Tasks for grade 7
Task 1. Travel Dunno.
At 4 o'clock in the evening, Dunno drove past a kilometer post on which 1456 km was written, and at 7 o'clock in the morning, past a post with an inscription 676 km. At what time will Dunno arrive at the station from which the distance is counted?
Task 2. Thermometer.
In some countries, such as the United States and Canada, temperature is measured not in Celsius, but in Fahrenheit. The figure shows such a thermometer. Determine the value of divisions of the Celsius scale and Fahrenheit scale and determine the temperature values.
Problem 3. Naughty glasses.
Kolya and his sister Olya began to wash the dishes after the guests left. Kolya washed the glasses and, turning them over, put them on the table, and Olya wiped them with a towel, then put them in the closet. But! .. The washed glasses adhered tightly to the oilcloth! Why?
Problem 4. Persian proverb.
A Persian proverb says, "The smell of nutmeg cannot be hidden." What physical phenomenon does this saying refer to? Explain the answer.
Problem 5. Horseback riding.
Preview:
Problems for grade 8.
Task 1. Riding a horse.
The traveler rode first on a horse and then on a donkey. What part of the journey and what part of the whole time did he ride a horse, if the average speed of the traveler was 12 km / h, the speed of riding a horse was 30 km / h, and on a donkey, 6 km / h?
Problem 2. Ice in water.
Problem 3. Elephant lift.
Young craftsmen decided to construct a lift for the zoo, with the help of which an elephant weighing 3.6 tons can be lifted from the cage to a platform located at a height of 10 m. According to the developed project, the lift is driven by a motor from a 100W coffee grinder, and energy losses are completely excluded. How long would each climb take under these conditions? Consider g \u003d 10m / s2 .
Problem 4. Unknown liquid.
In the calorimeter, different liquids are alternately heated using the same electric heater. The figure shows graphs of the dependence of the temperature t of liquids on time τ. It is known that in the first experiment the calorimeter contained 1 kg of water, in the second - another amount of water, and in the third 3 kg of some liquid. What was the mass of water in the second experiment? With what liquid was the third experiment carried out?
Task 5. Barometer.
Sometimes the inscriptions “Clear” or “Cloudy” are made on the barometer scale. Which of these records corresponds to the higher pressure? Why are barometer predictions not always correct? What will the barometer at the top of a high mountain predict?
Preview:
Problems for grade 9.
Objective 1.
Justify the answer.
Objective 2.
Objective 3.
A vessel with water at a temperature of 10 ° C was placed on an electric stove. After 10 minutes, the water boiled. How long does it take for the water to completely evaporate in the vessel?
Problem 4.
Task 5.
Ice was dropped into a glass filled with water. Will the water level in the glass change when the ice melts? How will the water level change if a lead ball was frozen into a piece of ice? (the volume of the ball is considered negligible compared to the volume of ice)
Preview:
Problems for grade 10.
Objective 1.
A person standing on the bank of a river 100m wide wants to cross to the other side, to the opposite point. He can do this in two ways:
- Swim at an angle to the current at all times so that the resulting speed is perpendicular to the shore at all times;
- Swim straight to the opposite bank, and then walk the distance that it will be carried by the current. Which way will get you across faster? He swims at a speed of 4 km / h, and goes at a speed of 6.4 km / h, the speed of the river is 3 km / h.
Objective 2.
In the calorimeter, different liquids are alternately heated using the same electric heater. The figure shows graphs of the dependence of the temperature t of liquids on time τ. It is known that in the first experiment the calorimeter contained 1 kg of water, in the second - a different amount of water, and in the third 3 kg of some liquid. What was the mass of water in the second experiment? With what liquid was the third experiment carried out?
Objective 3.
The body, having an initial velocity V0 \u003d 1 m / s, moved uniformly accelerated and, having passed a certain distance, acquired a speed V \u003d 7 m / s. What was the speed of the body at half this distance?
Problem 4.
Two bulbs read "220V, 60W" and "220V, 40W". What is the current power in each of the light bulbs when connected in series and in parallel, if the voltage in the network is 220V?
Task 5.
Ice was dropped into a glass filled with water. Will the water level in the glass change when the ice melts? How will the water level change if a lead ball was frozen into a piece of ice? (the volume of the ball is considered to be negligible in comparison with the volume of ice).
Objective 3.
Three identical charges q are located on one straight line, at a distance l from each other. What is the potential energy of the system?
Problem 4.
Weight m 1 is suspended from a spring of rigidity k and is in equilibrium. As a result of an inelastic hit of a bullet flying vertically upwards, the load began to move and stopped in a position where the spring was unstretched (and uncompressed). Determine the speed of the bullet if its mass is m2 ... Disregard the mass of the spring.
