The hot liquid slowly cooled. What to do if cold water flows from a hot tap? Problem with cold water from a hot tap. Summary

Part 1

A1. The figure shows a graph of the projection of body velocity versus time.

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

A2. Strip magnet with mass m brought to a massive steel plate weighing M. Compare the force of a magnet on a plate F 1 with the force of the plate on the 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 on a horizontal surface, a sliding friction force of 10 N acts on a body weighing 40 kg. What will the sliding friction force be after reducing the body's mass 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 truck's momentum to the car's momentum is 1.5?

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

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

1) will not change;

2) will increase by mgh;

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

4) will be unknown, because friction coefficient is not specified.

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

From the FIPI website http://www.fipi.ru. Instructions for completing the Unified State Exam-2009 work, criteria for evaluating solutions to problems in Part 3 for 1 and 2 points, conditions for recording solutions to tasks, as well as another option, see No. 3/09. – Ed.

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 you have to use to wash your face. If you have time, you can open the tap and drain cool “hot” water for 15-20 minutes until it reaches the desired temperature.

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

It often happens that “hot” water is not too different in temperature from “cold”. And instead of mixing hot and cold, you leave only the hot tap open. Lukewarm water flows from the faucet. And it stands like hot water.

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

Cold water from a hot tap: legislation

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

Requirements for the quality of hot water supply are specified in two documents:

• “Rules for the provision of utility 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 utility services”
• Sanitary and epidemiological rules and regulations SanPiN 2.1.4.2496-09 “Hygienic requirements for ensuring the safety of hot water supply systems”, approved by Resolution of the Chief State Sanitary Doctor of the Russian Federation dated April 7, 2009 N 20 “On approval of SanPiN 2.1.4.2496-09”

The following follows from these documents:

• The temperature of hot water in water supply points, regardless of the heating system used in an apartment building, must be no lower than 60°C and no higher than 75°C
• Before determining the hot water temperature, the water is drained for no more than 3 minutes.

Permissible deviation of 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

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

Firstly, the hours in 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 consumed water is made at the cold water supply tariff.

Secondly, if the temperature is below the legally established 60°C, but above 40°C, then the charge for hot water is reduced.

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

Why (physically) hot water turns out to be lukewarm?

Having understood the legal requirements for permissible hot water temperatures, we will consider the reasons why these requirements may not be met in your home.

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

Or incorrect adjustments of the hot water supply system. Simply put, for some reason the building management organization 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, they cut in a “goose” to hide the hot water pipe in the wall of the bathroom and thus free up space 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, solving the problem at one cost or another, but it is possible with the help of pressure on the management organization of your home.

More serious in its consequences is the option when the hot water does not have the required temperature for external reasons 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 up to you take hot water. And only then the water pipeline goes to your house. And if this line is not looped, then it turns out that in your dead-end branch the hot water cools down by the morning (and sometimes it does not warm up to the required temperature at all).

And in this case, the organization responsible for managing your home, with all its desire, will not be able to ensure that problems with hot water are eliminated. Work on relaying hot water supply lines (a) is too expensive, (b) is carried out in an area where your management company cannot manage.

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 home networks. The management organization cannot eliminate violations. This is a matter for the heat supply organization and municipal authorities. As practice shows, it is much more difficult to “put pressure” on them.

What to do if the hot water is lukewarm?

So, what should you do if lukewarm water flows from your hot tap? First of all, you need to inform your management organization about this, call its representative to the apartment so that he can take water measurements and draw up a corresponding report in your presence.

If measurements show a temperature below the established standard, then starting from the day the act is drawn up, the requirements of the law to reduce water charges come into force (which we discussed in the chapter on legislation). If, for example, it is determined that your water temperature is below 40°C, then you will pay for the cubic meters calculated by the hot water meter at the same rate as for cold water. This will continue until the next report is drawn up - on eliminating violations of the requirements for hot water temperature.

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

In this case, you need to contact the housing inspectorate of your region (locality). Inspections usually respond to such requests and they have effective leverage over the management 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 the license, etc.

In addition to the housing inspection, it is also possible to contact 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 at the required temperature, utility workers are also forced to pay compensation for moral and material damage.

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

But here, of course, you need to understand that when the matter reaches the level of litigation in court, there will not be a 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 with hot water may often depend not on the management organization, but on the owner of the heating networks and hot water supply networks. Infrastructure reconstruction may also require participation and funding from municipal authorities. In general, the process will be long, nervous, and most importantly, you will be without hot water all this time.

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

So it turns out that perhaps the most effective way to “fight” would be to switch to an autonomous hot water supply. In other words, install an electric water heater (boiler). Let's consider this issue from a practical point of view.
The heater can be flow-through or storage. It is better, as experience shows, to use a cumulative one. This is a container with a volume of up to 200 liters with a heating element (which heats the water) inside and a layer of thermal insulation material (which prevents the water from cooling) on ​​the outside.

