Preparation for the exam in physics. Studying the properties of a physical pendulum The student studies the properties of the pendulums at his disposal

pendulum length

Solid ball volume

The material the ball is made from

1.0 m

5 cm 3

steel

1.5 m

5 cm 3

steel

2.0 m

5 cm 3

aluminum

1.0 m

8 cm 3

steel

1.0 m

5 cm 3

copper

A bar of mass 0.8 kg moves along a horizontal table, connected to a load of mass 0.2 kg by a weightless inextensible thread thrown over a smooth weightless block. The load moves with an acceleration of 1.2 m/s2. Determine the friction coefficient of the bar on the table surface.

Answer: _____

Point B is in the middle of segment AC. Stationary point charges -q and -2q (q = 1 nC) are located at points A and C, respectively. What positive charge must be placed at point C instead of the charge - 2q, so that the modulus of the electric field strength at point B increases by 2 times?

Answer: _____ nK

A straight conductor with a length of I = 0.2 m, through which a current I = 2 A flows, is in a uniform magnetic field with induction B = 0.6 T and is located parallel to the vector⇀ BB⇀ . Determine the modulus of force acting on the conductor from the magnetic field.

Answer: _____ H.

Part 2.

The complete correct solution of each of the problems 27-31 should contain the laws and formulas, the application of which is necessary and sufficient to solve the problem, as well as mathematical transformations, calculations with a numerical answer and, if necessary, a figure explaining the solution.

A separate frog egg is transparent, its shell consists of a gelatinous substance; inside the egg is a dark embryo. In early spring, on sunny days, when the water temperature in reservoirs is close to zero, the caviar feels warm to the touch. Measurements show that its temperature can reach 30 degrees.

1) How can this phenomenon be explained?

2) Give similar examples found in everyday life or in nature.

Show answer

A person begins to climb the subway escalator moving up with an acceleration a = 0.21 m/s 2 . Having reached the middle of the escalator, he stops, turns and starts to go down with the same acceleration. Determine how long a person is on the escalator.

The length of the escalator is L=100 m, and its speed is V=2 m/s.

Show answer

The cylinder contains nitrogen with a mass m = 24 g at a temperature T = 300 K. The gas is cooled isochorically so that its pressure drops n = 3 times. The gas is then heated at constant pressure until its temperature reaches its original temperature. Determine the work A done by the gas.

Show answer

When the terminals of the galvanic cell are short-circuited, the current in the circuit is 2 A. When an electric lamp with an electrical resistance of 3 ohms is connected to the terminals of the galvanic cell, the current in the circuit is 0.5 A. Based on the results of these experiments, determine the internal resistance of the galvanic cell.

Show answer

A person reads a book, holding it at a distance of 50 cm from the eyes. If this is the distance of his best vision, then what optical power of glasses will allow him to read a book at a distance of 25 cm?