Task 5.
Ice was dropped into a glass filled with water. Will the water level in the glass change when the ice melts? How will the water level change if a lead ball was frozen into a piece of ice? (the volume of the ball is considered to be negligible in comparison with the volume of ice).
by movementfor the first 3 seconds of movement
8th grade
XLVI All-Russian Physics Olympiad for Schoolchildren. Leningrad region. Municipal stage
Grade 9
\u003d 2.7 10 3 kg / m 3, in \u003d 10 3 kg / m 3 and B \u003d 0.7 10 3 kg / m 3 ... Disregard air buoyancyg \u003d 10 m / s 2.
from\u003d 4.2 kJ / K?
XLVI All-Russian Physics Olympiad for Schoolchildren. Leningrad region. Municipal stage
Grade 10
H H is equal V.
Q
4
ρ
ρ
v... Define attitude ρ/ρ
v... Acceleration of gravity g.
XLVI All-Russian Physics Olympiad for Schoolchildren. Leningrad region. Municipal stage
Grade 11
v. R g.
3
. What is the maximum volume of water with a densityρ
1 \u003d 1.0 g / cm 3 can be poured into H-shaped asymmetrical tube with open top ends, partially filled with oil with a densityρ
2 \u003d 0.75 g / cm 3 ? The horizontal sectional area of \u200b\u200bthe vertical parts of the tube isS
... The volume of the horizontal part of the tube can be neglected. The vertical dimensions of the tube and the height of the oil column are shown in the figure (heighth
considered given).
Note.
4. What is the resistance of the wire frame in the form of a rectangle with sides and and inand the diagonal if the current flows from point A to point B? Resistance per unit length of wire .
The movement of a material point is described by the equation x (t) \u003d 0.2 sin (3.14t), where x is expressed in meters, t - in seconds. Determine the path covered by the point in 10 seconds of movement.
Possible solutions
7th grade
The graph shows the dependence of the path traveled by the body on time. Which of the graphs corresponds to the dependence of the speed of this body on time?
Decision: The correct answer is G.
2. From paragraph A to point B the car "Volga" left at a speed of 90 km / h. At the same time, towards him from the pointB the car "Zhiguli" left. At 12 o'clock in the afternoon, the cars drove past each other. At 12:49 Volga arrived at the pointB , and 51 minutes later the Zhiguli arrived atA ... Calculate the speed of the Zhiguli.
Decision: Volga "traveled from point A to the meeting point with" Zhiguli "during t x , and "Zhiguli" drove the same section for t 1 \u003d 100 minutes. In turn, "Zhiguli" drove from the point B to the meeting point with the "Volga" during t x , and "Volga" drove the same section for t 2 \u003d 49 minutes. Let's write these facts in the form of equations:
where υ 1 - the speed of the Zhiguli, and υ 2 - the speed of the Volga. Dividing one equation term by another, we get:
.
From here υ 1 = 0,7υ 2 \u003d 63 km / h.
3. A material point moves in a circle with a radius of R \u003d 2 m at a constant modulus of speed, making a full revolution in 4 s. Determine the average speed by movementfor the first 3 seconds of movement
Decision: Moving a material point in 3 s is 
The average travel speed is /3
4. The body moves in such a way that its velocities during each of n equal time intervals are equal to V 1, V 2, V 3,… ..V n, respectively. What is the average body speed?
Decision: 
XLVI All-Russian Physics Olympiad for Schoolchildren. Leningrad region. Municipal stage
Possible solutions
8th grade
Decision: 
F 1 mg \u003d F 1 + F 2 F 2
3 gV \u003d 1 gV 2/3 + 2 gV 1/3
mg 3 \u003d 1 2/3 + 2 1/3
3 \u003d (2 1 + 2) / 3
2. The intercity bus covered 80 km in 1 hour. The engine developed a power of 70 kW with an efficiency of 25%. How much diesel fuel (density 800 kg / m 3, specific heat of combustion 42 10 6 J / kg) did the driver save if the fuel consumption rate is 40 liters per 100 kilometers?
Decision: Efficiency \u003d A/ Q = Nt/ rm = Nt/ r V
V \u003d Nt / r efficiency
Calculations: V \u003d 0.03 m 3; from the proportion 80/100 \u003d x / 40 we determine the rate of fuel consumption per 80 km x \u003d 32 (liters)
V \u003d 32-30 \u003d 2 (liters)
3. A person is transported by boat from point A to point B, located at the shortest distance from A on the other side. The speed of the boat relative to the water is 2.5 m / s, the speed of the river is 1.5 m / s. What is the minimum time it will take for him to cross if the river is 800 m wide?
