The hot liquid cooled slowly. What to do if the water pressure in the faucet is poor? The problem of cold water from a hot tap. Summary

Weak pressure in the faucet can piss off even the most balanced homeowner. After all, the duration of filling the kettle or coffee maker, and the performance of the washing machine or dishwasher depend on the pressure.

In addition, with poor pressure, it is almost impossible to use either the toilet or the shower or bath. In a word, if there is no pressure in the tap, then the house will not have the comfort of living.

We understand the causes of low water pressure in the tap

What weakens the pressure of water in the faucet?

Why a weak water pressure in a tap can ruin even the happiest life, even in the most perfect house or apartment, we have already discussed with you. However, moaning will not help grief. Moreover, this problem is not as terrible as it seems. One has only to understand what has weakened the pressure, and you will get an almost ready-made recipe for eliminating this trouble.

At the same time, the list of TOP 3 reasons for the drop in pressure of hot or cold water is as follows:

• Clogged faucet . In this case, the intensity of the water jet is weakened by a cork made of rust and scale, which clogged the aerator, filter insert (mesh) or bushing. Moreover, only one tap in the house suffers from this problem. That is, if your tap water is not flowing well, for example, in the kitchen, but there are no problems in the bathroom, then you will have to disassemble and clean the problematic point of consumption.
• . In this case, the same particles of silt, rust or scale are to blame. Only now they block not the faucet aerator or the faucet mesh, but the filter built into the water supply. In the worst case, such deposits can block the flow diameter of the connecting fitting or the pipe fitting itself.
• . In this case, the cause of the weakening may be either a failure at the level of the pumping station, or a depressurization of the pipeline. Failure at the station can only be corrected by repair crews of utilities. The indicator of this breakdown is the lack of water in the entire microdistrict. Loss of tightness is diagnosed visually - by a stream of water spouting from the body of plumbing fittings. Any locksmith from a service company can fix this breakdown.
• In addition, speaking about the reasons for the weakening of pressure, it is necessary to mention possible miscalculations in the arrangement of a specific water supply line . Incorrect diameter (larger than the previous branch), excessive length (not matching the characteristics of the pressure equipment) - these are the main reasons for the pressure drop in the new water supply network.

If you don’t want to deal with them, order a water supply project from professionals.

Well, now that you already know the reasons for the drop in pressure in the tap, it's time to figure out how to eliminate this defect in the water supply.

What to do if cold and hot water from the tap does not flow well?

It all depends on the cause of the pressure drop.

For example, if your faucet is clogged, you will need to do the following:

Removing the faucet aerator for cleaning

• Take an adjustable wrench and twist it off the "spout" of the crane - Foaming jet of water nozzle. This part has very small nozzles. Therefore, aerators are clogged with a frequency of once every six months. And if we are talking about a mixer tap with hot / cold water, then the frequency of cleaning the nozzles is reduced to 2-3 months. The dismantled aerator is washed under running water.
• If the aerator is clean and the water is weak, you will have to dive even deeper into the faucet design. . Indeed, in this case, you need to get close to the locking unit - the box. To do this, dismantle the valve (faucet handle) and unscrew the lock washer holding the locking element in the body seat. Next, you remove the shut-off assembly from the housing and clean off silt or scale deposits from its surface. In the final, you will have to assemble the crane, acting in reverse.

Before dismantling the shut-off valve assembly, be sure to turn off the water supply by closing the water valve closest to the point of consumption. Otherwise, you will flood the entire apartment.

• If the source of the problem is not the faucet, but the “sprayer” in the shower or bathroom, you will have to proceed a little differently. First shut off the supply to the atomizer. Then remove it from the rack or metal hose using an adjustable wrench. Immerse the removed part of the atomizer in a saucepan of vinegar. Heat up this medium on a hot plate. Wash off the scale with water. Put the nozzle back in place.

If the smell of vinegar irritates you, try a 10% citric acid solution. To prepare it, it is enough to dissolve 100 grams of dry acid powder - it is sold in any confectionery department - in a liter of water.

If you do not have the desire to mess with the crane - call a locksmith from the management company. He will solve this problem right before your eyes.

What to do if the water pressure in the tap is poor, we hope you already understand.