Experimental study 1. B 23 No. 2402. A student studied the oscillations of a mathematical pendulum in the school laboratory. The results of measurements of what quantities will enable him to calculate the period of oscillation of the pendulum? 1) the mass of the pendulum m and the knowledge of the tabular value of the acceleration of free fall g 2) the length of the thread ma no l and knowledge of the tabular value of the acceleration of free fall g 3) amplitude oscillations of the pendulum A and its mass m 4) the amplitude of the oscillations of the pendulum A and knowledge of the tabular value of the free fall acceleration g 2. B 23 No. 2404. During the experiment, the student investigated the dependence the modulus of the elastic force of the spring on the length of the spring, which is expressed by the formula, where is the length of the spring in the undeformed state. The graph of the resulting dependency is shown in Fig. Unke. Which of the statements corresponds to the answer with your result of the ult of experience? A. The length of the spring in the non-deformed vane is therefore 3 cm. B. The rigidity of the spring is equal. 1) A 2) B 3) A and B 4) Neither A nor B 3. B 23 No. 2407. It is necessary to experimentally detect oscillations of a spring pendulum from hard with these springs. period dependence Which pair of pendulums can be used for this purpose? In the figure, springs and weights are shown in the state of equal weight. 1) A, C or D 2) only B 3) only C 4) only D 4. B 23 No. 2408. It is necessary to experimentally find out the dependence of the period of small oscillations of a mathematical pendulum on the substance from which the load is made. What pair of beacons (see fig.) can be taken for this purpose? Pendulum weights - hollow balls of copper and aluminum of the same mass and the same outer diameter. 1) 1 2) 2 3) 3 4) 4 5. B 23 No. 2410. When measuring the voltage at the ends of a wire helix, four students in different ways connect with a single volt meter. The result of these works is shown in the picture below. Which of the students under the united voltmeter is correct? 1) 1 2) 2 3) 3 4) 4 6. B 23 No. 2411. A beam of white light, passing through a prism, decomposes into a spectrum. It was hypothesized that the width of the spectrum obtained on the screen behind the prism depends on the angle of incidence of the beam on the face of the prism. It is necessary to test this hypothesis experimentally. What two experiments need to be carried out for such an investigation? 1) A and 2) B and 3) B and 4) C and B C D D 7. B 23 No. 2414. the same material. Which pair of conductors should be chosen in order to experimentally detect the dependence of the resistance of the conductor on its length? 1) 1 2) 2 3) 3 4) 4 8. B 23 No. 2415. Conductors are made from different materials. Which pair of conductors should be chosen in order to experimentally detect the dependence of the resistance of the conductor on its specific resistance? 1) 1 2) 2 3) 3 4) 4 9. B 23 No. 2416 three Which pair of capacitors should be chosen in order to experimentally detect the dependence of the capacitance of the ator on the area of ​​its plates? 1) 1 2) 2 3) 3 4) 4 10. B 23 No. 2417 three Which pair of capacitors should be chosen in order to experimentally detect the dependence of the capacitance of the ator on the distance between its plates? 1) 1 2) 2 3) 3 4) 4 11. B 23 No. 2418 mi. Which pair of capacitors should be chosen in order to experimentally detect the dependence of the capacitance of the condenser on the electrical conductor you? 1) 1 2) 2 3) 3 4) 4 12. B 23 No. 2419. When measuring the current strength in the wire spiral R, four students connected the ammeter in different ways. The result of the ultat is shown in the picture below. Indicate the correct connection for the ammeter. 1) 1 2) 2 3) 3 4) 4 13. B 23 No. 2421. To verify experimentally that the stiffness of an elastic rod depends on its length, a pair of steel rods 1) A and 2) B and 3) C and 4) B and B C D D 14. B 23 No. 2429. Two vessels are filled with different liquids. Which pair of vessels should be chosen in order to experimentally discover the dependence and pressure bridge of a column of liquid from its density? 1) 1 2) 2 3) 3 4) 4 15. B 23 No. 2430. Two vessels are filled with the same liquid. Which pair of vessels should be chosen in order to experimentally discover the dependence of the pressure of a liquid column on the height of the column? 1) 1 2) 2 3) 3 4) 4 16. B 23 No. 3119. Conductors made from the same material a la. Which pair of conductors should be chosen in order to experimentally detect the dependence of the resistance of the wire on its diameter? 1) 1 2) 2 3) 3 4) 4 17. B 23 No. 3122. It was hypothesized that the size of the virtual image of an object created by a diverging lens depends on the optical power of the lens. It is necessary to test this hypothesis experimentally. What two experiments can be carried out for such a study 1) A and 2) A and 3) B and 4) C and B C C D 18. B 23 No. 3124. A student studied oscillations in a school laboratory spring pendulum. What two measurements must he know in order to determine the stiffness of the spring and the pendulum? 1) the amplitude of the oscillation of the waveform A and its oscillation period T 2) the amplitude of the oscillation of the floating pendulum A and mass m of the load 3) acceleration of free fall g and amplitude of the wave pendulum A 4) period of oscillation of the pendulum T and mass m of the load 19. B 23 No. 3127. densities. Which pair of balls should be chosen in order to experimentally discover the dependence of the Archimedes force on the density of the fluid? 1) 1 2) 2 3) 3 4) 4 20. B 23 No. 3128. Two balls are made of different materials. What pair of balls should be chosen in order to experimentally detect the dependence and bridge of masses on density? 1) 1 2) 2 3) 3 4) 4 21. B 23 No. 3214. To determine the molar mass of a gas in equilibrium, it is necessary to know exactly measure 1) Gas temperature, mass and pressure 2) Gas density, its temperature and pressure 3) Gas density, its mass and temperature 4) Gas pressure , its volume and its temperature 22. B 23 No. 3215. The spring pendulum performs free harmonic oscillations. What value can be determined if the mass of the load m and the oscillation period T of the pendulum are known? 1) The length without stretching that spring 2) Max and small potential energy 3) Stiffness of the spring 4) The amplitude of the oscillation of the springs and the pendulum 23. B 23 No. 3246. During the laboratory work, it was necessary to measure the voltage across the resistance tiv leni. This can be done using the circuit 1) 1 2) 2 3) 3 4) 4 24. B 23 No. 3247. During the laboratory work, it was necessary to measure the current through the resistance This can be done using the circuit 1) 1 2) 2 3) 3 4) 4 25. B 23 No. 3248. During the laboratory work, it was necessary to measure the voltage on the resistor. This can be done using the scheme 1) 1 2) 2 3) 3 4) 4 26. B 23 No. 3249. A liquid is poured into a cylindrical vessel. It was hypothesized that the pressure of the liquid on the bottom of the vessel depends on the area of ​​the bottom of the vessel. To test this hypothesis, you need to choose the following two experiments from the ones given below. 1) A and 2) B and 3) A and 4) B and C C D D ​read 1) gas pressure p and its volume V 2) gas mass m and its temperature T 3) gas temperature T and its volume V 4 ) gas pressure p and gas temperature T 28. B 23 No. 3320. The mathematical pendulum performs free harmonic oscillations. What value can be determined if the length l and the oscillation period T of the light are known? 1) Amplitude A of oscillation of the beacon 2) Acceleration of free fall g 3) Max. ​small kinetic energy 4) mass m of the weight is swinging 29. B 23 No. 3347. The weights of the pendulums are copper balls. Which pair of pendulums (see figure) should be chosen in order to experimentally find out whether the period of small oscillations depends on the length of the thread? 1) A and 2) A and 3) A and 4) B and B C D C 30. B 23 No. 3391. A wire coil with current creates a magnetic field. It has been hypothesized that the magnetic flux through the cross section of the coil depends on the number of turns and the diameter. It is necessary to test this hypothesis experimentally. What two sets of coils should be taken for such an investigation? 1) A and 2) B and 3) B and 4) C and B C D D 31. B 23 No. 3392. Suppose you do not know the formula for calculating the period of oscillation of a mathematical pendulum. It is necessary to experimentally check whether this value depends on the mass of the load. Which beacons should be used for this verification? 1) A and 2) A and 3) B and 4) B and B D C D 32. B 23 No. 3395. The student studies the law of Archimedes, changing in experiments the volume of a body immersed in a liquid and the density of the liquid. Which pair of experiments should he choose to discover the dependence of the Archimedean force on the volume of the submerged body? (The figures indicate the density of the liquid.) 33. B 23 No. 3462. There is a deviation from Ohm's law for a chain section. This is due to the fact that 1) changes with i the number of electrons moving with i in a spiral 2) on blue ​gives photo effect 3) changes the resistance of the coil when heated 4 ) a magnetic field appears 34. B 23 No. 3467. The equipment shown in the figure was used to determine the efficiency of the inclined plane. Using a dynamometer, a student lifts a bar with two weights evenly along an inclined plane. The student entered the data of the experiment in the table. What is the efficiency of an inclined plane? Your answer is expressed as a percentage. Indication of the diameter when lifting the load, N 1.5 Length of the inclined plane, m 1.0 Weight of the bar with two behind, kg 0.22 Height of the inclined plane, m 0.15 1) 10% 2) 22% 3) 45% 4) 100% 35. B 23 No. 3595. A schoolboy conducts experiments with two lenses, directing a parallel beam of light at them. The course of rays in these experiments is shown in the figures. According to the results of these experiments, the focal length of the lens 1) is greater than the focal length of the lens 2) is less than the focal length The distance of the lens 3) is equal to the focal length of the lens 4) cannot be correlated with the focal length of the lens 36. B 23 No. 3608. The student conducts experiments with two lenses, directing a parallel beam of light at them. The course of rays in these experiments is shown in the figures. According to the results of these experiments, the focal length of the lens 1) is greater than the focal length of the lens 2) is less than the focal length distance of lens 3) is equal to focal length of lens 4) cannot be correlated with focal length of lens 37. B 23 No. 3644. In the recent past for accurate electrical measurements, resistance "stores" were used, which were a wooden box, under the lid of which a thick copper plate (1) with gaps (2) was placed, into which copper plugs (3) can be inserted (see figure). If all the plugs are firmly inserted, then the electric current flows through them directly along the plate, the resistance of which is negligible. If either of the plugs is missing, then the current flows through the wires (4), which close the gaps and have a precisely measured resistance. Tiv le ni eat. Determine what the resistance set on the resistance box is equal to, as shown in the following diagram, if,. 1) 8 ohm 2) 9 ohm 3) 0.125 ohm 4) 0.1 ohm What contributor can be determined from these data? 1) Avoga dro number 2) electric power 3) universal gas power 4) at 39. B 23 No. 3646. In the recent past, for accurate electrical measurements, resistance “stores” were used, which are a wooden box, under the lid of which a thick copper plate was placed ( 1) with gaps (2) into which copper plugs (3) can be inserted (see figure). If all the plugs are firmly inserted, then the electric current flows through them directly along the plate, the resistance of which is negligible. If either of the plugs is missing, then the current flows through the wires (4), which close the gaps and have a precisely measured resistance. Tiv le ni eat. Determine what the resistance is equal to, shown on the next diagram, if set to, store, resistance, . 1) 10 ohm 2) 16 ohm 3) 0.1 ohm 4) 0.625 ohm What contributor can be determined from these data? 1) Avoga dro number 2) electric power 3) universal gas power 4) according to Boltzman’s position at 41. B 23 No. 3718. To determine the power of a constant electric emitter in a cut and then re, use an ideal ammeter and voltmeter. What is the connection diagram of these devices connecting wires is neglected and can be small. 1) 1 2) 2 3) 3 4) 4 is correct? current, Resistance 42. B 23 No. 3719. To study gas laws, a laboratory assistant made a gas thermometer, which is a flask with air, hermetically connected to a curved tube, in the open vertical part of which there is a column of water. By heating the air in the flask, the laboratory assistant observed the movement of the water column inside the tube. At the same time, atmospheric pressure remained unchanged. Some stages of the experiment are shown in the figure. Which of the statements corresponds(s) to the results of this experiment, carried out under the indicated conditions? A) When heating a gas, the change in its volume is proportional to the change in temperature ry. B) When a gas is heated, its pressure will increase from I. 1) only A 2) only B 3) both A and B 4) neither A nor B . Using the data in the figure and the psychrometric table, determine what temperature (in degrees Celsius) the dry bulb meter shows if the relative humidity of the air and in the room ​nee 60%. 1) 10.5ºС 2) 21ºС 3) 11ºС 4) 29ºС measured the angles of twist of the thread, on which the hang was short. As a result of this experiment, G. Cavendish measured the value of 1) density of lead 2) coefficient of efficiency enta proportional to ti in Coulo’s law 3) gravitational to ti 4 ) acceleration of free fall on Earth 45. B 23 No. 4131. A meteorite weighing 10 tons is approaching a spherical planet. The radius of this planet is 2.5 106 m. Figure with unke (solid line). The acceleration of free fall on the surface from this planet is approximately equal to 1) 3.5 m/s 2 2) 50 m/s 2 3) 0.2 m/s 2 4) 1.4 m/s 2 46. B 23 No. 4356. There is a set of weights of 20g, 40g, 60g and 80g and a spring attached to the support in a vertical position. The weights are carefully hung in turn from the spring (see Figure 1). The dependence of the elongation of the spring on the mass of the load attached to the spring is shown in Figure 2. A load of what mass, being attached to this spring, can make small oscillations along the axis from the corner of the hour with that one? 1) 20 g 2) 40 g 3) 50 g 4) 80 g The weights are carefully hung in turn from the spring (see Figure 1). The dependence of the elongation of the spring on the mass of the load attached to the spring is shown in Figure 2. A load of what mass, being attached to this spring, can make small oscillations along the axis from the corner of the hour with that one? 1) 10 g 2) 40 g 3) 60 g 4) 100 g Using the data in the tables, determine the absolute humidity in the room where these thermometers are installed. The first table shows relative humidity expressed in %. 1) 2) 3) 4) 49. B 23 No. 4463. The readings of dry and wet thermometers installed in a certain room are respectively equal to and. Using the data in the tables, determine the absolute humidity in the room where these thermometers are installed. The first table shows relative humidity expressed in %. 1) 2) 3) 4) 50. B 23 No. 4498. The house stands on the edge of the field. From the balcony, from a height of 5 m, the boy threw a pebble in a horizontal direction. The initial speed of the pebble is 7 m/s, its mass is 0.1 kg. 2 s after the throw of the ki, the energy of the bag stone is approximately equal to 1) 15.3 J 2) 0 3) 7.4 J 4) 22.5 J 51. B 23 No. 4568. The house stands on the edge of the field. From the balcony, from a height of 5 m, the boy threw a pebble in a horizontal direction. The initial speed of the pebble is 7 m/s. 2 s after the throw, the speed of the sack is approximately equal to 1) 21 m/s 2) 14 m/s 3) 7 m/s 4) 0 52. B 23 no. 4603. The house stands on the edge of the field. From the balcony, from a height of 5 m, the boy threw a pebble in a horizontal direction. The initial speed of the pebble is 7 m/s, its mass is 0.1 kg. 2 s after throwing the pulse of the bag, approximately equal to 1) 0.7 kg m/s 2) 1.4 kg m/s 3) 2.1 kg m / s 4) 0 53. B 23 No. 4638. The house stands on the edge of the field. From the balcony, from a height of 5 m, the boy threw a pebble in a horizontal direction. The initial speed of the pebble is 7 m/s. 2 seconds after the throw, the pebbles will be at a height 1) 0 2) 14 m 3) 15 m 4) 25 m 54. B 23 No. 4743. Teacher demonstrated experience in observing the voltage that arises in a coil when a magnet passes through it (Fig. 1). The voltage from the coil then fell into the computer measuring system and was displayed on the monitor re (Fig. 2). What was done with the ice in the experiment? 1) dependence and power of the EMF of the field itself and the induction of the field from a change in the direction of the electric current 2) due to the dependence and bridge of the Ampere force on the current strength 3) a magnetic field will appear when the electric power changes from which field 4) depends on the direction of the induction current from the change in the magnetic field current 55. B 23 No. 4778. The teacher assembled the circuit shown in fig. 1 by connecting the coil to the capacitor. First, the capacitor was connected to a voltage source, then the switch was turned to position 2. The voltage from the inductor enters the computer measuring system, and the result ​These are displayed on the monitor (Fig. 2). What was done with the ice in the experiment? 1) automatic oscillatory process in the generator 2) required electromagnetic circuits 3) phenomenon of electromagnetic induction 4) free electromagnetic oscillations 56. B 23 No. 4813. The teacher demonstrated the experience of observing the voltage that occurs in the coil when a magnet passes through it (Fig. 1). The voltage from the coil then fell into the computer measuring system and was displayed on the monitor re (Fig. 2). In the experiment, it was studied 1) a magnetic field appeared when the electric field changed 2) the phenomenon of electromagnetic induction 3) the phenomenon of self-induction 4) the action of the Ampere force 57. B 23 No. 4848. The teacher demonstrated the experiment, the setup for which is shown in the photograph (Fig. 1). First, he connected the capacitor to a voltage source, and then turned the switch to position 2. The voltage from the inductor is fed into a computer measuring system, and the results of the change in voltage over time are displayed on the screen. Nothing (Fig. 2). What was observed in the experiment 1) free fluctuating oscillations in an ideal contour 2) free damped oscillations in the oscillatory circuit 3) the phenomenon occurs oscillatory circuit 4) you need the required electromagnetic oscillations ​in contour 58. B 23 No. 4953. The student measured the force of gravity acting on the load. The dynamometer readings are shown in the photograph. The measurement error is equal to the division value of the diameter of the meter. In which case is the indication of the meter’s dimen- sion per recording correct? 1) (2.0 ± 0.1) N 2) (2.0 ± 0.2) N 3) (2.0 ± 0.5) N 4) (2.0 ± 0.01) N 59. B 23 No. 5163. The student measured the force of gravity acting on the load. The dynamometer readings are shown in the photograph. The measurement error is equal to the division value of the diameter of the meter. In which case is the indication of the meter’s dimen- sion per recording correct? 1) (1.6 ± 0.2) N 2) (1.4 ± 0.2) N 3) (2.4 ± 0.1) N 4) (1.6 ± 0.1) N 60. B 23 No. 5198. The student measured the force of gravity acting on the load. The dynamometer readings are shown in the photograph. The measurement error is equal to the division value of the diameter of the meter. In which case is the indication of the meter’s dimen- sion per recording correct? 1) (1.8 ± 0.2) N 2) (1.3 ± 0.2) N 3) (1.4 ± 0.01) N 4) (1.4 ± 0.1) N 61. B 23 No. 5303. The student measured the force of gravity acting on the load. The dynamometer readings are shown in the photograph. The measurement error is equal to the division value of the dynamometer. In which case is the reading of the dynamometer recorded by us correct? 1) (4.3 ± 0.1) N 2) (4.3 ± 0.2) N 3) (4.6 ± 0.1) N 4) (4.3 ± 0.3) N 62. B 23 No. 6127. Using an oscilloscope, a student studied forced oscillations in an oscillatory circuit consisting of a wire coil connected in series, a capacitor and a resistor with a small resistance. The inductance of the coil is 5 mH. The figure shows the view of the oscilloscope screen when its probes are connected to the capacitor terminals for the case of resonance. The figure also shows the oscilloscope switch, which allows you to change the image scale along the horizontal axis: by turning this switch, you can set what period of time corresponds to one division of the oscilloscope screen. Determine what is the capacitance of the user in the oscillating circuit condensed with a tora? 1) 20 uF 2) ≈ 64 mF 3) ≈ 80 uF 4) 80 F . The capacitance of the capacitor is 16 microfarads. The figure shows the view of the oscilloscope screen when its probes are connected to the capacitor terminals for the case of resonance. The figure also shows the oscilloscope switch, which allows you to change the image scale along the horizontal axis: by turning this switch, you can set what period of time corresponds to one division of the oscilloscope screen. Determine what is the inductance of the coil used in the oscillating circuit. 1) 1 H 2) 25 mH 3) 0.17 H 4) 64 μH 64. B 23 No. 6206. Various wires are made from the same material. Which pair of wires should be chosen in order to experimentally verify the dependence of the resistance of the wire on its length? 1) 1 2) 2 3) 3 4) 4 65. B 23 No. 6241. It is necessary to experimentally detect the dependence of the oscillation period of a spring pendulum on the mass of the load. What pair of pendulums should be used for this purpose? 1) A and D 2) only B 3) only C 4) only D Which pair of pendulums should be used for this test? 1) 1 2) 2 3) 3 4) 4 67. B 23 No. 6314. It is necessary to experimentally find out the dependence of the period of small oscillations of a mathematical pendulum on the substance from which the load is made. What pair of pendulums can be taken for this purpose? Pendulum weights - hollow balls made of copper and aluminum of the same mass and the same outer diameter. 1) 1 2) 2 3) 3 4) 4 68. B 23 No. 6350. To perform laboratory work, the student was given a dynamometer, a load of unknown density and a beaker with water. Unfortunately, the scale division was not indicated on the dynamometer. Using the sketches of the experiment, determine the value of the division of the diameter scale per millimeter. 1) 0.1 N 2) 0.2 N 3) 0.4 N 4) 0.5 N Unfortunately, the scale division was not indicated on the beaker. Using sketches of the course of the experiment, determine the price of division of the scale of the change from the lesson. 1) 200 ml 2) 250 ml 3) 400 ml 4) 500 ml