Decision: To cross in the minimum time, it is necessary that the vector of the resulting velocity v be directed perpendicular to the coast
4. The body passes the same sections of the path with constant velocities within the section V 1, V 2, V 3,… .. V n. Determine the average speed along the entire path.
Decision: 
XLVI All-Russian Physics Olympiad for Schoolchildren. Leningrad region. Municipal stage
Possible solutions
Grade 9
A hollow ball made of aluminum, being in water, stretches the dynamometer spring with a force of 0.24 N, and in gasoline with a force of 0.33 N. Find the volume of the cavity. Densities of aluminum, water and gasoline, respectively \u003d 2.7 10 3 kg / m 3, in \u003d 10 3 kg / m 3 and B \u003d 0.7 10 3 kg / m 3 g \u003d 10 m / s 2.
Decision:
R 
solution: The cube is in balance under the influence of three forces: gravity mg
, Archimedean force F
A and the reaction force from the side of the supports, which, in turn, can be conveniently decomposed into two components: the component of the reaction force normal to the inclined bottom N
and the friction force on the supports F
tr.
Note that the presence of supports on which the cube rests plays an important role in the problem, since it is thanks to them that the water surrounds the cube from all sides, and to determine the force with which the water acts on it, you can use the Archimedes law. If the cube lay directly on the bottom of the vessel and water did not leak under it, then the resultant surface forces of water pressure on the cube would not push it up, but, on the contrary, would press it even more strongly to the bottom. In our case, a buoyant force acts on the cube F A \u003d a 3 gpointing up.
Projecting all forces onto the coordinate axis parallel to the bottom of the vessel, we write down the equilibrium condition of the cube in the form: F tr \u003d ( mg - F A) sin.
Considering that the mass of the cube m \u003d a a 3, we get the answer: F tr \u003d ( a – in ) a 3 g sin \u003d 8.5 (H).
A stone thrown at an angle 30 0 to the horizon was twice at the same height h; after time t 1 \u003d 3 s and time t 2 \u003d 5 s after the start of movement. Find the initial velocity of the body. The Earth's free fall acceleration is 9.81 m / s 2.
Decision: The movement of the body in the vertical direction is described by the equation:
From here at y \u003d h we get; 
Using the properties of the roots of the quadratic equation, according to which
get
The acceleration of gravity on the surface of the Sun is 264.6 m / s 2, and the radius of the Sun is 108 times the radius of the Earth. Determine the ratio of the densities of the Earth and the Sun. The Earth's free fall acceleration is 9.81 m / s 2.
Decision: We apply the law of universal gravitation to determine g
To measure the temperature of 66 g of water, a thermometer was immersed in it, having a heat capacity C T \u003d 1.9 J / K, which showed the temperature in the room t 2 \u003d 17.8 0 C. What is the actual water temperature if the thermometer shows 32.4 0 C . Heat capacity of water from\u003d 4.2 kJ / K?
Decision: The thermometer, when immersed in water, received the amount of heat 
.
This amount of heat is given to him by the water; hence 
.
From here 
XLVI All-Russian Physics Olympiad for Schoolchildren. Leningrad region. Municipal stage
Possible solutions
Grade 10
1. An air bubble rises from the bottom of a reservoir with a depth H... Find the dependence of the radius of an air bubble on the depth of its position at the current time, if its volume at a depth H is equal V.
Decision:Pressure at the bottom of the reservoir: 
at a depth h: 
Bubble volume at depth h: 
From here 
2. During the time t 1 \u003d 40 s, a certain amount of heat was released in a circuit consisting of three identical conductors connected in parallel and connected to the network Q... How long will it take to release the same amount of heat if the conductors are connected in series?
Decision:
3. Is it possible to connect two incandescent lamps with a power of 60 W and 100 W, designed for a voltage of 110 V, in series to a network with a voltage of 220 V, if the voltage on each lamp can be exceeded by no more than 10% of the nominal? The current-voltage characteristic (the dependence of the current in the lamp on the applied voltage) is shown in the figure.
Decision: At a rated voltage U n \u003d 110 V, the current flowing through a lamp with a power of P 1 \u003d 60 W is 
A. When the lamps are connected in series, the same current will go through a lamp with a power of P2 \u003d 100 W. According to the current-voltage characteristic of this lamp, at a current of 0.5 A, the voltage across this lamp should be 
B. Consequently, when two lamps are connected in series, the voltage across a 60 W lamp reaches the nominal voltage already at the mains voltage 
V. Therefore, with a voltage of 220 V, the voltage on this lamp will exceed the nominal by more than 10%, and the lamp will burn out.
4... Two identical balls of density ρ
connected by a weightless thread thrown across the block. Right ball immersed in a viscous fluid of density ρ
0, rises at a steady rate v... Define attitude ρ/ρ
0 if the steady-state velocity of a ball freely falling in a liquid is also v... Acceleration of gravity g.
