 3 s to t= 4 s)

Answer: 2.5.

The square frame is located in a uniform magnetic field in the plane of the magnetic induction lines (see figure). The direction of the current in the frame is shown by arrows. How is the force acting on the side directed? ab frames from the external magnetic field? (right, left, up, down, towards the observer, away from the observer)

Solution

The ampere force acts on the current-carrying frame from the magnetic field. The direction of the Ampere force vector is determined by the mnemonic rule of the left hand. We direct the four fingers of the left hand along the side current ab, induction vector IN, should enter the palm, then the thumb will show the direction of the Ampere force vector.

Answer: to the observer.

A charged particle flies at a certain speed into a uniform magnetic field perpendicular to the field lines. From a certain point in time, the magnetic field induction module increased. The charge of the particle has not changed.

How did the force acting on a moving particle in a magnetic field, the radius of the circle along which the particle moves, and the kinetic energy of the particle change after increasing the magnetic field induction modulus?

For each quantity, determine the corresponding nature of the change:

Increased;
Decreased;
Hasn't changed.

Write it down to the table selected numbers for each physical quantity. The numbers in the answer may be repeated.

Solution

A particle moving in a magnetic field is acted upon by the magnetic field by the Lorentz force. The Lorentz force modulus can be calculated using the formula:

F l = B · q· v sinα (1),

Where B– magnetic field induction, q– particle charge, v– particle speed, α – angle between the speed vector and the magnetic induction vector.

In our case, the particle flies in perpendicular to the lines of force, α = 90°, sin90 = 1.

From formula (1) it is clear that with increasing magnetic field induction, the force acting on a particle moving in a magnetic field increases.

The formula for the radius of the circle along which a charged particle moves is:

R =	mv	(2),
	qB

Where m – particle mass. Consequently, with increasing field induction, the radius of the circle decreases.

The Lorentz force does not do any work on a moving particle, since the angle between the force vector and the displacement vector (the displacement vector is directed along the velocity vector) is 90°.

Therefore, kinetic energy, regardless of the value of the magnetic field induction does not change.

Answer: 123.

Along a section of a DC circuit with resistance R current flows I. Establish a correspondence between physical quantities and formulas by which they can be calculated. For each position from the first column, select the corresponding position from the second column and write down the selected numbers in the table under the corresponding letters.

Where P– electric current power, A– work of electric current, t– the time during which an electric current flows through a conductor. The work, in turn, is calculated

A = I Ut (2),

Where I – electric current strength, U – tension in the area,

As a result of the reaction of the nucleus and α particle, a proton and a nucleus appeared:

Solution

Let's write the nuclear reaction for our case:

As a result of this reaction, the law of conservation of charge and mass number is satisfied. Z = 13 + 2 – 1 = 14; M = 27 + 4 – 1 = 30.

Therefore, the core is number 3)

The half-life of the substance is 18 minutes, the initial mass is 120 mg. What will be the mass of the substance after 54 minutes, the answer expressed in mg?

Solution

The task is to use the law of radioactive decay. It can be written in the form

Answer: 15 mg.

The photocathode of the photocell is illuminated with ultraviolet light of a certain frequency. How do the work function of the photocathode material (substance), the maximum kinetic energy of photoelectrons, and the red limit of the photoelectric effect change if the frequency of light is increased?

For each quantity, determine the corresponding nature of the change:

Increased;
Decreased;
Hasn't changed.

Write it down to the table selected numbers for each physical quantity. The numbers in the answer may be repeated.

Solution

It is useful to recall the definition of the photoelectric effect. This is the phenomenon of interaction of light with matter, as a result of which the energy of photons is transferred to the electrons of the substance. There are external and internal photoeffects. In our case we are talking about the external photoelectric effect. When, under the influence of light, electrons are ejected from a substance. The work function depends on the material from which the photocathode of the photocell is made, and does not depend on the frequency of the light. Therefore, as the frequency of ultraviolet light incident on the photocathode increases, the work function does not change.

Let's write Einstein's equation for the photoelectric effect:

hv = A out + E to (1),

hv– energy of a photon incident on the photocathode, A out – work function, E k is the maximum kinetic energy of photoelectrons emitted from the photocathode under the influence of light.

From formula (1) we express

E k = hv – A out (2),

therefore, as the frequency of ultraviolet light increases the maximum kinetic energy of photoelectrons increases.

red border

Answer: 313.

Water is poured into the beaker. Select the correct value for the volume of water, taking into account that the measurement error is equal to half the scale division.