Now let's move on to pipes:

• First of all, turn off the water by turning the central valve near the meter.
• Next, dismantle the plug of the coarse filter. Remove the wire cassette and wash it in a container. Then return the filter element to its place, renew the seal and screw the plug.
• After the revision of the coarse filter, proceed to check the fine filter system. First, disconnect it from the water supply and check the pressure in the free pipe by slightly opening the central valve. If everything is in order, change the liner, simultaneously washing the filter glass from particles of accumulated dirt. In the final, everything, of course, is mounted in its original place.
• If the filters are clean, and the water still does not come out of the tap with the proper force, then the cause of the drop in pressure is a blockage in the pipes themselves. Localization of this problem and its elimination is an extremely time-consuming task. Therefore, after unsuccessfully cleaning the filters, you will have to call the management company and report a problem with the patency of the pipes in the water supply.

If you did not change the wiring of the water supply system in the apartment, the management company will pay for cleaning the pipes. After all, it is she who should monitor the performance of "native" engineering communications.

Water / Cold and hot water meters

The situation is familiar to almost everyone: in the morning, a barely warm liquid runs from the hot water tap, which has to be washed. It is possible, if there is time, to open the tap and drain the cool “hot” water in 15-20 minutes until it reaches the desired temperature.

However, if there is a hot water meter in the apartment, cubic meters of lukewarm water poured into the sewer will cost the owner of the living space at the full cost of heated water, which is 4-6 times more expensive than cold water.

It often happens that “hot” water does not differ too much from “cold” in temperature. And instead of mixing hot and cold, you only leave the hot faucet open. Slightly warm water flows from the mixer. And it costs like hot water.

What to do in such a situation? Reconcile and overpay? And if you fight, how exactly? Let's figure it out together.

Cold water from a hot tap: legislation

To begin with, let's find out what the current legislation says about the requirements for the temperature of hot water supplied to an apartment building.

The requirements for the quality of hot water supply are spelled out in two documents:

• “Rules for the provision of public services to owners and users of premises in apartment buildings and residential buildings”, approved by Decree of the Government of the Russian Federation of May 6, 2011 N 354 Or rather, in its Appendix No. 1, which is called “Requirements for the quality of public services”
• Sanitary and epidemiological rules and norms SanPiN 2.1.4.2496-09 "Hygienic requirements for ensuring the safety of hot water supply systems", approved by the Decree of the Chief State Sanitary Doctor of the Russian Federation of April 7, 2009 N 20 "On approval of SanPiN 2.1.4.2496-09"

The following emerge from these documents:

• The temperature of hot water in the places of water intake, regardless of the heat supply system used in the apartment building, must not be lower than 60 ° C and not higher than 75 ° C
• Before determining the hot water temperature, the water is drained for no more than 3 minutes.

Tolerance for hot water temperature:

• at night (from 0.00 to 5.00 hours) - no more than 5 ° C;
• in the daytime (from 5.00 to 00.00 hours) - no more than 3 ° C

From the requirements for the quality of hot water supply, the terms of payment for this utility resource also follow if the water is not at the right temperature.

Firstly, the hours during which the supply of hot water with a temperature of less than 40 ° C is recorded are summed up. And during this period of time, payment for the consumed water is made at the rate of cold water supply.

Secondly, if the temperature is below 60°C, but above 40°C, the payment for hot water is reduced.

The mechanism is as follows: for every 3°C deviation from the permissible deviations in the temperature of hot water, the amount of water payment in the month in which the indicated deviation occurred is reduced by 0.1% for each hour when such a decrease was recorded.

Why does (physically) hot water turn out to be slightly warm?

Having dealt with the legal requirements for the permissible temperature of hot water, we will consider the reasons why these requirements may not be observed in your home.

First of all, these may be problems directly in your home. For example, the design flaws in the hot water supply system (there is no hot water circulation, and in order for the residents of the upper floors to get hot water in the morning, the water that was in the risers all night and had time to cool down must be drained).

Or incorrect adjustments of the hot water system. Simply put, for some reason, the managing organization of the house does not sufficiently heat the water that goes to the apartments.

Alternatively, the circulation of hot water may deteriorate due to a clogged pipe on the floor below (for example, a "goose" was inserted to hide the hot water pipe in the bathroom wall and thus make room for the bathroom).

Or - due to improper installation of an electric boiler (bidet, mixers, etc.) in one of the apartments along your riser.
In all these cases, to solve the problem with one or another cost, but it is possible with the help of pressure on the managing organization of your house.

More serious in its consequences is the option when hot water does not have the right temperature for external reasons that are not related to your home. For example, when your house is the end of the hot water supply line. Those. first, several high-rise buildings take hot water before you. And then the conduit goes to your house. And if this line is not looped, then it turns out that in your dead-end branch, hot water cools down by morning (and it happens that it does not warm up to the desired temperature at all).

And in this case, the organization responsible for managing your home, with all its desire, will not be able to ensure the elimination of problems with hot water. Work on the relocation of hot water lines (a) is too expensive, (b) are carried out on the territory where your management company cannot dispose of.

Exactly the same can be said if hot water is not supplied to the house due to an accident (destruction of the water supply) outside the house networks. The governing body cannot correct the violations. This is the business of the heat supply organization and the municipal authorities. “Pushing” them, as practice shows, is much more difficult.

What if the hot water is lukewarm?

So, what to do if you have slightly warm water flowing from a hot tap? First of all, you need to report this to your managing organization, call its representative to the apartment so that he can measure the water and draw up an appropriate act in your presence.

If the measurements showed the temperature is below the established standard, then starting from the day the act is drawn up, the requirements of the law to reduce water charges (which we talked about in the chapter on legislation) come into force. If, for example, it is established that your water temperature is below 40 ° C, then you will pay for the cubic meters that the hot water meter counted for you at the rate for cold water. This will continue until the day the next act is drawn up - on the elimination of violations of the requirements for the temperature of hot water.

What to do if you called the control room by phone and didn’t even write a statement, but there is no reaction, you ask? Or was the act drawn up, but the water remained cold?

In this case, you need to contact the housing inspection of your region (settlement). Inspections usually respond to such appeals and they have effective leverage on the managing organizations of apartment buildings. To begin with, an order may be issued, then a decision on a fine, transfer of the case to court, revocation of a license, etc.

In addition to the housing inspection, it is also possible to appeal to the prosecutor's office and directly to the court with a statement of claim. Courts consider such cases and make decisions in favor of citizens. In addition to the obligation to provide the apartment with hot water of the required temperature, public utilities are also forced to pay compensation for moral and material damage.

If you want to delve into the details of the process, you can see, for example, this decision of the Kirovsky District Court of the city of Perm in the case of cold water from a hot tap.

But here, of course, one must understand that when it comes to the level of litigation in court, there will be no quick solution to the problem. And the result is not guaranteed. Even if the court decides in your favor.

As mentioned above, the solution to the problem of hot water may often depend not on the managing organization, but on the owner of heating networks and hot water supply networks. Reconstruction of infrastructure may also require participation and funding from the municipal authorities. In general, the process will be long, nervous, and most importantly - all this time you will be without hot water.

Water heater as a way to solve the problem of cold hot water

So it turns out that perhaps the most effective way to "fight" will be the transition to autonomous hot water supply. In other words - put an electric water heater (boiler). Let's consider this question from a practical point of view.
The heater can be flow and accumulative. It is better, as experience shows, to put accumulative. This is a container with a volume of up to 200 liters with a heating element (which provides water heating) inside and a layer of heat-insulating material (which does not allow the water to cool down) outside.

The unit looks quite aesthetically pleasing. It consumes electricity, thanks to the thermal insulation layer, which does not allow the water to cool down, not much.

As calculations show, with not too active consumption of hot water, heating water in the boiler is comparable in price to centralized hot water supply. But, of course, it will no longer be possible to pour hot water from the heart - the capacity of the water heater is limited, and if you have drained all the water (for example, the children took turns splashing in the bathroom), you have to wait until it heats up again.

An important reminder - if you do not have a hot water meter in your apartment, then when installing the boiler, officially put a plug (seal the tap) at the entrance from the hot riser. Otherwise, you will still be charged for hot water, based on current regulations.