Decision: The forces of resistance to the motion of the balls due to the equality of their steady-state velocities are the same in both cases, although they are directed in opposite directions.
Let us write the dynamic equation of motion in projections onto the axis oUdirected vertically upward for the first and second cases (movement of a system of bodies and the fall of one ball in a liquid, respectively):
T - mg \u003d 0
T + F A - mg - F c \u003d 0
F A - mg + F c \u003d 0,
where mg - gravity module, T - modulus of thread tension force, F A - buoyancy module, F c - resistance force modulus.
Solving the system of equations, we get 
.
5. Athletes run at the same speed v with column length l 0. The coach runs towards the speed u (uPossible solutions
Grade 11
1. A wheel of radius R rolls without slipping at a constant speed of the wheel center v... A pebble falls off the top of the wheel rim. How long will it take for the wheel to hit this stone? Wheel radius R, acceleration of gravity g.
Decision: If the wheel axle moves at a speed v,without slipping, then the speed of the lower point is 0, and the upper one, like the horizontal speed of the pebble, is 2 v.
Pebble fall time 
Axis movement time horizontally 
twice as much.
This means that the collision will occur in 
.
2. The ant runs from the anthill in a straight line so that its speed is inversely proportional to the distance to the center of the anthill. At the moment when the ant is at point A at a distance l 1 \u003d 1 m from the center of the anthill, its speed is v 1 \u003d 2 cm / s. How long does it take for an ant to run from point A to point B, which is located at a distance of l 2 \u003d 2 m from the center of the anthill?
Decision: The speed of an ant does not change linearly over time. Therefore, the average speed on different sections of the path is different, and we cannot use the well-known formulas for the average speed to solve. We divide the path of the ant from point A to point B into small sections traversed in equal time intervals 
... Then ρ 2 \u003d 0.75 g / cm 3? The horizontal sectional area of \u200b\u200bthe vertical parts of the tube is S ... The volume of the horizontal part of the tube can be neglected. The vertical dimensions of the tube and the height of the oil column are shown in the figure (height h considered given).
Note. It is forbidden to plug the open ends of the tube, tilt it or pour oil out of it.
Decision: It is important that as little oil as possible remains in the short knee. Then, in a tall tube, it will be possible to create a pole with a maximum height exceeding 4 h on x... To do this, start pouring water into the right knee. This will continue until the water level reaches 2 h in the right knee, and the oil level, respectively, is 3 h in the left. Further displacement of the oil is impossible, since the oil-water interface in the right knee will become higher than the connecting pipe, and water will begin to flow into the left knee. The water addition process will have to be stopped when the top of the oil in the right knee reaches the top of the knee. The condition of equality of pressures at the level of the connecting tube gives:
5. The movement of a material point is described by the equation x (t) \u003d 0.2 sin (3.14t), where x is expressed in meters, t - in seconds. Determine the path covered by the point in 10 seconds of movement.
Decision:The movement is described by the equation:
;
hence T \u003d 1 s During 10 s, the point will make 10 complete oscillations. During one complete oscillation, the point travels a path equal to 4 amplitudes.
Full path is 10x 4x 0.2 \u003d 8 m
Select a document from the archive to view:
Methodological recommendations for conducting and assessing the school stage of the Olympiad.docx
Library
materials
At the school stage, it is recommended to include 4 tasks in the assignment for students in grades 7 and 8. Allocate 2 hours for their implementation; for students in grades 9, 10 and 11 - 5 tasks each, for which 3 hours are allocated.
The tasks of each age parallel are compiled in one version, so the participants must sit one at a time at the table (desk).
Before the start of the round, the participant fills out the cover of the notebook, indicating his data on it.
Participants work with blue or purple ink pens. Do not use red or green ink pens to write solutions.
During the Olympiad it is allowed to use a simple engineering calculator by the Olympiad participants. And on the contrary, the use of reference books, textbooks, etc. is unacceptable. If necessary, students should be provided with periodic tables.
The system for evaluating the results of the Olympiad
The number of points for each task theoretical round is in the range from 0 to 10 points.
If the problem is partially solved, then the stages of solving the problem are subject to assessment. It is not recommended to enter fractional points. As a last resort, they should be rounded "in favor of the student" to whole points.
It is not allowed to deduct points for "bad handwriting", sloppy notes, or for solving a problem in a way that does not coincide with the method proposed by the methodological commission.
Note. In general, one should not follow the author's grading system too dogmatically (these are just recommendations!). The decisions and approaches of schoolchildren may differ from those of the author's and may not be rational.
Special attention should be paid to the applied mathematical apparatus used for problems that do not have alternative solutions.