On our website, you can prepare well for passing the exam in physics, because every week new options for tasks appear on our website.

1. The figure shows a graph of the bus movement along a straight road along the X axis. Determine the projection of the bus speed on the X axis in the time interval from 0 to 30 minutes.

Answer: _____ km/h

2.In an inertial frame of reference, the force ⇀ F

Tells a body of mass m acceleration, modulo 2 m/s 2 . What is the acceleration modulus of a body with mass m2 under force 2 ⇀ F

in this frame of reference?

Answer: _____ m/s 2

3. On a trolley with a mass of 50 kg, rolling along the track at a speed of 0.8 m / s, 200 kg of sand are poured on top. Determine the speed of the trolley after loading

Answer: _____

4. What is the weight of a person in the air, taking into account the action of the force of Archimedes? The volume of a person V \u003d 50 dm 3, the density of the human body is 1036 kg / m 3. Air density 1.2 kg/m 3 .

Answer: _____ N

5. The figure shows graphs of the dependence of coordinates on time for two bodies: A and B, moving in a straight line, along which the X axis is directed. Choose two correct statements about the movement of bodies.

1. The time interval between the meetings of bodies A and B is 6 s.

2. Body A moves at a speed of 3 m/s.

3. Body A moves with uniform acceleration.

4. For the first 5 s, body A has traveled 15 m.

5. Body B moves with constant acceleration.

Answer:_____;

6. The load of the spring pendulum shown in the figure makes harmonic oscillations between points 1 and 3. How do the potential energy of the pendulum spring and the speed of the load change when the pendulum load moves from point 3 to point 2?

1. increases

2. decreases

3. does not change

7. A puck of mass m slides down a hill from a state of rest. The free fall acceleration is g. At the foot of the hill, the kinetic energy of the puck is equal to E k. The friction of the puck on the hill is negligible. Establish a correspondence between physical quantities and formulas by which they can be calculated. For each position of the first column, select the corresponding position of the second and write down the selected numbers under the corresponding letters.

PHYSICAL QUANTITY

A) hill height

B) the momentum module of the puck at the foot of the hill

1) Ek√ 2 mg

2) √ 2 mEk

3) √ 2 Ekgm

4) Ekgm

Answer:____;

8. There is an ideal gas in the vessel under the piston. The gas pressure is 100 kPa. At constant temperature, the volume of the gas was increased by 4 times. Determine the pressure of the gas in the final state.

Answer: _____ kPa.

9. Gas is transferred from state 1 to state 3 as shown in the p-V diagram. What is the work done by the gas in the process 1-2-3, if p 0 \u003d 50 kPa, V 0 \u003d 2 l?

Answer: _____ J.

10. How much heat does a cast-iron part weighing 10 kg give off when its temperature drops by 20 K?

Specific heat capacity of cast iron C= DwellToGOWITH

Answer: _____ kJ.

11. The dependence of the volume of the constant mass of an ideal gas on temperature is shown in the V-T diagram (see figure). Choose two correct statements about the process that occurs with the gas.

1. The gas pressure is at its minimum in state A.

2. During the transition from state D to state A, the internal energy decreases.

3. During the transition from state B to state C, the work done by the gas is negative all the time.

4. The pressure of the gas in state C is greater than the pressure of the gas in state A.

5. The pressure of the gas in state D is greater than the pressure of the gas in state A.

Answer:____;

12. Figures A and B show graphs of two processes 1-2 and 3-4, each of which is performed by one mole of argon. Graphs are plotted in p-V and V-T coordinates, where p is pressure, V is volume and T is the absolute temperature of the gas. Establish a correspondence between the graphs and statements that characterize the processes depicted on the graphs.

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

STATEMENTS

1) The internal energy of the gas decreases, while the gas gives off heat.

2) Work is done on the gas, while the gas gives off heat.

3) The gas receives heat but does no work.

4) The gas receives heat and does work.

13. The same currents I flow through three thin long straight parallel conductors (see figure). How is the Ampere force directed on the conductor 3 from the other two (up, down, left, right, from the observer, to the observer)? The distances between adjacent conductors are the same. Write your answer in word(s).

Answer: _____

14. The figure shows a section of the electrical circuit. What is the ratio of the amounts of heat Q 1 /Q 2 released on the resistors R 1 and R 2 at the same time?

Answer: _____

16. A beam of light falls on a flat mirror. The angle between the incident beam and the mirror is 30°. Determine the angle between the incident and reflected rays.

Answer: _____ °.

16. Two uncharged glass cubes 1 and 2 are brought close together and placed in an electric field, the intensity of which is directed horizontally to the right, as shown in the upper part of the figure. Then the cubes were moved apart and only then the electric field was removed (lower part of the figure). Choose from the proposed list two statements that correspond to the results of the experimental studies, and indicate their numbers.

1. After the cubes were moved apart, the charge of the first cube turned out to be negative, the charge of the second one was positive.

2. After being placed in an electric field, the electrons from the first cube began to pass into the second one.

3. After the cubes were moved apart, the charges of both cubes remained equal to zero.

4. Before the separation of the cubes in the electric field, the left surface of the 1st cube was negatively charged.

5. Before the separation of the cubes in the electric field, the right surface of the 2nd cube was negatively charged.

Answer:_____;

17. How will the frequency of natural oscillations and the maximum current strength in the coil of the oscillatory circuit (see figure) change if the key K is moved from position 1 to position 2 at the moment when the capacitor charge is 0?

1. increase

2. decrease

3. will not change

18. Establish a correspondence between the resistance of a section of a DC circuit and a schematic representation of this section of the circuit. The resistances of all resistors in the figures are the same and equal to R.

SECTION RESISTANCE

DC SECTION

Answer:_____;

19. What is the number of protons and neutrons in the nitrogen isotope 14 7 N?

20. Half-life of sodium isotope 22 11 Na

equals 2.6 years. Initially, there were 208 g of this isotope. How much will it be in 5.2 years?

Answer: ______

21. For some atoms, a characteristic feature is the possibility of capturing by the atomic nucleus one of the electrons closest to it. How do the mass number and charge of the nucleus change in this case?

For each value, determine the appropriate nature of the change:

1. increases

2. decreases

3. does not change

Write down the selected numbers for each physical quantity. Numbers in the answer may be repeated.

Introduction

Section 1. Fluctuations

1 Periodic oscillations

Section 2. Physical pendulum

1 Basic formulas

3 Friction pendulum Froud

Introduction

Studying the phenomenon, we simultaneously get acquainted with the properties of the object and learn how to apply them in technology and in everyday life. As an example, let us turn to an oscillating filament pendulum. Any phenomenon is "usually" peeped in nature, but can be predicted theoretically, or accidentally discovered when studying another. Even Galileo drew attention to the vibrations of the chandelier in the cathedral and "there was something in this pendulum that made it stop." However, observations have a major drawback, they are passive. In order to stop depending on nature, it is necessary to build an experimental setup. Now we can reproduce the phenomenon at any time. But what is the purpose of our experiments with the same filament pendulum? Man took a lot from "our smaller brothers" and therefore one can imagine what experiments an ordinary monkey would have carried out with a thread pendulum. She would have tasted it, sniffed it, pulled the string, and lost all interest in it. Nature taught her to study the properties of objects very quickly. Edible, inedible, tasty, tasteless - this is a short list of the properties that the monkey has studied. However, the man went further. He discovered such an important property as periodicity, which can be measured. Any measurable property of an object is called a physical quantity. No mechanic in the world knows all the laws of mechanics! Is it possible to single out the main laws by means of theoretical analysis or the same experiments? Those who managed to do this forever inscribed their name in the history of science.

In my work, I would like to study the properties of physical pendulums, to determine to what extent the already studied properties can be applied in practice, in people's lives, in science, and can be used as a method for studying physical phenomena in other areas of this science.

Section 1. Fluctuations

Oscillations are one of the most common processes in nature and technology. High-rise buildings and high-voltage wires oscillate under the influence of the wind, the pendulum of a wound clock and a car on springs during movement, the level of the river during the year and the temperature of the human body during illness.

One has to deal with oscillatory systems not only in various machines and mechanisms, the term "pendulum" is widely used in application to systems of various nature. So, an electric pendulum is called a circuit consisting of a capacitor and an inductor, a chemical pendulum is a mixture of chemicals that enter into an oscillatory reaction, an ecological pendulum is two interacting populations of predators and prey. The same term is applied to economic systems in which oscillatory processes take place. We also know that most sources of sound are oscillatory systems, that the propagation of sound in air is possible only because the air itself is a kind of oscillatory system. Moreover, in addition to mechanical oscillatory systems, there are electromagnetic oscillatory systems in which electrical oscillations can occur, which form the basis of all radio engineering. Finally, there are a lot of mixed - electromechanical - oscillatory systems used in a wide variety of technical fields.

We see that sound is fluctuations in the density and pressure of air, radio waves are periodic changes in the strength of electric and magnetic fields, visible light is also electromagnetic vibrations, only with slightly different wavelengths and frequencies. Earthquakes - soil vibrations, ebbs and flows - changes in the level of the seas and oceans, caused by the attraction of the moon and reaching 18 meters in some areas, pulse beats - periodic contractions of the human heart muscle, etc. Change of wakefulness and sleep, work and rest, winter and summer. Even our everyday going to work and returning home falls under the definition of fluctuations, which are interpreted as processes that repeat exactly or approximately at regular intervals.

So, vibrations are mechanical, electromagnetic, chemical, thermodynamic and various others. Despite this diversity, they all have much in common and are therefore described by the same differential equations. A special section of physics - the theory of oscillations - deals with the study of the laws of these phenomena. Shipbuilders and aircraft builders, industry and transport specialists, creators of radio engineering and acoustic equipment need to know them.

Any fluctuations are characterized by amplitude - the largest deviation of a certain value from its zero value, period (T) or frequency (v). The last two quantities are interconnected by an inversely proportional relationship: T=1/v. The oscillation frequency is expressed in hertz (Hz). The unit of measurement is named after the famous German physicist Heinrich Hertz (1857-1894). 1Hz is one cycle per second. This is the rate at which the human heart beats. The word "hertz" in German means "heart". If desired, this coincidence can be seen as a kind of symbolic connection.

The first scientists who studied oscillations were Galileo Galilei (1564...1642) and Christian Huygens (1629...1692). Galileo established isochronism (independence of the period from the amplitude) of small oscillations, watching the swinging of the chandelier in the cathedral and measuring the time by the beats of the pulse on his hand. Huygens invented the first clock with a pendulum (1657) and in the second edition of his monograph "Pendulum Clock" (1673) investigated a number of problems associated with the movement of the pendulum, in particular, found the center of swing of a physical pendulum. A great contribution to the study of oscillations was made by many scientists: English - W. Thomson (Lord Kelvin) and J. Rayleigh<#"justify">.1 Periodic vibrations

Among the various mechanical movements and oscillations that take place around us, repetitive movements are often encountered. Any uniform rotation is a repetitive movement: with each revolution, any point of a uniformly rotating body passes the same positions as during the previous revolution, and in the same sequence and at the same speeds. If we look at how the branches and trunks of trees sway in the wind, how a ship sways on the waves, how the pendulum of a clock moves, how the pistons and connecting rods of a steam engine or diesel engine move back and forth, how the needle of a sewing machine jumps up and down; if we observe the alternation of the ebb and flow of the sea, the rearrangement of the legs and the waving of the arms when walking and running, the beating of the heart or the pulse, then in all these movements we will notice the same feature - the repeated repetition of the same cycle of movements.

In reality, repetition is not always and under all conditions exactly the same. In some cases, each new cycle very accurately repeats the previous one (swinging of a pendulum, movements of parts of a machine operating at a constant speed), in other cases, the difference between successive cycles can be noticeable (ebb and flow, swinging branches, movements of machine parts during its operation). start or stop). Deviations from an absolutely exact repetition are very often so small that they can be neglected and the motion can be considered as repeating quite exactly, i.e., it can be considered periodic.

Periodic is a repetitive movement in which each cycle exactly reproduces any other cycle. The duration of one cycle is called a period. The period of oscillation of a physical pendulum depends on many circumstances: on the size and shape of the body, on the distance between the center of gravity and the point of suspension, and on the distribution of body mass relative to this point.

Section 2. Physical pendulum

1 Basic formulas

A physical pendulum is a rigid body that can swing around a fixed axis. Consider small oscillations of the pendulum. The position of the body at any moment of time can be characterized by the angle of its deviation from the equilibrium position (Fig. 2.1).

We write the equation of moments about the axis of rotation OZ (axis OZ passes through the suspension point O perpendicular to the plane of the figure "from us"), neglecting the moment of friction forces if the moment of inertia of the body is known

Here is the moment of inertia of the pendulum about the axis OZ,

The angular velocity of the pendulum,

Mz=- - moment of gravity relative to the OZ axis,

a is the distance from the center of gravity of the body C to the axis of rotation.

If we assume that during rotation, for example, counterclockwise, the angle increases, then the moment of gravity causes a decrease in this angle and, therefore, at the moment Mz<0. Это и отражает знак минус в правой части (1)

Considering that and, taking into account the smallness of oscillations, we rewrite equation (1) in the form:

(we took into account that for small fluctuations, where the angle is expressed in radians). Equation (2) describes harmonic oscillations with a cyclic frequency and period

A special case of a physical pendulum is a mathematical pendulum. The entire mass of the mathematical pendulum is practically concentrated at one point - the center of inertia of the pendulum C. An example of a mathematical pendulum is a small massive ball suspended on a long light inextensible thread. In the case of a mathematical pendulum, a = l, where l is the length of the thread, and formula (3) goes into the well-known formula

Comparing formulas (3) and (4), we conclude that the period of oscillation of a physical pendulum is equal to the period of oscillation of a mathematical pendulum with length l, called the reduced length of the physical pendulum:

Oscillation period of a physical pendulum<#"5" height="11" src="doc_zip19.jpg" />) depends nonmonotonically on the distance. This is easy to see if, in accordance with the Huygens-Steiner theorem, the moment of inertia is expressed in terms of the moment of inertia about a parallel horizontal axis passing through the center of mass: Then the oscillation period will be equal to:

The change in the oscillation period when the axis of rotation is removed from the center of mass O in both directions by a distance a is shown in Fig. 2.2.

2 Kinematics of pendulum oscillations

A pendulum is any body suspended so that its center of gravity is below the point of suspension. A hammer hanging on a nail, scales, a load on a rope - all these are oscillatory systems, similar to the pendulum of a wall clock (Fig. 2.3).

Any system capable of performing free oscillations has a stable equilibrium position. For a pendulum, this is the position at which the center of gravity is on the vertical below the suspension point. If we take the pendulum out of this position or push it, then it will begin to oscillate, deviating either in one direction or the other from the equilibrium position. The largest deviation from the equilibrium position, to which the pendulum reaches, is called the amplitude of oscillation. The amplitude is determined by the initial deflection or push with which the pendulum was set in motion. This property - the dependence of the amplitude on the conditions at the beginning of the movement - is characteristic not only for the free oscillations of the pendulum, but in general for the free oscillations of very many oscillatory systems.

If we attach a hair to the pendulum - a piece of thin wire or an elastic nylon thread - and we move a smoked glass plate under this hair, as shown in Fig. 2.3. If you move the plate at a constant speed in a direction perpendicular to the plane of oscillation, then the hair will draw a wavy line on the plate (Fig. 2.4). In this experiment we have the simplest oscilloscope - this is the name of the instruments for recording oscillations. The traces that an oscilloscope records are called waveforms. Thus, fig. 2.2.3. is an oscillogram of pendulum oscillations. The oscillation amplitude is depicted on this oscillogram by the segment AB, which gives the greatest deviation of the wavy curve from the straight line ab, which the hair would draw on the plate with the pendulum stationary (resting in the equilibrium position). The period is represented by a segment CD, equal to the distance that the plate moves during the period of the pendulum.

Recording the oscillations of a pendulum on a sooty plate

Oscillogram of pendulum oscillations: AB - amplitude, CD - period

Since we are moving the smoked plate uniformly, any movement of it is proportional to the time during which it took place. We can therefore say that along the straight line ab, on a certain scale (depending on the speed of the plate), time is plotted. On the other hand, in the direction perpendicular to ab, the hair marks on the plate the distances of the end of the pendulum from its equilibrium position, i.e. the distance traveled by the end of the pendulum from this position. Thus, the oscillogram is nothing more than a motion graph - a graph of the path versus time.

As we know, the slope of the line on such a graph represents the speed of movement. The pendulum passes through the equilibrium position with the greatest speed. Accordingly, the slope of the wavy line in Fig. 2.2.3. greatest at those points where it intersects the line ab. On the contrary, at the moments of the greatest deviations the speed of the pendulum is equal to zero. Accordingly, the wavy line in Fig. 4 at those points where it is furthest from ab has a tangent parallel to ab, i.e., a slope equal to zero.

3 Dynamics of pendulum oscillations

The pendulums shown in fig. 2.6 are extended bodies of various shapes and sizes, oscillating around a suspension or support point. Such systems are called physical pendulums. In a state of equilibrium, when the center of gravity is on the vertical below the point of suspension (or support), the force of gravity is balanced (through the elastic forces of the deformed pendulum) by the reaction of the support. When deviating from the equilibrium position, gravity and elastic forces determine the angular acceleration of the pendulum at each moment of time, i.e. determine the nature of its movement (oscillation). Let us now consider the dynamics of oscillations in more detail using the simplest example of the so-called mathematical pendulum, which is a small weight suspended on a long thin thread.

In a mathematical pendulum, we can neglect the mass of the thread and the deformation of the weight, i.e. we can assume that the mass of the pendulum is concentrated in the weight, and the elastic forces are concentrated in the thread, which is considered inextensible. Let us now look under the influence of what forces our pendulum oscillates after it is brought out of equilibrium in some way (by push, deflection). The restoring force P1 when the pendulum deviates from the equilibrium position.

Figure 2.6

When the pendulum is at rest in the equilibrium position, the force of gravity acting on its weight and directed vertically downwards is balanced by the tension in the thread. In the deflected position (Fig. 2.6), the force of gravity P acts at an angle to the tension force F, directed along the thread. Let us decompose the force of gravity into two components: in the direction of the thread (P2) and perpendicular to it (P1). When the pendulum oscillates, the tension force of the thread F slightly exceeds the component P2 - by the value of the centripetal force, which causes the load to move in an arc. The component P1 is always directed towards the equilibrium position; she seems to be striving to restore this position. Therefore, it is often called the restoring force. Modulo P1, the more, the more the pendulum is deflected.

So, as soon as the pendulum during its oscillations begins to deviate from the equilibrium position, say, to the right, a force P1 appears that slows down its movement the more it is deflected. Ultimately, this force will stop him and drag him back to the equilibrium position. However, as we approach this position, the force P1 will become less and less and will turn to zero in the equilibrium position itself. Thus, the pendulum passes through the equilibrium position by inertia. As soon as it starts to deviate to the left, the force P1, growing with increasing deviation, will again appear, but now directed to the right. The movement to the left will again slow down, then the pendulum will stop for a moment, after which the accelerated movement to the right will begin, etc.

What happens to the energy of a pendulum as it swings?

Twice during the period - at the largest deviations to the left and to the right - the pendulum stops, i.e. at these moments, the speed is zero, which means that the kinetic energy is also zero. But it is precisely at these moments that the center of gravity of the pendulum is raised to the greatest height and, consequently, the potential energy is greatest. On the contrary, at the moments of passage through the equilibrium position, the potential energy is the smallest, and the speed and kinetic energy reach the maximum value.

We assume that the forces of friction of the pendulum on the air and the friction at the point of suspension can be neglected. Then, according to the law of conservation of energy, this maximum kinetic energy is exactly equal to the excess of potential energy in the position of greatest deviation over the potential energy in the equilibrium position.

So, when the pendulum oscillates, a periodic transition of kinetic energy into potential energy and vice versa occurs, and the period of this process is half as long as the period of oscillation of the pendulum itself. However, the total energy of the pendulum (the sum of potential and kinetic energies) is constant all the time. It is equal to the energy that was imparted to the pendulum at the start, no matter whether it is in the form of potential energy (initial deflection) or in the form of kinetic energy (initial push).

This is the case for all vibrations in the absence of friction or any other processes that take energy from the oscillating system or impart energy to it. That is why the amplitude remains unchanged and is determined by the initial deviation or the force of the push.

We get the same changes in the restoring force P1 and the same transition of energy if, instead of hanging the ball on a thread, we make it roll in a vertical plane in a spherical cup or in a trough curved around the circumference. In this case, the role of the thread tension will be assumed by the pressure of the walls of the cup or trough (again, we neglect the friction of the ball against the walls and air).

Section 3. Properties of a physical pendulum

1 Using a pendulum in clocks

The study of the properties of the pendulum has taken root in the deep distance. The first devices to use these properties were watches. The period of oscillations (rotations) practically does not change. If at first the oscillations occur with a very large deviation, say 80 ° from the vertical, then with damping of oscillations up to 60 ° , 40° , 20 ° the period will decrease by only a few percent, with a decrease in deviations from 20 ° to barely noticeable, it will change by less than 1%. For deviations less than 5 ° the period will remain unchanged with an accuracy of 0.05% This property of the independence of the pendulum from the amplitude, called isochronism, formed the basis of the mechanism.

The oldest spindle pendulum appeared in the 14th century. It had the form of a rocker arm with movable adjusting weights. It was planted on a shaft (spindle) with two pallets (plates at the ends). The pallets entered in turn between the teeth of the escape wheel, which was spun by a descending weight. Rotating, it pressed a tooth on the upper pallet and turned the spindle half a turn. The lower one got stuck between two teeth and slowed down the wheel. Then the cycle was repeated.

The spindle pendulum was replaced by an anchor mechanism, which in its appearance resembled an anchor. It serves as a link between the pendulum (balancer) and the escape wheel. In 1675, Huylens proposed a torsion pendulum - a balancer with a spiral - as a regulator of oscillations. The Guilens system is still used in wristwatches and mechanical table clocks. Balancer - a wheel to which a thin spiral spring (hair) is attached. Turning, the balancer shakes the anchor. Synthetic ruby ​​anchor pallets alternate between the teeth of the escape wheel. During one swing period of the balancer, the wheel rotates by the width of one tooth. At the same time, it pushes the anchor bracket and, turning, twists the balancer.

In the middle of the 17th century, the minute and second hands appeared, which immediately affected the accuracy of the watch. The reason for this is the material of the pendulum (spiral), which, expanding and contracting with an increase or decrease in temperature, oscillates at different frequencies. This leads to errors in timing. Therefore, scientists have invented a special material that is resistant to temperature changes - invar (an alloy of iron and nickel). With its use, the error per day does not exceed half a second.

In the 30s of the 19th century, the first attempts to create a compact watch were presented, but they did not appear until a century later. The first electromechanical clock was invented. An electric current passed through the contacts, controlling the pendulum and moving the arrows. With the advent of compact batteries, the world saw electric watches, which in their structure had a balancer, and their electrical circuit was closed by mechanical contacts, more advanced models were watches on semiconductor and integrated circuits. A little later, electromechanical watches appeared with quartz oscillators as oscillatory systems, the error of which was less than two seconds per day!

Another step forward was fully electronic watches. The main components are an electronic circuit, digital indicators on liquid crystals. These are miniature specialized electronic computing devices (generator, dividers, shapers, multipliers of electronic oscillations).

Separately, I would like to say about the astronomical clock, which is used in observing the heavenly bodies and keeping time. Their error is only 0.000000001 seconds per day. Molecular clocks, which are based on the ability of some molecules to absorb electromagnetic vibrations of a strictly defined frequency (for example, cesium atoms 1c for 10,000 years), have an even smaller error. But quantum clocks can boast of super accuracy, where electromagnetic oscillations of a hydrogen quantum generator are used and make up an error of 1 s in 100,000 years.

It is interesting to consider the two most striking varieties of pendulums, which separately went down in history, bear the names of their discoverers and are naturally famous precisely because they have amazing properties.

On January 3, 1851, Jean Bernard Léon Foucault conducted a successful experiment with the pendulum, which later received his name. For the experiment, the Paris Pantheon was chosen, since it was possible to strengthen the thread of the pendulum 67 meters long in it. At the end of a steel wire thread, a cast-iron ball weighing 28 kilograms was reinforced. Before launch, the ball was taken aside and tied with a thin string encircling the ball along the equator. A round platform was made under the pendulum, along the edge of which a roller of sand was poured. One complete oscillation of the pendulum lasted 16 seconds, and with each swing, the tip attached under the ball of the pendulum drew a new line on the sand, clearly showing the rotation of the platform under it, and, consequently, of the entire Earth.

The experiment is based on the property of the pendulum to maintain the plane of oscillation, regardless of the rotation of the support to which the pendulum is suspended. An observer rotating with the Earth sees a gradual change in the direction of the swing of the pendulum relative to the surrounding terrestrial objects.

In the practical implementation of the experiment with the Foucault pendulum, it is important to eliminate the causes that violate its free swing. To do this, they make it very long, with a heavy and symmetrical load at the end. The pendulum must have the same ability to swing in all directions, be well protected from the wind. The pendulum is fixed either on a cardan joint or on a horizontal ball bearing that rotates along with the swing plane of the pendulum. Of great importance for the results of the experiment is the launch of the pendulum without a lateral push. At the first public demonstration of Foucault's experience in the Pantheon, it was for this that the pendulum was tied with twine. When the pendulum, after tying, came to a state of complete rest, the rope was burned out and it began to move.

Since the pendulum in the Pantheon made one complete oscillation in 16.4 seconds, it soon became clear that the plane of swing of the pendulum rotated clockwise relative to the floor. With each subsequent swing, the metal tip swept sand about 3 mm by 1 ° from the previous location. In an hour, the rocking plane turned more than 11 ° , in about 32 hours, made a complete revolution and returned to its previous position. This impressive demonstration drove the audience downright into hysterics; it seemed to them that they felt the rotation of the Earth under their feet.

To find out why the pendulum behaves in this way, consider a sand ring. North Point 51 ° the ring is 3 m from the center, and given that the Pantheon is located at 48 north latitude, this part of the ring is 2.3 m closer to the earth's axis than the center. within 24 hours the northern edge of the ring will be closer. Therefore, when the Earth rotates 360 ° it will move in a circle with a smaller radius than the center, and will cover 14.42 m less per day. Therefore, the difference in the velocities of these points is 1 cm/min. Similarly, the southern edge of the ring is moving 14.42 meters per day, or 1 cm/min, faster than the center of the ring. Due to this speed difference, the line connecting the northern and southern points of the ring always remains directed from north to south. At the earth's equator, the northern and southern ends of such a small space would be at the same distance from the earth's axis and, therefore, moving at the same speed. Therefore, the surface of the Earth would not revolve around a vertical column standing at the equator, and Foucault's pendulum would swing along the same line. The rotation speed of the swing plane would be zero, and the time for a complete revolution would be infinitely long. If the pendulum were set exactly at one of the geographic poles, then it would turn out that the swing plane rotates in 24 hours. (A surface of 1 ° every hour and makes a complete rotation of 360 ° exactly 15 m per day around the earth's axis.). At 360 latitudes, the Foucault effect manifests itself to varying degrees, while its effect becomes more evident as it approaches the poles.

The longest thread - 98 meters - was at the Foucault pendulum, located in St. Isaac's Cathedral in St. Petersburg. The pendulum was removed in 1992, as it did not correspond to the purpose of the building. Now in the north-west of Russia there is only one Foucault pendulum - in the St. Petersburg Planetarium. The length of its thread is small - about 8 meters, but this does not reduce the degree of visibility. This exhibit of the Planetarium is of constant interest to visitors of all ages.

The Foucault Pendulum, currently located in the visitors' lobby of the United Nations General Assembly Building in New York, is a gift from the government of the Netherlands. This pendulum is a 200-pound, 12-inch-diameter, gold-plated ball, partially filled with copper, suspended from a stainless steel wire from the ceiling above a ceremonial staircase 75 feet from the floor. The upper end of the wire is fixed with a universal joint, which allows the pendulum to swing freely in any vertical plane. With each oscillation, the ball passes over an embossed metal ring with an electromagnet, as a result of which an electric current is induced in the copper inside the ball. This interaction provides the necessary energy to overcome friction and air resistance and ensures that the pendulum swings evenly.

3 Friction pendulum Froud

There is a physical pendulum located on a rotating shaft. The friction force between the shaft and the pendulum decreases with increasing relative speed.

If the pendulum moves in the direction of rotation and its speed is less than the speed of the shaft, then a sufficiently large moment of friction force acts on it from the side of the shaft, pushing the pendulum. When moving in the opposite direction, the speed of the pendulum relative to the shaft is large, so the moment of friction is small. So the self-oscillating system itself regulates the flow of energy to the oscillator.

The pendulum oscillates relative to the new equilibrium position, shifted towards the rotation of the shaft, and its speed in the steady state does not exceed the speed of the shaft. You can change the initial conditions, for example, set the initial speed of the pendulum to be greater than the shaft rotation speed. In this case, oscillations with the same amplitude will be established after some time, and the phase curve will tend to the same attractor.

4 Relationship between period and pendulum length

Are there relationships between quantities? Any relationship between quantities, expressed mathematically in the form of a table, graph or formula, is called a physical law. We are trying to establish a connection between the period and the length of the pendulum. For this, a table is usually compiled (Table 3.1), in which the results of the experiments are entered.

Table 3.1.

M00.250,50,751T, s011,41,72

The table clearly shows that with increasing length of the pendulum, its period of oscillation increases. It is even clearer to present this table in the form of a graph (Fig. 3.1), but it is even better to express it approximately in the form of a formula: T? 2. The formula-law makes it possible to quickly calculate the period of oscillation of a thread pendulum, and this is its beauty. But this is not only the main value of the law. Now you can change the period of oscillation and, therefore, adjust the course of the clock so that it shows the exact time. All other laws of oscillation of a threaded pendulum have also found application in the clocks already described above, and in other technical devices.

Figure 3.1

Having studied this topic, I determined the main properties of the pendulum. The main and most used is the isochronism (from the Greek - “uniform”) of the pendulum movement at small amplitudes, that is, the independence of the oscillation period from the amplitude. When the amplitude is doubled, the period of the pendulum remains unchanged, although the weight travels twice as far. But still, the period of oscillation of a physical pendulum is affected by the size and shape of the body, the distance between the center of gravity and the point of suspension, the distribution of body mass relative to this point.

With an increase in the length of the pendulum, the period of its oscillations also increases; the clock mechanism and the construction of a number of other technical devices are based on this property. The pendulum is widely used in applications to systems of various nature. For example, an electric pendulum is a circuit consisting of a capacitor and an inductor, an ecological pendulum is two interacting populations of predators and prey.

Any uniform rotation is a repetitive movement (periodic): with each revolution, we can observe how any point of a uniformly rotating body passes the same positions as during the previous revolution, and with the same sequence.

When the pendulum oscillates, a periodic transition of kinetic energy into potential energy and vice versa occurs, and the period of this entire process is half as long as the period of oscillation of the pendulum itself. But when finding the sum of potential and kinetic energies, its constancy becomes noticeable. It is equal to the energy that was imparted to the pendulum at the start, no matter whether it is in the form of potential energy (initial deflection) or in the form of kinetic energy (initial push).

For any physical pendulum, one can find such positions of lentils and prisms at which the pendulum will oscillate with the same period. This fact is the basis of the theory of a revolving pendulum, which measures the acceleration of free fall. Another important factor is that when measuring in this way, it is not necessary to determine the position of the center of mass, which greatly increases the accuracy of measurements. To this end, it is necessary to measure the dependence of the period of oscillation of the pendulum on the position of the axis of rotation and, from this experimental dependence, find the reduced length. The length thus determined, combined with the period of oscillation about both axes measured with good accuracy, makes it possible to calculate the acceleration due to gravity. Also, with the help of pendulums and their mathematical models, the phenomena inherent in nonlinear oscillatory systems, which are particularly complex, are demonstrated.

Two wonderful pendulums have interesting properties: the Foucault pendulum and the Froud friction pendulum. The first one is based on the ability to maintain the plane of oscillation regardless of the rotation of the support to which the pendulum is suspended. An observer rotating with the Earth sees a gradual change in the direction of the swing of the pendulum relative to the surrounding terrestrial objects. The second is located on a rotating shaft. If the pendulum moves in the direction of rotation and its speed is less than the speed of the shaft, then a sufficiently large moment of friction force acts on it from the side of the shaft, pushing the pendulum. When moving in the opposite direction, the speed of the pendulum relative to the shaft is large, so the moment of friction is small. So the self-oscillating system itself regulates the flow of energy to the oscillator.

Based on the study of the dependence of the oscillation period of the bottle on the observation time and the change in the mass of the substance in it, it can be safely asserted that with oscillation amplitudes not exceeding 1 cm, the moment of inertia of the physical pendulum does not affect the period of its oscillation.

So, summing up all of the above, it can be argued that the properties of a physical pendulum and oscillatory systems, in general, are used in very many areas of a diverse nature, and note, both by themselves and as part of a single whole, and as a method either method of research or conducting a series of experiments.

kinematics physical pendulum oscillation

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Lishevsky V. Science and life, 1988, No. 1.

Malinetsky G.G., Potapov A.B., Podlazov A.V. Nonlinear Dynamics: Approaches, Results, Hopes. - M.: URSS, 2006.

Malov N.N. Fundamentals of the theory of oscillations. - Moscow, "Enlightenment", 1971.

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The answers to tasks 1-24 are a word, a number, or a sequence of numbers or numbers. Write your answer in the appropriate field on the right. Write each character without spaces. Units of measurement of physical quantities do not need to be written.

1

The figure shows a graph of the bus movement along a straight road along the X axis. Determine the projection of the bus speed on the X axis in the time interval from 0 to 30 minutes.

Answer: _____ km/h

2

In the inertial frame of reference, the force \overset\rightharpoonup F informs a body of mass m an acceleration equal in modulus to 2 m/s 2 . What is the modulus of acceleration of a body with mass \frac m2 under the action of a force 2\overset\rightharpoonup F in this frame of reference?

Answer: _____ m/s 2

3

On a trolley with a mass of 50 kg, rolling along the track at a speed of 0.8 m / s, 200 kg of sand are poured on top. Determine the speed of the trolley after loading

Answer: _____

4

What is the weight of a person in the air, taking into account the action of the Archimedes force? The volume of a person V \u003d 50 dm 3, the density of the human body is 1036 kg / m 3. Air density 1.2 kg/m 3 .

Answer: _____ N

5

The figure shows graphs of the dependence of coordinates on time for two bodies: A and B, moving in a straight line, along which the X axis is directed. Choose two correct statements about the movement of bodies.

1. The time interval between the meetings of bodies A and B is 6 s.

2. Body A moves at a speed of 3 m/s.

3. Body A moves with uniform acceleration.

4. For the first 5 s, body A has traveled 15 m.

5. Body B moves with constant acceleration.

6

The load of the spring pendulum shown in the figure performs harmonic oscillations between points 1 and 3. How do the potential energy of the pendulum spring and the speed of the load change when the pendulum load moves from point 3 to point 2?