If you have a hot water meter, then when installing a water heater, you do not need to drown out the hot water riser. Just close the inlet valve. And also check that hot water from your boiler is not mixed into the house water supply system.

Hot water meter with temperature sensor

Finally, it is worth mentioning another way to save money on the family budget - a hot water meter with a temperature sensor.

This device takes into account separately the consumption of really hot water (which has a temperature that meets the standard) and actually cold water (the one that comes from the hot water riser, but in reality is a little warm).

The principle of operation of such devices is based on the distinction between the volumes of water consumed: the volumes of hot water and the water that comes from the hot tap, but its temperature is below normal, are taken into account separately. Cubic meters, which the meter counted in the second case, you add to the volume of cold water consumption and pay at the appropriate rate.

An example is the Sayany T-RMD hot water meter, this is the most common device of this kind. Although there are others that are similar.

At first glance, everything looks nice - without contacting the public utilities, you pay only for that “hot water” that meets the standards. However, as is usually the case, there are a few "buts".

Firstly, the recalculation of payment for hot water that does not meet the requirements of the law must be carried out in accordance with the requirements of this very legislation. That is, according to the procedure, with the calls of the representative, "acts", etc. The legislation does not mention automatic recalculation of readings based on the readings of the “thermal sensor”. This is the position of public utilities and there are several decisions of the courts that supported it.

Secondly, it is worth remembering that it is not enough to install the meter, it must also be sealed and “put into operation”. Without public utilities (employees of the managing organization), this will not work. Whether they will accept the counter or not is an open question. Some are loyal, some are not.

Thirdly, taking into account the consumption of water from a hot riser as cold, you thus shift the payment of this volume to general house needs. That is, for all the inhabitants of the house.

Fourth, and this is the main thing! - a meter with a temperature sensor does not provide you with hot water. And this brings us back to the problem of installing a water heater.

The problem of cold water from a hot tap. Summary

So, a short summary. Cold water from a hot tap can be fought. And if we are talking about problems within the house system, then it is quite possible to win. Especially if the problem is related to the system settings or its not very complex reconstruction.

If the quality of hot water supply is low due to problems outside the house system, then you may not be able to solve the issue. In this case, you will have to install a water heater, there seems to be no other way out.

Part 1

A1. The figure shows a graph of the dependence of the projection of the body's velocity on time.

The projection of the acceleration of the body in the time interval from 12 to 16 s is represented by the graph:

A2. Bar magnet mass m brought to a massive steel plate with a mass M. Compare the force of the magnet on the stove F 1 with plate action force on magnet F 2 .

1) F 1 = F 2 ; 2) F 1 > F 2 ; 3) F 1 < F 2 ; 4) F 1 / F 2 = m/m.

A3. When moving along a horizontal surface, a sliding friction force of 10 N acts on a body with a mass of 40 kg. What will be the sliding friction force after a decrease in body weight by 5 times if the friction coefficient does not change?

1) 1 N; 2) 2 N; 3) 4 N; 4) 8 N.

A4. A car and a truck are moving at speeds υ 1 = 108 km/h and υ 2 = 54 km/h. Car weight m= 1000 kg. What is the mass of the truck if the ratio of the momentum of the truck to the momentum of the car is 1.5?

1) 3000 kg; 2) 4500 kg; 3) 1500 kg; 4) 1000 kg.

A5. Sledge weight m pulled uphill at a constant speed. When the sled rises to the top h from the initial position, their total mechanical energy is:

1) will not change;

2) increase by mgh;

3) will be unknown, because the slope of the hill is not set;

4) will be unknown, because the coefficient of friction is not set.

1) 1; 2) 2; 3) 1/4; 4) 4.

According to the FIPI website http://www.fipi.ru. Instructions for completing the work of the Unified State Exam-2009, criteria for evaluating solutions to problems of part 3 for 1 and 2 points, conditions for recording the solution of tasks, as well as one more option, see No. 3/09. - Ed.

Unified State Examination in Physics, 2009,
demo version

Part A

A1. The figure shows a graph of the dependence of the projection of the body's velocity on time. The graph of the dependence of the projection of the acceleration of the body on time in the time interval from 12 to 16 s coincides with the graph

1)
2)
3)
4)

Solution. It can be seen from the graph that in the time interval from 12 to 16 s, the velocity changed uniformly from –10 m/s to 0 m/s. The acceleration was constant and equal

The acceleration graph is shown in the fourth figure.

Correct answer: 4.

A2. Bar magnet mass m brought to a massive steel plate with a mass M. Compare the force of the magnet on the plate with the force of the plate on the magnet.

Solution. According to Newton's third law, the force with which the magnet acts on the plate is equal to the force with which the plate acts on the magnet.

Correct answer: 1.

A3. When moving along a horizontal surface, a sliding friction force of 10 N acts on a body with a mass of 40 kg. What will be the sliding friction force after a decrease in body weight by 5 times if the friction coefficient does not change?

Solution. With a decrease in body weight by 5 times, body weight will also decrease by 5 times. This means that the sliding friction force will decrease by 5 times and will be 2 N.

Correct answer: 2.

A4. A car and a truck are moving at speeds And . Car weight m= 1000 kg. What is the mass of the truck if the ratio of the momentum of the truck to the momentum of the car is 1.5?

Solution. The momentum of the car is . The momentum of the truck is 1.5 times greater. The mass of the truck is .

Correct answer: 1.

A5. Sledge weight m pulled uphill at a constant speed. When the sled rises to the top h from the initial position, their total mechanical energy

Solution. Since the sled is pulled at a constant speed, its kinetic energy does not change. The change in the total mechanical energy of the sledge is equal to the change in their potential energy. The total mechanical energy will increase by mgh.

Correct answer: 2.

Solution. The ratio of wavelengths is inversely proportional to the ratio of frequencies: .

Correct answer: 4.

A7. The photograph shows a setup for studying uniformly accelerated sliding of a carriage (1) weighing 0.1 kg along an inclined plane set at an angle of 30° to the horizon.

At the moment of the start of movement, the upper sensor (A) turns on the stopwatch (2), and when the carriage passes the lower sensor (B), the stopwatch turns off. The numbers on the ruler indicate the length in centimeters. What expression describes the dependence of the carriage speed on time? (All quantities are in SI units.)

Solution. It can be seen from the figure that during t= 0.4 s caret traveled path s= 0.1 m. Since the initial speed of the carriage is zero, we can determine its acceleration:

.

Thus, the speed of the carriage depends on time according to the law .

Correct answer: 1.

A8. With a decrease in the absolute temperature of a monatomic ideal gas by 1.5 times, the average kinetic energy of the thermal motion of its molecules

Solution. The average kinetic energy of the thermal motion of ideal gas molecules is directly proportional to the absolute temperature. With a decrease in absolute temperature by 1.5 times, the average kinetic energy will also decrease by 1.5 times.

Correct answer: 2.

A9. The hot liquid was slowly cooling in the glass. The table shows the results of measurements of its temperature over time.

In the beaker, 7 min after the start of measurements, there was a substance

Solution. It can be seen from the table that between the sixth and tenth minutes the temperature in the beaker remained constant. This means that at this time the crystallization (solidification) of the liquid took place; the substance in the glass was both in liquid and solid states.

Correct answer: 3.

A10. What work is done by the gas during the transition from state 1 to state 3 (see figure)?

Solution. Process 1–2 is isobaric: the gas pressure is equal, the volume increases by , while the gas does work. Process 2–3 is isochoric: the gas does no work. As a result, during the transition from state 1 to state 3, the gas does work of 10 kJ.

Correct answer: 1.

A11. In a heat engine, the temperature of the heater is 600 K, the temperature of the refrigerator is 200 K lower than that of the heater. The maximum possible efficiency of the machine is

Solution. The maximum possible efficiency of a heat engine is equal to the efficiency of a Carnot engine:

.

Correct answer: 4.

A12. A container contains a constant amount of ideal gas. How will the temperature of the gas change if it passes from state 1 to state 2 (see figure)?

Solution. According to the equation of state for an ideal gas at a constant amount of gas

Correct answer: 1.