An example of the correspondence between the points awarded and the solution given by the participant of the Olympiad
Points
Correctness (erroneousness) of the decision
Complete correct solution
The right decision. There are some minor bugs that generally do not affect the decision.
Selected document for viewing School stage of the Olympiad in physics grade 9.docx
Library
materials
Grade 9
1. Train movements.
t 1 = 23 ct 2 = 13 c
2. Calculation of electrical circuits.
R 1 = R 4 \u003d 600 Ohm,R 2 = R 3 \u003d 1.8 kΩ.
3. Calorimeter.
t 0 , 0 about FROM . M , its specific heatfrom , λ m .
4. Colored glasses.
5. Flask in water.
3 with a capacity of 1.5 liters has a mass of 250 g. Weight, what mass must be placed in the flask so that it sinks in water? Density of water 1 g / cm 3 .
1. The experimenter Gluck observed the oncoming traffic of a fast train and electric train. It turned out that each of the trains passed by Gluck at the same time.t 1 = 23 c... Meanwhile, Gluck's friend, the theorist Bug, was on the train and determined that the fast train passed him fort 2 = 13 c... How many times do the lengths of a train and an electric train differ?
Decision.
Evaluation criteria:
Writing the equation of motion of a fast train - 1 point
Writing the equation of motion of the electric train - 1 point
Writing the equation of motion when a fast train and an electric train approach - 2 points
Solving the equation of motion, writing the formula in general form - 5 points
Mathematical calculations -1 point
2. What is the resistance of the circuit when the switch is open and closed?R 1 = R 4 \u003d 600 Ohm,R 2 = R 3 \u003d 1.8 kΩ.
Decision.
With the key open:R o \u003d 1.2 kΩ.
With a closed key:R o \u003d 0.9 kΩ
Equivalent circuit with closed key:
Evaluation criteria:
Finding the total resistance of the circuit with an open key - 3 points
Equivalent circuit with closed key - 2 points
Finding the total resistance of the circuit with a closed key - 3 points
Mathematical calculations, unit conversion - 2 points
3. Into the calorimeter with water, the temperature of whicht 0 , threw a piece of ice that had a temperature 0 about FROM . After thermal equilibrium was established, it turned out that a quarter of the ice had not melted. Considering the known mass of waterM , its specific heatfrom , specific heat of melting of iceλ , find the initial mass of the ice blockm .
Decision.
Evaluation criteria:
Drawing up an equation for the amount of heat given off by cold water - 2 points
Solution of the heat balance equation (writing the formula in general form, without intermediate calculations) - 3 points
Conclusion of units of measurement for checking the calculation formula - 1 point
4. On the notebook is written in red pencil "excellent" and "green" - "good". There are two glasses - green and red. What glass do you need to look through to see the word "excellent"? Explain your answer.
Decision.
If the red glass is brought to the record with a red pencil, then it will not be visible, because red glass only lets through red rays and the entire background will be red.
If we look at the writing in red pencil through the green glass, then on the green background we will see the word “excellent” written in black letters, because green glass blocks red light rays.
To see the word “excellent” in a notebook, you need to look through the green glass.
Evaluation criteria:
Complete answer - 5 points
5. Glass flask with a density of 2.5 g / cm 3 with a capacity of 1.5 liters has a mass of 250 g. What mass must be placed in a flask so that it sinks in water? Density of water 1 g / cm 3 .
Decision.
Evaluation criteria:
Writing the formula for finding the gravity force acting on a flask with a load - 2 points
Writing the formula for finding the Archimedes force acting on a flask immersed in water - 3 points
Selected document for viewing School stage of the Olympiad in physics grade 8.docx
Library
materials
School stage of the physics Olympiad.
8th grade
Traveler.
Parrot Kesha.
That morning, the parrot Keshka, as usual, was going to make a report on the benefits of banana growing and banana eating. After having breakfast with 5 bananas, he took a megaphone and climbed to the “tribune” - to the top of a palm tree 20 m high. Halfway through, he felt that he could not reach the top with a megaphone. Then he left the megaphone and climbed further without it. Will Keshka be able to make a report if the report needs an energy reserve of 200 J, one eaten banana allows you to do work of 200 J, the mass of a parrot is 3 kg, the mass of a megaphone is 1 kg? (when calculating, acceptg= 10 N / kg)
Temperature.
about
Ice floe.
ice density
Answers, instructions, solutions to the Olympiad problems
1. The traveler rode for 1 hour 30 minutes at a speed of 10 km / h on a camel and then for 3 hours - on a donkey at a speed of 16 km / h. What was the average speed of the traveler along the way?
Decision.