Solution

The task tests the ability to record the readings of a measuring device, taking into account a given measurement error. Let's determine the price of the scale division

The measurement error according to the condition is equal to half the division value, i.e.

We write the final result in the form:

V= (100 ± 5) ml

The conductors are made of the same material. Which pair of conductors should be chosen in order to experimentally discover the dependence of the wire resistance on its diameter?

Solution

The task states that the conductors are made of the same material, i.e. their resistivities are the same. Let’s remember what values the conductor resistance depends on and write the formula for calculating the resistance:

R =	pl	(1),
	S

Where R– conductor resistance, p– resistivity material, l– length of the conductor, S– cross-sectional area of the conductor. In order to identify the dependence of the conductor on the diameter, you need to take conductors of the same length, but different diameters. Loan that the cross-sectional area of a conductor is defined as the area of a circle:

S = π	d 2	(2),
	4

Where d– conductor diameter. Therefore, answer option: 3.

A projectile with a mass of 40 kg, flying in a horizontal direction at a speed of 600 m/s, breaks into two parts with masses of 30 kg and 10 kg. Most of it moves in the same direction at a speed of 900 m/s. Determine the numerical value and direction of the velocity of the smaller part of the projectile. In response, write down the magnitude of this speed.

At the moment of shell explosion (∆ t→ 0) the effect of gravity can be neglected and the projectile can be considered as a closed system. According to the law of conservation of momentum: the vector sum of the momentum of the bodies included in a closed system remains constant for any interactions of the bodies of this system with each other. For our case we write:

m= m 1 1 + m 2 2 (1)

– projectile speed; m- mass of the projectile before bursting; 1 – speed of the first fragment; m 1 – mass of the first fragment; m 2 – mass of the second fragment; 2 – speed of the second fragment.

Let us choose the positive direction of the X axis, which coincides with the direction of the projectile velocity, then in the projection onto this axis we write equation (1):

mv x = m 1 v 1 x + m 2 v 2x (2)

Let us express from formula (2) the projection of the velocity vector of the second fragment.

The smaller part of the projectile at the moment of explosion has a speed of 300 m/s, directed in the direction opposite to the initial movement of the projectile.

Answer: 300 m/s.

In a calorimeter, 50 g of water and 5 g of ice are in thermal equilibrium. What must be the minimum mass of a bolt having a specific heat capacity of 500 J/kg K and a temperature of 339 K so that all the ice melts after it is lowered into the calorimeter? Neglect heat losses. Give the answer in grams.

Solution

To solve the problem, it is important to remember the heat balance equation. If there are no losses, then heat transfer of energy occurs in the system of bodies. As a result, the ice melts. Initially, water and ice were in thermal equilibrium. This means that the initial temperature was 0 ° C or 273 K. Remember the conversion from degrees Celsius to degrees Kelvin. T = t+ 273. Since the condition of the problem asks about the minimum mass of the bolt, the energy should only be enough to melt the ice.

With b m b ( t b – 0) = λ m l (1),

where λ is the specific heat of fusion, m l – mass of ice, m b – bolt mass.

Let us express from formula (1)

Answer: 50 g.

In the circuit shown in the figure, the ideal ammeter shows 6 A. Find the emf of the source if its internal resistance is 2 ohms.

Solution

We carefully read the problem statement and understand the diagram. There is one element in it that may be overlooked. This is a blank wire between the 1 ohm and 3 ohm resistors. If the circuit is closed, then the electric current will pass through this wire with the least resistance and through the 5 ohm resistor.

Then we write Ohm’s law for the complete circuit in the form:

I =	ε	(1)
	R + r

where is the current strength in the circuit, ε is the source emf, R– load resistance, r– internal resistance. From formula (1) we express the emf

ε = I (R + r) (2)

ε = 6 A (5 Ohm + 2 Ohm) = 42 V.

Answer: 42 V.

In the chamber from which the air was pumped out, an electric field was created with a intensity and magnetic field with induction . The fields are homogeneous and the vectors are mutually perpendicular. A proton flies into the chamber p, the velocity vector of which is perpendicular to the intensity vector and the magnetic induction vector. The magnitudes of the electric field strength and magnetic field induction are such that the proton moves in a straight line. Explain how the initial part of the proton trajectory will change if the magnetic field induction is increased. In your answer, indicate what phenomena and patterns you used to explain. Neglect the influence of gravity.