The unit looks quite aesthetically pleasing. Thanks to the thermal insulation layer, which prevents the water from cooling, it does not consume much electricity.

As calculations show, if the consumption of hot water is not too active, heating water in a boiler turns out to be comparable in price to centralized hot water supply. But, of course, you won’t be able to pour hot water from the heart - the water heater’s capacity is limited, and if you have drained all the water (for example, the children took turns splashing to their hearts’ content in the bathroom), you have to wait until it warms up again.

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

If you have a hot water meter, then when installing a water heater, there is no need to plug the hot water riser. Simply close the inlet valve. Also, make sure that hot water from your boiler is not mixed into the home 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 flow of really hot water (whose temperature corresponds to the standard) and actually cold water (that which comes from the hot water supply riser, but in reality is slightly warm).

The principle of operation of such devices is based on the differentiation of consumed volumes of water: the volumes of hot water and the water that comes from a hot tap, but its temperature is below normal, are taken into account separately. You add the cubic meters that the meter counted in the second case 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 utility companies, you only pay for the “hot water” that meets the standards. However, as is usually the case, there are several “buts”.

Firstly, the recalculation of payments for hot water that does not meet the requirements of the law must occur in accordance with the requirements of this very legislation. That is, according to the procedure, with calls from a 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 the utility companies and there are several court decisions that support it.

Secondly, it is worth remembering that it is not enough to install the meter; it must also be sealed and “put into operation.” This cannot be done without utility workers (employees of the management organization). Whether they will accept the meter or not is an open question. In some places they are loyal, in others they are not.

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

Fourthly, 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.

Problem with cold water from a hot tap. Summary

So, a quick summary. Cold water from a hot tap can be a problem. 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 the hot water supply is low due to problems outside the home system, then you may not be able to resolve the issue. In this case, you will have to install a water heater; there seems to be no other way out.

228. The faulty heater in the electric kettle was replaced with a heater with twice the power. The boiling point of water is

229. The hot liquid cooled slowly in the glass. The table shows the results of measuring its temperature over time.

There was a substance in the glass 7 minutes after the start of measurements

230. Melting a piece of tin that has already been heated to its melting point requires 1.8 kJ of energy. This piece was placed in the oven. The dependence of tin temperature on heating time is shown in the figure. At what speed did the furnace transfer heat to the tin?

232. The figure shows graphs of changes in temperature of four substances over time. At the beginning of heating, all these substances were in a liquid state. Which substance has the highest boiling point?

234. At the initial moment of time, the substance was in a crystalline state. The figure shows a graph of its temperature T versus time t. Which point corresponds to the end of the hardening process?

235. (B). To determine the specific heat of fusion, pieces of melting ice were thrown into a vessel with water weighing 300 g and a temperature of 20°C with continuous stirring. By the time the ice stopped melting, the mass of water had increased by 84 g. Determine the specific heat of melting of ice from the experimental data. Express your answer in kJ/kg.

236. (B). In an insulated vessel with plenty of ice at a temperature t 1 = 0 °C fill m= 1 kg of water at temperature t 2 = 44 °C. What is the mass of ice D m will melt when thermal equilibrium is established in the vessel? Express your answer in grams.

237. (B). A tube is lowered into a vessel with water. Steam is passed through a tube through water at a temperature of 100°C. Initially, the mass of water increases, but at some point the mass of water stops increasing, although steam is still passing through. The initial mass of water is 230 g and the final mass is 272 g. What is the initial temperature of the water in Celsius? Neglect heat losses.

238. (C). The calorimeter contained 1 kg of ice. What was the temperature of the ice if, after adding 15 g of water at a temperature of 20°C to the calorimeter, thermal equilibrium was established in the calorimeter at - 2°C? Neglect heat exchange with the environment and the heat capacity of the calorimeter.

Weak pressure from a faucet can upset even the most level-headed homeowner. After all, the duration of filling a kettle or coffee maker and the performance of a washing machine or dishwasher depend on the pressure.

In addition, if the pressure is poor, it is almost impossible to use either the toilet, shower or bath. In a word, if there is no pressure in the tap, then there will be no comfortable living in the house.

We understand the reasons for low water pressure in the tap

What weakens the water pressure in the tap?

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

In this case, the list of TOP 3 reasons for a drop in hot or cold water pressure is as follows:

• Faucet clogged . In this case, the intensity of the water jet is weakened by a plug of rust and scale that has clogged the aerator, filter insert (mesh) or axle box. Moreover, only one tap in the house suffers from this problem. That is, if your tap water flows poorly, for example, in the kitchen, but there are no problems in the bathroom, then you will have to disassemble and clean the problem point of consumption.
• . In this case, the same particles of silt, rust or scale are to blame. Only now they are not blocking the faucet aerator or 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 pipeline fitting itself.
• . In this case, the cause of the weakening may be either a failure at the level of the pumping station or depressurization of the pipeline. A failure at a station can only be corrected by utility service repair teams. An indicator of this breakdown is the lack of water in the entire neighborhood. Loss of tightness is diagnosed visually - by a stream of water gushing from the body of the water supply fittings. Any mechanic 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 when installing a specific water supply line . Incorrect diameter (larger than the previous branch), excessive length (inappropriate for the characteristics of the pressure equipment) - these are the most important reasons for the drop in pressure 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 ways to eliminate this water supply defect.

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

It all depends on the reason for the drop in pressure.

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

Removing the faucet aerator for cleaning

• Take an adjustable wrench and unscrew it from the spout of the faucet. – foaming water jet nozzle. This part has very small nozzles. Therefore, aerators are clogged every six months. And if we are talking about a faucet mixer 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 flows weakly, 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 axle box. To do this, you need to dismantle the valve (faucet handle) and unscrew the lock washer holding the locking element in the body seat. Next, you remove the locking assembly from the body and clean off any deposits of silt or scale from its surface. In the final, you will have to assemble the crane using the reverse procedure.

Before dismantling the faucet shut-off unit, be sure to shut 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 “spray” in the shower stall or bathroom, you'll have to do things a little differently. First, turn off the supply to the sprayer. Then remove it from the stand or metal hose using an adjustable wrench. Immerse the removed part of the sprayer in a saucepan with vinegar. Warm up this medium on the hotplate. Rinse off the scale with water. Return the nozzle to its 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 don’t want to tinker with the crane, call a mechanic from the management company. He will solve this problem right before your eyes.

We hope you already understand what to do if there is poor water pressure in the tap.

Now let's move on to the pipes:

• First, turn off the water by turning the central valve near the meter.
• Next, remove the coarse filter plug. Remove the wire cassette and wash it in a container. Then return the filter element to its place, renew the seal and screw in the plug.
• After checking the coarse filter, proceed to checking the fine cleaning 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 rinsing the filter glass from particles of accumulated dirt. In the final, everything, of course, is mounted in its original place.
• If the filters are cleaned, but water still does not come out of the tap with the required force, then the reason for the drop in pressure is a blockage in the pipes themselves. Locating this problem and eliminating it is an extremely time-consuming task. Therefore, after cleaning the filters without results, you will have to call the management company and report a problem with the passage of pipes in the water supply.

If you have not changed 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 must monitor the performance of the “native” engineering communications.

Unified state exam in physics, 2009,
demo version

Part A

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

1)
2)
3)
4)

Solution. The graph shows that in the time interval from 12 to 16 s, the speed 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. Strip magnet with mass m brought to a massive steel plate weighing 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 on a horizontal surface, a sliding friction force of 10 N acts on a body weighing 40 kg. What will the sliding friction force be after reducing the body's mass by 5 times, if the friction coefficient does not change?

Solution. If your body weight decreases by 5 times, your body weight will also decrease by 5 times. This means that the sliding friction force will decrease by 5 times and amount to 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 truck's momentum to the car's momentum is 1.5?

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

Correct answer: 1.

A5. Mass sled 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 sled is equal to the change in its potential energy. Total mechanical energy will increase by mgh.

Correct answer: 2.

Solution. The wavelength ratio is inversely proportional to the frequency ratio: .

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 horizontal.

At the moment the movement begins, 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 carriage speed on time? (All values ​​are in SI units.)

Solution. From the figure it can be seen that during the time t= 0.4 s the carriage has traveled the distance s= 0.1 m. Since the initial speed of the carriage is zero, its acceleration can be determined:

.

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

Correct answer: 1.

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

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

Correct answer: 2.

A9. The hot liquid cooled slowly in the glass. The table shows the results of measuring its temperature over time.

There was a substance in the glass 7 minutes after the start of measurements

Solution. The table shows that in the period between the sixth and tenth minutes the temperature in the glass remained constant. This means that at this time crystallization (solidification) of the liquid took place; the substance in the glass was simultaneously in both liquid and solid states.

Correct answer: 3.

A10. What work does the gas do when transitioning from state 1 to state 3 (see figure)?

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

Correct answer: 1.

A11. In a heat engine, the temperature of the heater is 600 K, the temperature of the refrigerator is 200 K less 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 machine:

.

Correct answer: 4.

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

Solution. According to the equation of state of 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. The forces of interaction between them

Solution. When the distance between two point electric charges decreases by 3 times, the force of interaction between them increases by 9 times. Increasing 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 key K is closed? (Each of the resistors has a resistance R.)

Solution. After closing the key, the terminals will be short-circuited, and the resistance of this section of the circuit will become zero.

Correct answer: 4.

A15. The figure shows a coil of wire through which 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 magnetic field induction vector of the current is directed

Solution. According to the right hand rule: “If you clasp 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 extended thumb will show the direction of the magnetic field lines inside the solenoid (coil with current).” Having mentally performed these actions, we find that at 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. The graph shows 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 plane mirror ab. The image S of this source in the mirror is shown in the figure

Solution. The image of an object obtained using a plane mirror is located symmetrically to the object relative 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 interface decreases with increasing radiation frequency. The path of rays for the three primary colors when white light falls from 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 shorter its wavelength, the more the beam deviates from its original direction. Blue has the shortest wavelength, red has the longest. The blue beam will deviate the most (1 - blue), the red beam will deviate the least (3 - red), leaving 2 - green.

Correct answer: 4.

A19. At the entrance to the electrical circuit of the apartment there is a fuse 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, the power of each of which is 400 W, can be turned on simultaneously in the apartment?

Solution. An electric current with a force 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 = 7.28 A) will be less than 10 A, and when three kettles are turned on - 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 the Rutherford model of the atom. Black dots indicate electrons. The atom corresponds to the diagram

1)
2)
3)
4)

Solution. The number of electrons in a neutral atom coincides with the number of protons, which is written below 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 undergone one α-decay and two β-decays, turned into an isotope

Solution. During α decay, the mass of the nucleus decreases by 4 a. 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 a. 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 Einstein's equation for the photoelectric effect for the initial frequency of light and for the changed frequency. Subtracting the first from the second equality, we obtain the relation:

Correct answer: 2.

A24. 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?

1)
2)
3)
4)

Solution. To experimentally discover the dependence of wire resistance 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 a 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 equal to 0.05 µC and 0.25 kV, respectively. The capacitance of the capacitor is approximately equal to

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

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

Correct answer: 3.

Part B

IN 1. Load weight 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 in the first column, select the corresponding position in the second and write down the selected numbers in the table under the corresponding letters.

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

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

As the mass decreases, the oscillation period will decrease (A - 2). The frequency is inversely proportional to the period, which means 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.

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

Transfer the resulting sequence of numbers to the answer form (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). There is no heat exchange with surrounding bodies in the adiabatic process (B - 4).

AT 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° with a speed of 50 m/s, and the second at an angle of 30° with a speed of 100 m/s. Find the ratio of the mass of the first fragment to the mass of the second fragment.

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

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

Solution. When cooling, the water will give up an 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's image. Express your answer in centimeters (cm).

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

.

The increase will be

.

The image height is

Part C

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

(Refer to the table for the vapor pressure of water to answer 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 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. Room air, in contact with the glasses, cools. The table shows that if the room air cools to 11 ° C or lower, when the partial pressure of water vapor becomes greater than the pressure of saturated vapor, the water vapor condenses - the glasses will fog up. The temperature outside should be no higher than 11 °C.

Answer: no higher than 11 °C.

C2. A small puck, after being hit, slides up an inclined plane from a point A(see picture). At the point IN the inclined plane without a break passes into the outer surface of a horizontal pipe with a radius R. If at the point A the speed of the puck exceeds , then at the point IN the washer 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 is μ = 0.2. Find the outer radius of the pipe R.

Solution. Let's 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 that the support reaction force is equal to zero. Centripetal acceleration is caused only by gravity, and for the minimum initial speed for which the puck comes 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 there be air inside the shell for the ball to begin to rise? The shell of the ball is inextensible and has a small hole in the lower part.

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

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

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

Where T- temperature of the air inside the shell.

Solving the inequality, we find the minimum temperature T:

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

Answer: 266 °C.

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

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

Aluminum is a conductor, so an induced emf will arise 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 emf of the current source is 12 V, the capacitance of the capacitor is 2 mF, the inductance of the coil is 5 mH, the lamp resistance is 5 ohms and the resistor is 3 ohms. At the initial moment of time, key K is closed. What energy will be released in the lamp after the key is opened? Neglect the internal resistance of the current source, as well as the resistance of the coil and wires.

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

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

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

.

After the switch is opened, transient processes will occur in the system until the capacitor is discharged and the current becomes zero. All the energy will be released as heat in the lamp and resistor. At each moment of time, an 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 the heat generated will be in proportion to the resistances. Thus, energy will be released in the lamp

Answer: 0.115 J.

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

Solution. In the reference frame where the primary -meson is at rest, its momentum is zero and its energy is equal to the rest energy. According to the law of conservation of momentum, γ quanta will fly away in opposite directions with equal momentum. This means that the energies of the 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