Evaluation criteria:
Writing the formula for the average speed of movement - 1 point
Finding the distance traveled at the first stage of movement - 1 point
Finding the distance traveled at the second stage of movement - 1 point
Mathematical calculations, unit conversion - 2 points
2. That morning, the parrot Keshka, as usual, was going to make a report on the benefits of banana growing and banana eating. After having breakfast with 5 bananas, he took a megaphone and climbed up to the “tribune” - to the top of a 20m high palm tree. Halfway through, he felt that he could not reach the top with the megaphone. Then he left the megaphone and climbed further without it. Will Keshka be able to make a report if the report needs an energy reserve of 200 J, one eaten banana allows you to do work of 200 J, the mass of a parrot is 3 kg, the mass of a megaphone is 1 kg?
Decision.
Evaluation criteria:
Finding the total supply of energy from eaten bananas - 1 point
Energy expended to raise the body to a height h - 2 points
Energy spent by Keshka to climb the podium and perform - 1 point
Mathematical calculations, correct formulation of the final answer - 1 point
3. Into water weighing 1 kg, the temperature of which is 10 about C, pour in 800 g of boiling water. What will be the final temperature of the mixture? Specific heat of water
Decision.
Evaluation criteria:
Drawing up an equation for the amount of heat received by cold water - 1 point
Drawing up an equation for the amount of heat given off by hot water - 1 point
Heat balance equation writing - 2 points
Solution of the heat balance equation (writing the formula in general form, without intermediate calculations) - 5 points
4. A flat ice floe 0.3 m thick is floating in the river. What is the height of the part of the ice that protrudes above the water? Density of water ice density
Decision.
Evaluation criteria:
Recording the swimming conditions of bodies - 1 point
Writing the formula for finding the force of gravity acting on an ice floe - 2 points
Writing the formula for finding the Archimedes force acting on an ice floe in water - 3 points
Solving a system of two equations - 3 points
Mathematical calculations - 1 point
Selected document for viewing School stage of the Olympiad in physics Grade 10.docx
Library
materials
School stage of the physics Olympiad.
Grade 10
1. Average speed.
2. Escalator.
A metro escalator lifts a passenger standing on it in 1 minute. If a person walks along a stopped escalator, it will take 3 minutes to climb. How long will it take to climb if a person walks along an upward moving escalator?
3. Ice bucket.
M from \u003d 4200 J / (kg about λ = 340,000 J / kg.
t˚,FROM
t, min
t, min minminmin
4. Equivalent circuit.
Find the resistance of the circuit shown in the figure.
2 R
2 R
2 R
2 R
2 R
2 R
R - ?
5. Ballistic pendulum.
m
Answers, instructions, solutions to the Olympiad problems
1 . The traveler traveled from city A to city B, first by train, and then by camel. What was the average speed of a traveler if he traveled two-thirds of the way by train and one-third of the way by camel? Train speed 90 km / h, camel speed 15 km / h.
Decision.
Let's denote the distance between points by s.
Then the travel time by train:
Evaluation criteria:
Writing the formula for finding the time at the first stage of the journey - 1 point
Writing the formula for finding the time at the second stage of movement - 1 point
Finding the entire movement time - 3 points
Derivation of the calculation formula for finding the average speed (writing the formula in general form, without intermediate calculations) - 3 points
Mathematical calculations - 2 points.
2. A metro escalator lifts a passenger standing on it in 1 min. If a person walks along a stopped escalator, it will take 3 minutes to climb. How long will it take to climb if a person walks along an upward moving escalator?
Decision.
Evaluation criteria:
Drawing up the equation of motion for a passenger on a moving escalator - 1 point
Drawing up the equation of motion for a passenger moving on a stationary escalator - 1 point
Drawing up the equation of motion for a moving passenger on a moving escalator –2 points
Solving the system of equations, finding the travel time for a moving passenger on a moving escalator (derivation of the calculation formula in general form without intermediate calculations) - 4 points
Mathematical calculations - 1 point
3. The bucket contains a mixture of ice water with a total massM \u003d 10 kg. The bucket was brought into the room and the temperature of the mixture was measured immediately. The resulting temperature versus time dependence is shown in the figure. Specific heat of waterfrom \u003d 4200 J / (kg about FROM). Specific heat of melting of iceλ = 340,000 J / kg. Determine the mass of ice in the bucket when it was brought into the room. Neglect the heat capacity of the bucket.
t˚, ˚ FROM
t, min minminmin
Decision.
Evaluation criteria:
Drawing up an equation for the amount of heat received by water - 2 points
Drawing up an equation for the amount of heat required to melt ice - 3 points
Heat balance equation recording - 1 point
Solving a system of equations (writing a formula in general form, without intermediate calculations) - 3 points
Mathematical calculations - 1 point
4. Find the resistance of the circuit shown in the figure.
2 R
2 R
2 R
2 R
2 R
2 R
R - ?
Decision:
The two right-hand resistances are connected in parallel and together giveR .
This resistance is connected in series with the rightmost resistance of the valueR ... Together they provide resistance of2 R .
Thus, moving from the right end of the circuit to the left, we get that the total resistance between the inputs of the circuit isR .
Evaluation criteria:
Calculation of parallel connection of two resistors - 2 points
Calculation of the series connection of two resistors - 2 points
Equivalent circuit diagram - 5 points
Mathematical calculations - 1 point
5. A box of mass M, suspended by a thin thread, is hit by a bullet with massmflying horizontally at a speed , and gets stuck in it. To what height H does the box rise after being hit by a bullet?
Decision.
Butterfly - 8 km / h
Fly - 300 m / min
Cheetah - 112 km / h
Turtle - 6 m / min
2. Treasure.
A record about the location of the treasure was found: “From the old oak tree go north 20 m, turn left and walk 30 m, turn left and walk 60 m, turn right and walk 15 m, turn right and walk 40 m; dig here. " What is the path that, according to the record, must be taken in order to get from oak to treasure? At what distance from the oak is the treasure. Complete the task drawing.
3. Cockroach Mitrofan.
Cockroach Mitrofan walks through the kitchen. For the first 10 s, he walked at a speed of 1 cm / s in the direction to the north, then turned west and walked 50 cm in 10 s, stood for 5 s, and then in the direction northeast at a speed of 2 cm / s, made a path 20 see Here he was overtaken by a human foot. How long did the cockroach Mitrofan walk in the kitchen? What is the average speed of movement of the cockroach Mitrofan?
4. Race on the escalator.
Answers, instructions, solutions to the Olympiad problems
1. Write down the names of the animals in descending order of speed:
Shark - 500 m / min
Butterfly - 8 km / h
Fly - 300 m / min
Cheetah - 112 km / h
Turtle - 6 m / min
Decision.
Evaluation criteria:
Cheetah - 31.1 m / s
Shark - 500 m / min
Fly - 5 m / s
Butterfly - 2.2 m / s
Turtle - 0.1 m / s
Converting the speed of a butterfly into the International System of Units - 1 point
Converting the speed of the fly to SI - 1 point
Conversion of the speed of movement of a cheetah into SI - 1 point
Converting the speed of movement of the turtle to SI - 1 point
Writing the names of animals in descending order of speed - 1 point.
2. A record about the location of the treasure was found: “From the old oak tree go north 20 m, turn left and walk 30 m, turn left and walk 60 m, turn right and walk 15 m, turn right and walk 40 m; dig here. " What is the path that, according to the record, must be taken in order to get from oak to treasure? At what distance from the oak is the treasure. Complete the task drawing.
Decision.
Evaluation criteria:
Drawing the plan of the trajectory, taking the scale: 1cm 10m - 2 points
Finding the passed path - 1 point
Understanding the difference between the distance traveled and body movement - 2 points
3. Cockroach Mitrofan walks through the kitchen. For the first 10 s, he walked at a speed of 1 cm / s towards the north, then turned west and walked 50 cm in 10 s, stood for 5 s, and then towards the northeast at a speed of 2 cm / s, made a path 20 cm.
Here a man's foot overtook him. How long did the cockroach Mitrofan walk in the kitchen? What is the average speed of movement of the cockroach Mitrofan?
Decision.
Evaluation criteria:
Finding the time of movement at the third stage of movement: - 1 point
Finding the traversed path at the first stage of the cockroach movement - 1 point
Writing the formula for finding the average speed of movement of a cockroach - 2 points
Mathematical calculations - 1 point
4. Two kids Petya and Vasya decided to arrange races on the escalator moving down. Starting at the same time, they ran from one point, located exactly in the middle of the escalator, in different directions: Petya - down, and Vasya - up the escalator. The time spent on the distance by Vasya turned out to be 3 times more than Petya's. At what speed does the escalator move if friends at the last competition showed the same result, having run the same distance at a speed of 2.1 m / s?
Find material for any lesson,
On February 21, the Government House of the Russian Federation hosted the ceremony of awarding the Government Prizes in Education for 2018. The awards were presented to the laureates by the Deputy Prime Minister of the Russian Federation T.A. Golikova.
Among the laureates of the award are employees of the Laboratory for Working with Gifted Children. The award was received by the teachers of the Russian national team at the IPhO Vitaly Shevchenko and Alexander Kiselev, the teachers of the Russian national team at the IJSO Elena Mikhailovna Snigireva (chemistry) and Igor Kiselev (biology) and the head of the Russian national team, MIPT vice-rector Artyom Anatolyevich Voronov.
The main achievements for which the team was awarded a government award - 5 gold medals for the Russian team at IPhO-2017 in Indonesia and 6 gold medals for the team at IJSO-2017 in Holland. Every student brought home gold!
This is the first time a Russian team has achieved such a high result at the International Physics Olympiad. In the entire history of the IPhO since 1967, neither the Russian team nor the USSR national team have ever managed to win five gold medals before.
The complexity of the Olympiad tasks and the level of training of teams from other countries is constantly growing. However, the Russian national team has been in the top five teams in the world in recent years. In order to achieve high results, the teachers and the leadership of the national team are improving the system of preparation for the internship in our country. Educational schools have appeared, where students study in detail the most difficult sections of the program. A base of experimental tasks is being actively created, by performing which the guys are preparing for the experimental tour. Remote work is carried out on a regular basis; during the year of preparation, the children receive about ten theoretical homework assignments. Much attention is paid to the high-quality translation of the conditions of the problems at the Olympiad itself. Training courses are being improved.
High results in international Olympiads are the result of a long work of a large number of teachers, employees and students of MIPT, personal teachers in the field, and the hard work of the students themselves. In addition to the aforementioned award winners, a huge contribution to the preparation of the national team was made by:
Fedor Tsybrov (creating tasks for qualifying fees)
Alexey Noyan (experimental preparation of the national team, development of an experimental workshop)
Alexey Alekseev (creating tasks for qualifying fees)
Arseny Pikalov (preparation of theoretical materials and conducting seminars)
Ivan Erofeev (many years of work in all areas)
Alexander Artemiev (checking homework)
Nikita Semenin (creating tasks for qualifying fees)
Andrey Peskov (development and creation of experimental installations)
Gleb Kuznetsov (experimental training of the national team)
Olympiad tasks in physics grade 10 with a solution.
Olympiad tasks in physics grade 10
Olympiad tasks in physics. Grade 10.In the system shown in the figure, a block of mass M can slide along the rails without friction.
The load is retracted at an angle a from the vertical and released.
Determine the mass of the load m if the angle a does not change when the system moves.
A thin-walled gas-filled cylinder with mass M, height H, and base area S floats in water.
As a result of the loss of tightness in the lower part of the cylinder, the depth of its immersion increased by D H.
The atmospheric pressure is P 0, the temperature does not change.
What was the initial gas pressure in the cylinder?
The closed metal chain is connected by a thread to the axis of the centrifugal machine and rotates with an angular velocity w.
In this case, the thread makes an angle a with the vertical.
Find the distance x from the center of gravity of the chain to the axis of rotation.
Inside a long tube filled with air, a piston is moved at a constant speed.
In this case, an elastic wave propagates in the pipe at a speed of S \u003d 320 m / s.
Assuming the pressure drop at the wave propagation boundary equal to P \u003d 1000 Pa, estimate the temperature drop.
Pressure in undisturbed air P 0 \u003d 10 5 Pa, temperature T 0 \u003d 300 K.
The figure shows two closed processes with the same ideal gas 1 - 2 - 3 - 1 and 3 - 2 - 4 - 2.
Determine in which of them the gas did the great job.
Solutions to Olympiad problems in physics
Let T be the tension force of the thread, a 1 and a 2 - the accelerations of bodies with masses M and m.
Writing down the equations of motion for each of the bodies along the x axis, we obtain
a 1 M \u003d T · (1-sina), a 2 m \u003d T · sina.
Since the angle a does not change during motion, then a 2 \u003d a 1 (1-sina). It is easy to see that
|
From here
Considering the above, we finally find
|
To solve this problem, it should be noted that
that the center of mass of the chain rotates along a circle of radius x.
In this case, only the gravity force applied to the center of mass and the thread tension T force act on the chain.
It is obvious that centripetal acceleration can be provided only by the horizontal component of the thread tension force.
Therefore, mw 2 x \u003d Tsina.
In the vertical direction, the sum of all forces acting on the chain is zero; then mg- Tcosa \u003d 0.
From the obtained equations we find the answer
Let the wave move in the pipe with constant velocity V.
Let us associate this value with a given pressure drop D P and a density difference D r in unperturbed air and a wave.
The pressure difference accelerates the "excess" of air with the density D r to the speed V.
Therefore, in accordance with Newton's second law, we can write
Dividing the last equation by the equation P 0 \u003d R r T 0 / m, we obtain
|
Since D r \u003d D P / V 2, r \u003d P 0 m / (RT), we finally find
A numerical estimate, taking into account the data given in the problem statement, gives the answer D T »0.48K.
To solve the problem, it is necessary to build graphs of circular processes in coordinates P-V,
since the area under the curve in such coordinates is equal to work.
The result of this construction is shown in the figure.