A13. The distance between two point electric charges was reduced by 3 times, and one of the charges was increased by 3 times. Forces of interaction between them

Solution. With a decrease in the distance between two point electric charges by 3 times, the force of interaction between them increases by 9 times. An increase in one of the charges by 3 times leads to the same increase in force. As a result, the strength of their interaction became 27 times greater.

Correct answer: 4.

A14. What will be the resistance of the circuit section (see figure) if the key K is closed? (Each of the resistors has a resistance R.)

Solution. After closing the key, the terminals will be shorted, the resistance of this section of the circuit will become zero.

Correct answer: 4.

A15. The figure shows a coil of wire through which an electric current flows in the direction indicated by the arrow. The coil is located in a vertical plane. At the center of the coil, the current magnetic field induction vector is directed

Solution. According to the rule of the right hand: "If you grasp the solenoid (coil with current) with the palm of your right hand so that four fingers are directed along the current in the coils, then the left thumb will show the direction of the magnetic field lines inside the solenoid (coil with current)". Having mentally performed the indicated actions, we obtain that in the center of the coil the magnetic field induction vector is directed horizontally to the right.

Correct answer: 3.

A16. The figure shows a graph of harmonic current oscillations in an oscillatory circuit. If the coil in this circuit is replaced by another coil, the inductance of which is 4 times less, then the oscillation period will become equal to

Solution. It can be seen from the graph that the period of current oscillations in the oscillatory circuit is 4 μs. When the inductance of the coil is reduced by 4 times, the period will decrease by 2 times. After replacing the coil, it will become equal to 2 μs.

Correct answer: 2.

A17. Light source S reflected in a flat mirror ab. The image S of this source in the mirror is shown in the figure.

Solution. The image of an object obtained with a flat mirror is located symmetrically to the object with respect to the plane of the mirror. The image of the source S in the mirror is shown in Figure 3.

Correct answer: 3.

A18. In a certain spectral range, the angle of refraction of rays at the air-glass boundary decreases with increasing radiation frequency. The course of rays for the three primary colors when white light falls from the air onto the interface is shown in the figure. Numbers correspond to colors

Solution. Due to the dispersion of light, when passing from air to glass, the beam deviates more from its original direction, the shorter its wavelength. Blue has the shortest wavelength, red has the longest. The blue beam will deviate the most (1 - blue), the red beam will deviate the weakest (3 - red), leaving 2 - green.

Correct answer: 4.

A19. There is a fuse at the entrance to the electrical circuit of the apartment that opens the circuit at a current of 10 A. The voltage supplied to the circuit is 110 V. What is the maximum number of electric kettles, each with a power of 400 W, that can be turned on simultaneously in the apartment?

Solution. An electric current with a power of 400 W passes through each kettle: 110 V 3.64 A. When two kettles are turned on, the total current strength (2 3.64 A \u003d 7.28 A) will be less than 10 A, and when three kettles are turned on, it will be more 10 A (3 3.64 A = 10.92 A). No more than two kettles can be turned on at the same time.

Correct answer: 2.

A20. The figure shows diagrams of four atoms, corresponding to Rutherford's model of the atom. Black dots represent electrons. Atom corresponds to the scheme

1)
2)
3)
4)

Solution. The number of electrons in a neutral atom coincides with the number of protons, which is written at the bottom before the name of the element. There are 4 electrons in an atom.

Correct answer: 1.

A21. The half-life of the nuclei of radium atoms is 1620 years. This means that in a sample containing a large number of radium atoms,

Solution. It is true that half of the original radium nuclei decay in 1620 years.

Correct answer: 3.

A22. Radioactive lead, having experienced one α-decay and two β-decays, turned into an isotope

Solution. During α-decay, the mass of the nucleus decreases by 4 amu. e. m., and during β-decay, the mass does not change. After one α-decay and two β-decays, the mass of the nucleus will decrease by 4 AU. eat.

During α-decay, the charge of the nucleus decreases by 2 elementary charges, and during β-decay, the charge increases by 1 elementary charge. After one α-decay and two β-decays, the charge of the nucleus will not change.

As a result, it will turn into an isotope of lead.

Correct answer: 3.

A23. The photoelectric effect is observed by illuminating the metal surface with light of a fixed frequency. In this case, the retarding potential difference is equal to U. After changing the frequency of light, the retarding potential difference increased by Δ U= 1.2 V. How much has the frequency of the incident light changed?

1)
2)
3)
4)

Solution. Let's write the Einstein equation for the photoelectric effect for the initial frequency of light and for the changed frequency . Subtracting the first equality from the second equality, we obtain the relation:

Correct answer: 2.

A24. The conductors are made from the same material. Which pair of conductors should be chosen in order to experimentally discover the dependence of the resistance of the wire on its diameter?

1)
2)
3)
4)

Solution. In order to experimentally detect the dependence of the resistance of a wire on its diameter, you need to take a pair of conductors that differ only thick. The length of the conductors must be the same. You need to take the third pair of conductors.

Correct answer: 3.

A25. The dependence of the voltage on the plates of an air capacitor on the charge of this capacitor was studied. The measurement results are presented in the table.

Measurement errors q And U were 0.05 μC and 0.25 kV, respectively. The capacitance of the capacitor is approximately

Solution. We calculate for each measurement the value of the capacitance of the capacitor () and average the resulting values.

The calculated capacitance value is closest to the third answer option.

Correct answer: 3.

Part B

IN 1. Load of mass m, suspended on a spring, performs harmonic oscillations with a period T and amplitude. What will happen to the maximum potential energy of the spring, the period and frequency of oscillations, if the mass of the load is reduced at a constant amplitude?

For each position of the first column, select the corresponding position of the second and write down the selected numbers in the table under the corresponding letters.

Transfer the resulting sequence of numbers to the answer sheet (without spaces).

Solution. The period of oscillation is related to the mass of the load and the stiffness of the spring. k ratio

With a decrease in mass, the oscillation period will decrease (A - 2). The frequency is inversely proportional to the period, which means that the frequency will increase (B - 1). The maximum potential energy of the spring is equal to, with a constant amplitude of oscillations, it will not change (B - 3).

Answer: 213.

IN 2. Using the first law of thermodynamics, establish a correspondence between the features of the isoprocess described in the first column in an ideal gas and its name.

Transfer the resulting sequence of numbers to the answer sheet (without spaces or any symbols).

Solution. The internal energy of an ideal gas remains unchanged at a constant gas temperature, that is, in an isothermal process (A - 1). Heat exchange with the surrounding bodies is absent in the adiabatic process (B - 4).

IN 3. A flying projectile breaks into two fragments. With respect to the direction of movement of the projectile, the first fragment flies at an angle of 90° at a speed of 50 m/s, and the second at an angle of 30° at a speed of 100 m/s. Find the ratio of the mass of the first fragment to the mass of the second fragment.

R solution. Let's depict the directions of movement of the projectile and two fragments (see figure). Let us write down the law of conservation of the momentum projection on the axis perpendicular to the direction of the projectile motion:

AT 4. In a heat-insulated vessel with a large amount of ice at a temperature, pour m= 1 kg of water with temperature . What is the mass of ice Δ m melts when thermal equilibrium is established in the vessel? Express your answer in grams.

Solution. When cooled, the water will give off the amount of heat. This heat will melt the ice mass

Answer: 560.

AT 5. An object 6 cm high is located on the main optical axis of a thin converging lens at a distance of 30 cm from its optical center. The optical power of the lens is 5 diopters. Find the height of the object image. Express your answer in centimeters (cm).

Solution. Denote the height of the object h\u003d 6 cm, distance from the lens to the object, the optical power of the lens D= 5 diopters. Using the formula for a thin lens, we determine the position of the object image:

.

The increase will be

.

The height of the image is

Part C

C1. A man wearing glasses entered the warm room from the street and found that his glasses were fogged up. What should be the outside temperature for this phenomenon to occur? The temperature in the room is 22°C and the relative humidity is 50%. Explain how you got the answer.

(Use the table for saturated vapor pressure of water when answering this question.)

Saturated vapor pressure of water at different temperatures

Solution. From the table we find that the saturated vapor pressure in the room is 2.64 kPa. Since the relative humidity of the air is 50%, the partial pressure of water vapor in the room is 2.164 kPa50% = 1.32 kPa.