1. increases

2. decreases

3. does not change

7

A puck of mass m slides down a hill from rest. The free fall acceleration is g. At the foot of the hill, the kinetic energy of the puck is equal to E k. The friction of the puck on the hill is negligible. Establish a correspondence between physical quantities and formulas by which they can be calculated. For each position of the first column, select the corresponding position of the second and write down the selected numbers under the corresponding letters.

PHYSICAL QUANTITY

A) hill height

B) the momentum module of the puck at the foot of the hill

1) E_k\sqrt(\frac(2m)g)

2) \sqrt(2mE_k)

3) \sqrt(\frac(2E_k)(gm))

4) \frac(E_k)(gm)

8

An ideal gas is contained in a vessel under a piston. The gas pressure is 100 kPa. At constant temperature, the volume of the gas was increased by 4 times. Determine the pressure of the gas in the final state.

Answer: _____ kPa.

9

The gas is transferred from state 1 to state 3 as shown in the p-V diagram. What is the work done by the gas in the process 1-2-3, if p 0 \u003d 50 kPa, V 0 \u003d 2 l?

Answer: _____ J.

10

How much heat is given off by a 10 kg cast-iron part when its temperature is lowered by 20 K?

Specific heat capacity of cast iron C=500\frac(J)(kg^\circ C)

Answer: _____ kJ.

11

The dependence of the volume of a constant mass of an ideal gas on temperature is shown in the V-T diagram (see figure). Choose two correct statements about the process that occurs with the gas.

1. The gas pressure is at its minimum in state A.

2. During the transition from state D to state A, the internal energy decreases.

3. During the transition from state B to state C, the work done by the gas is negative all the time.

4. The pressure of the gas in state C is greater than the pressure of the gas in state A.

5. The pressure of the gas in state D is greater than the pressure of the gas in state A.

12

Figures A and B show graphs of two processes 1-2 and 3-4, each of which is performed by one mole of argon. Graphs are plotted in p-V and V-T coordinates, where p is pressure, V is volume and T is the absolute temperature of the gas. Establish a correspondence between the graphs and statements that characterize the processes depicted on the graphs.

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

A)

B)

STATEMENTS

1) The internal energy of the gas decreases, while the gas gives off heat.

2) Work is done on the gas, while the gas gives off heat.

3) The gas receives heat but does no work.

4) The gas receives heat and does work.

13

The same currents I flow through three thin long straight parallel conductors (see figure). How is the Ampere force directed on the conductor 3 from the other two (up, down, left, right, from the observer, to the observer)? The distances between adjacent conductors are the same. Write your answer in word(s).

Answer: _____

14

The figure shows a section of an electrical circuit. What is the ratio of the amounts of heat Q 1 /Q 2 released on the resistors R 1 and R 2 at the same time?

Answer: _____

15

A beam of light falls on a flat mirror. The angle between the incident beam and the mirror is 30°. Determine the angle between the incident and reflected rays.

Answer: _____ °.

16

Two uncharged glass cubes 1 and 2 are brought close together and placed in an electric field whose intensity is directed horizontally to the right, as shown in the upper part of the figure. Then the cubes were moved apart and only then the electric field was removed (lower part of the figure). Choose from the proposed list two statements that correspond to the results of the experimental studies, and indicate their numbers.

1. After the cubes were moved apart, the charge of the first cube turned out to be negative, the charge of the second one was positive.

2. After being placed in an electric field, the electrons from the first cube began to pass into the second one.

3. After the cubes were moved apart, the charges of both cubes remained equal to zero.

4. Before the separation of the cubes in the electric field, the left surface of the 1st cube was negatively charged.

5. Before the separation of the cubes in the electric field, the right surface of the 2nd cube was negatively charged.

17

How will the frequency of natural oscillations and the maximum current strength in the coil of the oscillatory circuit (see figure) change if the key K is moved from position 1 to position 2 at the moment when the capacitor charge is 0?

1. increase

2. decrease

3. will not change

18

Establish a correspondence between the resistance of a section of a DC circuit and a schematic representation of this section of the circuit. The resistances of all resistors in the figures are the same and equal to R.

SECTION RESISTANCE

DC SECTION

4)

19

What is the number of protons and neutrons in the nitrogen isotope ()_7^(14)N ?

20

The half-life of the sodium isotope ()_(11)^(22)Na is 2.6 years. Initially, there were 208 g of this isotope. How much will it be in 5.2 years?

Answer: ______

21

For some atoms, a characteristic feature is the possibility of capture by the atomic nucleus of one of the electrons closest to it. How do the mass number and charge of the nucleus change in this case?

For each value, determine the appropriate nature of the change:

1. increases

2. decreases

3. does not change

Write down the selected numbers for each physical quantity. Numbers in the answer may be repeated.

22

The figure shows a stopwatch, to the right of it there is an enlarged image of a part of the scale and an arrow. The stopwatch hand makes a complete revolution in 1 minute.

Write down the stopwatch readings, taking into account that the measurement error is equal to the division of the stopwatch.

Answer: (_____ ± _____)

23

The student studies the properties of pendulums. He has at his disposal pendulums, the parameters of which are given in the table. Which of the pendulums should be used in order to experimentally discover the dependence of the period of oscillation of the pendulum on its length?

24

Consider a table containing information about the terrestrial planets of the solar system.

Choose two statements that correspond to the characteristics of the planets and indicate their numbers.

1) Of the terrestrial planets, Venus revolves in the most elongated orbit around the Sun.

2) The free fall acceleration on Mars is approximately 3.8 m/s 2 .

3) The first cosmic velocity for Mercury is less than for the Earth.

4) Among the planets of the terrestrial group, the frequency of revolution around the Sun is maximum at Venus.

5) The average density of Mercury is less than that of Venus.

25

A bar of mass 0.8 kg moves along a horizontal table, connected to a load of mass 0.2 kg by a weightless inextensible thread thrown over a smooth weightless block. The load moves with an acceleration of 1.2 m/s2. Determine the friction coefficient of the bar on the table surface.

Answer: _____

26

Point B is in the middle of segment AC. Stationary point charges -q and -2q (q = 1 nC) are located at points A and C, respectively. What positive charge must be placed at point C instead of the charge - 2q, so that the modulus of the electric field strength at point B increases by 2 times?

Answer: _____ nK

27

A straight conductor of length I = 0.2 m, through which current I = 2 A flows, is in a uniform magnetic field with induction B = 0.6 T and is parallel to the vector \overset\rightharpoonup B. Determine the module of the force acting on the conductor with side of the magnetic field.

Answer: _____ H.

Part 2.

The complete correct solution of each of the problems 28-32 should contain the laws and formulas, the application of which is necessary and sufficient to solve the problem, as well as mathematical transformations, calculations with a numerical answer and, if necessary, a figure explaining the solution.

A separate frog egg is transparent, its shell consists of a gelatinous substance; inside the egg is a dark embryo. In early spring, on sunny days, when the water temperature in reservoirs is close to zero, the caviar feels warm to the touch. Measurements show that its temperature can reach 30 degrees.

1) How can this phenomenon be explained?

S=Vt_1+\\frac(at_1^2)2.

Let's write the equation in a different form:

\\frac(0,21)2t_1^2+2t_1-50=0.

The solution is two numbers: 14.286 and -33.333.

Only positive values ​​have physical meaning, then t 1 =14.286s.

The second part of the way the person moves uniformly accelerated, but the acceleration is directed in the opposite direction of the speed of the escalator. Let's write a formula describing this movement:

S=\\frac(at_2^2)2-Vt_2;

let's substitute the values:

\\frac(0,21)2t_2^2-2t_2-50=0.

When solving, we get two values: -14.286 and 33.333.

Only positive values ​​have physical meaning, then t 2 \u003d 33.333 s.

Total time spent on the escalator: t=t 1 +t 2 =14.286+33.333=47.6 s.

The cylinder contains nitrogen with a mass m = 24 g at a temperature T = 300 K. The gas is cooled isochorically so that its pressure drops n = 3 times. The gas is then heated at constant pressure until its temperature reaches its original temperature. Determine the work A done by the gas.

When the terminals of the galvanic cell are short-circuited, the current in the circuit is 2 A. When an electric lamp with an electrical resistance of 3 ohms is connected to the terminals of the galvanic cell, the current in the circuit is 0.5 A. Based on the results of these experiments, determine the internal resistance of the galvanic cell.

The eye and the lens of the glasses make up the optical system, the optical power of which can be calculated by the formula: D=D 1 +D 2 .

Then, D_1+D_2=\frac1F;

D_2=\frac1F-D_1;

D_2=\frac1(0.25\;m)-2\;dptr=2\;dptr.

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