Solution

In solving the problem, it is necessary to focus on the initial motion of the proton and the change in the nature of the motion after a change in the magnetic field induction. The proton is acted upon by a magnetic field by the Lorentz force, the modulus of which is equal to F l = qvB and an electric field with a force whose modulus is equal to F e = qE. Since the proton charge is positive, then e is codirectional with the voltage vector electric field. (See figure) Since the proton initially moved rectilinearly, these forces were equal in magnitude according to Newton’s second law.

With increasing magnetic field induction, the Lorentz force will increase. The resultant force in this case will be different from zero and directed towards the greater force. Namely in the direction of the Lorentz force. The resultant force imparts an acceleration to the proton directed to the left; the proton's trajectory will be curvilinear, deviating from the original direction.

The body slides without friction along an inclined chute, forming a “dead loop” with a radius R. From what height should the body begin to move in order not to break away from the chute at the top point of the trajectory?

Solution

We are given a problem about the unevenly variable motion of a body in a circle. During this movement, the position of the body in height changes. It is easier to solve the problem using the equations of the law of conservation of energy and the equations of Newton’s second law normal to the trajectory of motion. We made a drawing. Let's write down the formula for the law of conservation of energy:

A = W 2 – W 1 (1),

Where W 2 and W 1 – total mechanical energy in the first and second positions. For the zero level, select the position of the table. We are interested in two positions of the body - this is the position of the body at the initial moment of movement, the second is the position of the body at the top point of the trajectory (this is point 3 in the figure). During movement, two forces act on the body: gravity = and ground reaction force. The work of gravity is taken into account in the change in potential energy, the force does not do work, so it is perpendicular to the displacement everywhere. A = 0 (2)

To position 1: W 1 = mgh(3), where m- body mass; g- acceleration of gravity; h– the height from which the body begins to move.

In position 2 (point 3 in the figure):

v 2 + 4gR – 2gh = 0 (5)

At the top point of the loop, two forces act on the body, according to Newton's second law

Solving equations (5) and (7) we obtain h= 2.5 R

Answer: 2.5 R.

Air volume in the room V = 50 m 3 has a temperature t = 27° C and relative air humidity φ 1 = 30%. How long τ must a humidifier operate, spraying water with a productivity of μ = 2 kg/h, so that the relative humidity in the room increases to φ 2 = 70%. Saturated water vapor pressure at t = 27°C equals p n = 3665 Pa. The molar mass of water is 18 g/mol.

Solution

When starting to solve problems on steam and humidity, it is always useful to keep in mind the following: If the temperature and pressure (density) of the saturating steam are given, then its density (pressure) is determined from the Mendeleev-Clapeyron equation. Write down the Mendeleev-Clapeyron equation and the relative humidity formula for each state.

For the first case, at φ 1 = 30%, we express the partial pressure of water vapor from the formula:

Where T = t+ 273 (K), R– universal gas constant. Let us express the initial mass of steam contained in the room using equations (2) and (3):

The time that the humidifier should operate can be calculated using the formula

τ 2 =	(m 2 – m 1)	(6)
	μ

let's substitute (4) and (5) into (6)

Let's substitute the numerical values and get that the humidifier should work for 15.5 minutes.

Answer: 15.5 min.

Determine the emf of the source if, when connecting a resistor with a resistance R voltage at source terminals U 1 = 10 V, and when connecting a resistor 5 R voltage U 2 = 20 V.

Solution

Let's write down the equations for two cases.

Ɛ = I 1 R + I 1 r (1)

U 1 = I 1 R (2)

Where r– internal resistance of the source, Ɛ – emf of the source.

Ɛ = I 2 5R + I 2 r(3)

U 2 = I 2 5R (4)

Taking into account Ohm's law for a section of the circuit, we rewrite equations (1) and (3) in the form:

Ɛ = U 1 +	U 1–	r (5)
	R

The last substitution for calculating the EMF. Let's substitute formula (7) into (5)

Answer: 27 V.

When a plate made of some material is illuminated with light with a frequency v 1 = 8 1014 Hz and then v 2 = 6 · 1014 Hz it was found that the maximum kinetic energy of electrons changed by a factor of 3. Determine the work function of electrons from this metal.

Solution

If the frequency of the light quantum causing the photoelectric effect decreases, then the kinetic energy also decreases. Therefore, the kinetic energy in the second case will also be three times less. Let's write Einstein's equation for the photoelectric effect for two cases.

hv 1 = A + E to (1)

for the first frequency of light

formula for kinetic energy.

From equation (1) we express the work function and substitute expression (3) instead of kinetic energy

The final expression will look like: