Answers to the tasks of the school stage of the All-Russian Olympiad
students in physics in 2015 - 2016 academic year
8th grade.
1. The cyclist covered the first half of the journey at a speed V 1 = 10 km/h. He then drove faster but blew a tire. After trying to repair the puncture, the cyclist was forced to walk the rest of the way. What is the average speed of the cyclist for the entire journey, if the first third of the time spent by him on the second half of the journey, he rode at a speed of V 2 \u003d 20 km / h, the second third was engaged in a puncture and the last third was walking at a speed V 4 = 5 km/h?
Solution. The average speed on a certain section of the path, according to the definition, is equal to the ratio the distance traveled to the time during which this path was traveled
According to the conditions of the task:
0, 5S = V 1 t 1 ,
0, 5S = V 2 t 2 +0∙t 3 + v 4 t 4 ,
t 2 = t 3 =t 4 .
From here you can find:
t 1 = 0,5 S/V 1 , (2)
t 2 = t 3 = t 4 = 0,5 S/(V 2 + V 4). (3)
Substituting relations (2) and (3) into formula (1), we obtain:
.
Complete correct solution
A solution is found for one of two possible cases.
2 . The figure shows levers that have hooks attached at regular intervals. The hooks are numbered from -3 to 3, with 0 being the middle of the lever. Some hooks are attached to several weights of the same mass. There is another similar unsuspended load. To the hook with what number n does it need to be suspended so that the lever is in balance? Solve the problem for each of the three cases shown in the figure.
Solution.
Denote by 
the mass of one load, 
is the distance between adjacent hooks. Let's apply the rule of leverage for each case:
(a) from here 
,
(b) , hence ,
(c), from here .
Correctness (falseness) of the decision
Complete correct solution
The right decision. There are some minor flaws that do not affect the overall solution.
The solution as a whole is correct, however, it contains significant errors (not physical, but mathematical).
The equations of the moments of forces are written and a solution is obtained - 3 points each for cases (a) and (b), 4 points - case (c).
The correct answer is received without the equation of the moments of forces, for each lever
There are separate equations related to the essence of the problem in the absence of a solution (or wrong decision).
The solution is incorrect or missing.
3. From what height must water fall so that it boils when it hits the ground? 50% of the consumption goes to water heating mechanical energy, the initial water temperature is 20 0 С.
Solution:
According to the condition, for heating water with a mass m energy is consumed equal to mgh .
Therefore, according to the law of conservation of energy: E=Q; mgh = mc (t 2 - t 1 ), where t 2 =100 0 C. From here h = .
The calculations give: h = = 70∙10 3 (m).
The result obtained shows how great the energy released and absorbed in thermal processes.
Answer: 70km.
Correctness (falseness) of the decision
Complete correct solution
The right decision. There are some minor flaws that do not affect the overall solution.
The solution as a whole is correct, however, it contains significant errors (not physical, but mathematical).
The law of conservation of energy is written down. The formula for calculating the potential energy and the amount of heat is written. Each formula 1 point
1250 kg
Answer: M=1250 kg.
Correctness (falseness) of the decision
Complete correct solution
The right decision. There are some minor flaws that do not affect the overall solution.
The solution as a whole is correct, however, it contains significant errors (not physical, but mathematical).
The power formula is written, the gravity work formula is written, 2 points for each
There is an understanding of the physics of the phenomenon, but one of the equations necessary for solving has not been found; as a result, the resulting system of equations is not complete and it is impossible to find a solution.
There are separate equations related to the essence of the problem in the absence of a solution (or in case of an erroneous solution).
The solution is incorrect or missing.
The car traveled a distance L = 160 km from the city to the village in time T = 2 hours. Its speed on the first, good section of the path was ∆V = 10 km/h more than the average speed on the entire path, and on the second, bad section, it was ∆V = 10 km/h less than the average speed on the entire path. What is the length s bad site way?
Possible Solution
The average speed of the car all the way V cf = L / T = 80 km/h. Then, on the first section of the path, the car had a speed V 1 = 90 km / h, and on the second - V 2 = 70 km / h.
The average speed over the entire journey can be expressed in terms of the lengths of the sections of the path and the speeds on them:
Answer: S = 70 km
Evaluation criteria
Task 2
A small copper cube is placed in the middle of a flat ice floe with a thickness H = 60 cm floating in water, as a result of which the depth of the ice floe immersion increases by Δh = 0.5 cm. cube to put an iron cube with twice the side? The density of ice ρ l \u003d 900 kg / m 3, the density of water ρ w \u003d 1000 kg / m 3, the density of copper ρ m \u003d 8900 kg / m 3, the density of iron ρ w \u003d 7800 kg / m 3.
Possible Solution
In the absence of cubes, the force of gravity acting on the ice floe is balanced by the force of Archimedes. A part of an ice floe with a height h = H / 10 = 6 cm protrudes above the water.
This follows from the float condition:
S∙H∙ρ l = S∙ρ in ∙g∙(H-h),
where S is the area of the ice floe.
The force of gravity acting on the cube is balanced by the additional force of Archimedes. Let us write down the equilibrium conditions only for additional forces. For a copper cube: S∙Δh∙ρ in = ρ m ∙a 3 ∙g. For an iron cube: S∙ΔH∙ρ in ∙g = ρ f ∙8a 3 ∙g, where ΔH is the additional depth of immersion of an ice floe with an iron cube. Dividing one equation by the other, we get:
Hence H p \u003d (H - h) + ΔH \u003d 57.5 cm.
This value is less than the thickness of the ice floe, therefore, it will not sink.
Evaluation criteria
Task 3
Vessels partially filled with mercury, over which there is air, are connected by tubes. The left upper vessel and the upper tube are open to the atmosphere. Mercury does not flow through the pipes. Find the air pressure at point A, express the answer in mm Hg. Art.
Determine the height L of the mercury column in the upper tube. Height h = 5 cm. Atmosphere pressure p 0 \u003d 760 mm Hg. Art.
Possible Solution
Since the fluid in the system is in equilibrium, the hydrostatic pressures at different depths can be related to each other.
The air pressure in the lower vessel is equal to the pressure on the surface of the mercury adjacent to it: p 1 = p 0 + 8 ρ∙g∙h = 1160 mm Hg. Art. (here ρ is the density of mercury). The same air pressure is in the upper right vessel (that is, at point A).
On the surface of the liquid in the middle vessel, the pressure is p 2 = p 0 + 11 ρ∙g∙h, but otherwise it can be expressed in terms of the height L as follows: p 2 = p 0 + ρ∙g∙(L + 4h)
Hence L = 7h = 35 cm.
Answer:L=35cm
Task 4
Ten portions of water were mixed in a calorimeter. The first portion had a mass m = 1 g and a temperature t = 1 °C, the second one had a mass 2m and a temperature 2t, the third one 3m and 3t, and so on, and the tenth one had a mass 10m and a temperature 10t. Determine the steady state temperature of the mixture. Ignore heat loss.
Possible Solution
Since by condition the system is thermally isolated, we will use the law of conservation of energy. Let us determine the amount of heat that will be released when all portions of water cool down to 0 °C.
Q = cmt + 2m∙c∙2t + … + 10m∙c∙10t = 385 cmt
Let this amount of heat be used to heat all the water with a mass m + 2m + ... + 10m = 55m from 0 °C to the desired temperature t x: Q = 55cmt x = 385 cmt, whence t x = 7 °C.
Answer: t x \u003d 7 ° С
- Points for each correct action add up.
- In case of an arithmetic error (including an error in the conversion of units of measurement), the estimate reduced by 1 point.
- Maximum for 1 task - 10 points.
- Total for work - 40 points.
I present to your attention the tasks of the All-Russian Olympiad school tour in physics for grade 8 with the correct answers to them.
These tasks can be used in the 8th grade, giving students a chance to learn and systematize previously covered topics, as well as determine how well students are ready for such Olympiad tasks.
1. When cooling by 15°C, the body lost an amount of heat equal to 2500 J. How much heat will it lose by cooling down by 45°C?
- A) 75 J
- B) 750 J
- C) 7500 J
2. Magnetic line magnetic field- this is...
- A) a line along which iron filings move
- B) a line that shows the effect of a magnetic field on magnetic arrows
- C) a line along which the axes of magnetic needles are set in a magnetic field
3. At the beginning of the 20th century, the Russian scientist Alexander Chizhevsky first expressed the idea of the influence solar activity on living beings and social processes. What was the name given to the significant increase in solar activity?
- A) solar wind
- B) magnetic storm
- B) dark spot
- D) Chizhevsky effect
4. How much heat is needed to heat a piece of ice weighing 4.5 kg from a temperature of 0 o C to a temperature of 100 o C? Specific heat of melting ice 3.4 ∙ 10 5 J / kg, specific heat water 4200 J / (kg ∙ o C).
- A) 17.1 ∙ 10 5 J
- B) 34.2 ∙ 10 5 J
- C) 3.2 ∙ 10 5 J
- D) 51 ∙ 10 5 J
5. What source of light is the Sun?
- A) thermal
- B) Luminescent
- B) reflective
- D) artificial
6. How long will it take for an electric current to complete 400 J of work in the circuit at a voltage of 100 V and a current of 0.2 A?
- A) 2 s
- B) 20 s
- C) 2 minutes
- D) 20 minutes
7. What substance is called a conductor of electricity?
- A) a substance that has an electrical charge
- B) A substance that is easily electrified
- C) A substance through which only positive charges can pass from a charged body to others
- D) A substance through which any electric charge can pass from a charged body to others
8. What charge will we get on a glass rod if we rub it with silk?
- A) negative
- B) Positive
- B) neutral
- D) any of the above
9. What work does the electric motor do in 1 minute, if the current in the motor winding is 5 A, the voltage at its terminals is 220 V? Engine efficiency 80%.
- A) 2112 J
- B) 1375 J
- C) 880 J
- D) There is no correct answer
10. Phenomena associated with the heating or cooling of bodies, with a change in temperature, are called ...
- A) electrical
- B) condensing
- B) thermal
- D) melting phenomena
11. When the voltage at the ends of the conductor is 8 V, the current strength in it is 0.4 A. What will the current strength in the conductor be equal to when the voltage at its ends decreases to 2 V?
- A) 1.6 A
- B) 0.1 A
- B) 0.8 A
- D) 0.2 A
12. The same conductor is included first in one, then in another electrical circuit, where current strengths are set in it, respectively, 2 A and 4 A. In which circuit will it highlight large quantity heat and by how much?
- A) In the circuit where I \u003d 4A, 2 times
- B) In the circuit where I \u003d 4A, 4 times
- C) In the circuit where I \u003d 2A, 2 times
- D) In the circuit where I \u003d 2A, 4 times
13. The body radiates energy the more intensely than ...
- A) it is more
- B) more of its density
- B) it moves faster
- D) higher temperature
14. German physicist, after whom the unit of magnetic flux is named.
- A) Heinrich Hertz
- b) Albert Einstein
- B) Erwin Schrodinger
- D) Wilhelm Weber
15. In which case is it about changing the internal energy of the body by heat transfer?
- A) Heating of skis due to friction on snow
- B) Heating of the skates when rubbing against the ice
- C) Ignition of a match when rubbing against a matchbox
- D) Heating water in a test tube
16. Finish the phrase: Due to the electrification of the body ...
- A) warms up
- B) cool down
- B) is in motion
- D) acquires the ability to attract other bodies to itself
17. What instruments are needed to determine the work electric current?
- A) Rheostat, galvanometer, voltmeter
- B) Voltmeter, battery, clock
- C) Ammeter, battery, voltmeter
- D) Voltmeter, ammeter, clock
18. The dependence of the current on what physical quantities establishes Ohm's law?
- A) quantity of electricity and time
- B) Voltage and resistance
- C) Resistance and amount of electricity
- D) Voltages and quantities of electricity
19. Due to what energy is the separation of charged particles in a galvanic cell?
- A) due to mechanical energy
- B) due to internal energy
- C) due to the energy of chemical reactions
- D) due to the energy of light
20. Is the statement true: what more water When boiling receives heat, the higher its temperature?
- a) Yes, because internal energy increases with heat
- B) Yes, because when heat is received, the temperature of the water increases
- C) No, because all the heat received goes to overcome the interaction of water particles and their release to the surface
- D) No, because how much water takes in heat, it gives off so much to the surrounding air
Answers to the All-Russian Olympiad in Physics Grade 8
This table provides answers to test tasks in physics for the school stage of the All-Russian Olympiad
| Job number | Correct answer |
| 1 | AT |
| 2 | AT |
| 3 | B |
| 4 | B |
| 5 | BUT |
| 6 | B |
| 7 | G |
| 8 | B |
| 9 | G |
| 10 | AT |
| 11 | B |
| 12 | B |
| 13 | G |
| 14 | G |
| 15 | G |
| 16 | G |
| 17 | G |
| 18 | B |
| 19 | AT |
| 20 | AT |
1. An alloy of gold and silver weighing 400 g has a density of 1.4 104 kg/m³. Assuming the volume of the alloy is equal to the sum of its volumes constituent parts, determine the mass of gold in the alloy.
Solution: The mass of the alloy is always equal to the sum of the masses of its constituent parts: m cn \u003d m c + m s. According to the condition of the problem, the volume of the alloy is equal to the sum of the volumes of its constituent parts: V cn \u003d V c + V c. From the formula for the density p=m/V it follows that V=m/p.
Substituting the expression for the volumes into the last formula and expressing the mass of silver in terms of the mass of the alloy and the mass of gold, we obtain:
We solve these equations together for an unknown mass m z: 
. Where 
Performing the appropriate algebraic transformations, we find the desired value: 
. The calculations give the following results:
2.
Water is poured into vessels connected by a tube to a tap (see figure). Hydrostatic pressure at points BUT and AT equals p A = 4 kPa and p B = 1 kPa respectively, the cross-sectional areas of the left and right vessels are SA = 3 dm² and SB = 6 dm², respectively. Which hydrostatic pressure set at points BUT and AT if you open the faucet?
Solution: Before opening the tap, the mass of water in the left vessel is equal to p A S A /g, in the right vessel p B S B /g. After opening the tap at the points BUT and AT the same hydrostatic pressure p is set, so the total mass of water in the vessels is equal to p(S A +S B)/g. Since the mass of water is conserved, then p A S A + p B S B = p(S A + S B). In this way, 
3. A paraffin candle burns in such a way that its length decreases at a speed of v = 5 · 10 −5 m/s, and the evaporating paraffin burns out completely without flowing down. A candle floats in a wide vessel filled with water. She is slightly supported in vertical position so that it doesn't tip over. With what speed V does the candle move relative to the vessel during combustion? The density of water p W = 1000 kg / m³, the density of paraffin p P = 900 kg / m³.
Solution: Let L be the length of the candle at some point in time, H the length of its underwater part, S the area of its cross section. According to the condition of bodies floating, p В gHB = p П gLS, whence H/L = p П /p В. During the time Δt, the length of the candle decreased by ΔL = vΔt, and the depth of immersion of its lower end decreased by 
. Consequently, the lower end of the candle (like the entire candle) moves at a speed relative to the vessel.
4.
The bar is located on the boundary of two liquids having densities p 1 and p 2 , displacing the volumes V 1 and V 2 of the corresponding liquids (see figure). What Archimedean force F A acts on the bar?
Solution: Archimedean force is the pressure force of a fluid on each of the sections of the surface of the body. AT this case this resultant is equal to the difference between the pressure forces on the lower and upper faces of the bar: F A \u003d F H - F B \u003d S (p H and p B). Here S is the area of the lower and upper faces, p H and p B are the fluid pressures on the corresponding faces. Let us denote by h 1 and h 2 the heights of the parts of the bar that are in the corresponding liquids. Then p H - p B \u003d p 1 gh 1 + p 2 gh 2, whence F A \u003d p 1 gSh 1 + p 2 gSh 2 \u003d p 1 V 1 + p 2 V 2. So, the Archimedean force is equal to the total weight of the liquid displaced by the bar.
Othe main goals and objectives of the Olympiad are the identification and development of students creativity and interest in research activities, the creation necessary conditions to support gifted children, promotion of scientific knowledge.
Lead time:
60 min -7, 8 classes - 4 tasks;
1 hour 30 min - Grade 9 - 4 tasks
2 hours - 10.11 classes - 5 tasks.
The Olympiad is held in one round of individual competitions of participants. Participants submit a report on the work done in writing. Additional oral questioning not allowed.
To complete the tasks, students are recommended to use a calculator and a set of tables. For successful implementation workin the 9th grade, it is necessary to give students a table of heat capacities and specific heat melting.
The jury of the Olympiad evaluates the entries given in the clean copy. Drafts are not checked. All notes in the work of the participant, the members of the jury do onlyred ink. Points for intermediate calculations are placed near the corresponding places in the work. The final score for the problem is given at the end of the solution. The jury member enters the score in the table on the first page of the work and puts his signature.
In case of an incorrect decision, it is necessary to find and mark the error that led to it.
The correct answer given without justification or obtained from incorrect reasoning is not taken into account. If the task is not completely solved, then the stages of its solution are evaluated in accordance with the evaluation criteria for this task.
Maximum amount points with the correct solution of the problem for 7 - 9 classes - 5 points.
Verification of works is carried out according to the standard methodology for evaluating solutions:
| Points | Correctness (falseness) of the decision |
| Complete correct solution |
|
| The right decision. There are some minor flaws that do not affect the overall solution. |
|
| The solution as a whole is correct, however, it contains significant errors (not physical, but mathematical). |
|
| A solution is found for one of two possible cases. |
|
| There is an understanding of the physics of the phenomenon, but one of the equations necessary for solving has not been found; as a result, the resulting system of equations is not complete and it is impossible to find a solution. |
|
| There are separate equations related to the essence of the problem in the absence of a solution (or in case of an erroneous solution). |
|
| The solution is incorrect or missing. |
The maximum number of points for grades 7, 8, 9 is 20, for grades 10, 11 -25 points.
school stage. 2015-2016 academic year.
8th grade
A stool with a mass of 2 kg stands on four legs, the footprint of each of which has the shape of a square with a side of 3 cm. What is the mass of a cat sitting on a stool if the pressure of the stool together with the cat on the floor is 20 kPa?
The figure shows levers that have hooks attached at regular intervals. The hooks are numbered from -3 to 3, with 0 being the middle of the lever. Some hooks are attached to several weights of the same mass. There is another similar unsuspended load. To the hook with what number n does it need to be suspended so that the lever is in balance? Solve the problem for each of the three cases shown in the figure.
3. From Nizhny Novgorod In the direction of Moscow with an interval of 10 minutes, two electric trains left at a speed of 54 km/h. What was the speed of the oncoming train if it met the second train 4 minutes after the first?
4. A metal rod is heated by placing one end of it in a flame (see figure). After some time, the temperature of the metal at point A rises. How is energy transferred?
All-Russian Olympiad for schoolchildren in physics.
school stage.
2015-2016 academic year.
Answers and Quick Solutions
8th grade
1. Solution: Let's write down the expression for the pressure p , which the stool (together with the cat) exerts on the floor: where m and M - masses of a stool and a cat, S - footprint area of one leg. From here we find the mass of the cat: .
Answer: 5.2 kg.
2. Solution . Denote by the mass of one load, - the distance between adjacent hooks. Let's apply the rule of leverage for each case:
(a) from here,
(b) , hence ,
(c) , hence .
3. Solution.
Distance between electric trains
km. The oncoming train travels the same distance in minutes at a speed of . Therefore, where km/h.Answer: 81 km/h
4. Answer : mainly by conduction.