The first moment a person enters from the street, his glasses are at street temperature. The room air, in contact with the glasses, is cooled. It can be seen from the table that if the room air is cooled to 11 °C or lower, when the partial pressure of the water vapor becomes greater than the saturated vapor pressure, the water vapor will condense - the glasses will fog up. The temperature outside should be no higher than 11 °C.

Answer: not higher than 11 °C.

C2. A small puck after impact slides up the inclined plane from the point BUT(see picture). At the point IN the inclined plane passes without a break into the outer surface of a horizontal pipe with a radius R. If at the point BUT the speed of the puck exceeds , then at the point IN the puck comes off the support. Inclined plane length AB = L= 1 m, angle α = 30°. The coefficient of friction between the inclined plane and the washer μ = 0.2. Find the outer radius of the pipe R.

Solution. Find the speed of the puck at the point B using the law of conservation of energy. The change in the total mechanical energy of the washer is equal to the work of the friction force:

The separation condition is the equality of the reaction force of the support to zero. Centripetal acceleration is caused only by the force of gravity, while for the minimum initial speed for which the washer is lifted off, the radius of curvature of the trajectory at the point B equals R(for higher speeds, the radius will be larger):

Answer: 0.3 m.

C3. A balloon whose shell has mass M= 145 kg and volume, filled with hot air at normal atmospheric pressure and ambient temperature. What is the minimum temperature t must have air inside the shell for the balloon to start rising? The shell of the ball is inextensible and has a small hole at the bottom.

Solution. The ball will begin to rise when the force of Archimedes exceeds the force of gravity. The strength of Archimedes is . The density of the outside air is

where p- normal atmospheric pressure, μ - molar mass of air, R- gas constant, - outdoor air temperature.

The mass of the ball is the sum of the mass of the shell and the mass of air inside the shell. The force of gravity is

where T- air temperature inside the shell.

Solving the inequality , we find the minimum temperature T:

The minimum air temperature inside the enclosure shall be 539 K or 266 °C.

Answer: 266°C.

C4. A thin aluminum bar of rectangular cross section, having a length L= 0.5 m, slides from rest on a smooth inclined plane of dielectric in a vertical magnetic field with induction B= 0.1 T (see figure). The plane is inclined to the horizon at an angle α = 30°. The longitudinal axis of the bar during movement maintains a horizontal direction. Find the value of the induction emf at the ends of the bar at the moment when the bar passes the distance along the inclined plane l= 1.6 m.

Solution. Let's find the speed of the bar in the lower position, using the law of conservation of energy:

Aluminum is a conductor, so an EMF of induction will occur in the bar. The induced emf at the ends of the bar will be equal to

Answer: 0.17 V.

C5. In the electrical circuit shown in the figure, the current source emf is 12 V, the capacitance is 2 mF, the coil inductance is 5 mH, the lamp resistance is 5 ohms, and the resistance of the resistor is 3 ohms. At the initial moment of time, the key K is closed. What energy will be released in the lamp after opening the key? Ignore the internal resistance of the current source, as well as the resistance of the coil and wires.

Solution. Let's introduce the notation: ε - EMF of the current source, C- capacitance of the capacitor, L- coil inductance, r- lamp resistance, R is the resistance of the resistor.

While the key is closed through the capacitor and the lamp, no current flows, but current flows through the resistor and coil

The energy of the system capacitor - lamp - coil - resistor is equal to

.

After opening the key, transient processes will occur in the system until the capacitor is discharged and the current becomes zero. All energy will be released as heat in the lamp and resistor. At each moment of time, the amount of heat is released in the lamp, and in the resistor -. Since the same current will flow through the lamp and the resistor, the ratio of heat released will be in proportion to the resistances. Thus, energy is released in the lamp

Answer: 0.115 J.

C6.-meson mass decays into two γ-quanta. Find the momentum modulus of one of the resulting γ-quanta in the reference frame where the primary -meson is at rest.

Solution. In the reference frame where the primary -meson is at rest, its momentum is zero, and the energy is equal to the rest energy. According to the law of conservation of momentum, γ-quanta will scatter in opposite directions with the same momentum. This means that the energies of γ-quanta are the same and, therefore, equal to half the energy of the -meson: . Then the momentum of the γ-quantum is equal to

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