There are nine questions in this volume, and the full score is 140.
1.( 15) Fill in the blanks.
1.a. The atomic size is in the order of m. 。
B. the size of the nucleus is of the order of m.
C. the mass of helium atom is about kilograms.
D. the energy of visible photons is of the order of j.
E In the standard state, the number of molecules in 1cm3 gas is about.
(Planck constant H = 6.63× 10-34J s avogadro constant Na = 6.02× 1023 mol? - 1)
2. As we all know, the light energy reflected by a plane mirror is 80% of the incident light energy. Try to judge whether the following statement is correct, and briefly explain the reasons.
A. The number of reflected photons is 80% of the number of incident photons;
The energy of each reflected photon is 80% of that of the incident photon.
2. (15min) Two small blocks with the mass of m 1 and m2 are connected by a light rope, and the rope passes through the light pulley at the top of a smooth inclined plane with an inclination angle of A = 30, ignoring the friction between the pulley and the rotating shaft, and fixing the inclined plane on a horizontal table, as shown in the figure. Suspend m 1 for the first time and put m2 on the inclined plane. T is used to indicate the time required for m2 to move from the bottom of the slope to the top of the slope. Exchange the positions of m 1 and m2 for the second time, so that m2 is suspended and m 1 is placed on the inclined plane. It is found that the time required for m 1 to move from the bottom of the inclined plane to the top of the inclined plane is. Find the ratio of m 1 to m2.
(15min) The experimental device for measuring the electron charge-mass ratio (the ratio of charge Q to mass M q /m) is shown in the figure. In the vacuum glass tube, the electrons emitted by cathode K are accelerated by the high voltage between anode A and cathode K, forming a very fine electron flow, and the electron flow enters the area between the two plates C and D at a speed parallel to the plate of the flat capacitor. If there is no voltage between the two plates C and D, if a voltage U is applied between the two plates, the electrons leaving the plate area will hit point P on the screen; If a uniform magnetic field with a magnetic induction of B perpendicular to the paper surface is added between the plates, the light spot produced by the electron hitting the screen will return to the O point. Now it is known that the length of the board is l = 5.00cm, the distance between c and d is d = 1.50cm, and the distance from the midpoint of the board area to the midpoint of the screen is L = 12.50 cm, and u =
(15) In order to make an artificial earth communication satellite (synchronous satellite) cover the area between 75.0 E and 135.0 E on the equator, which longitude range should the satellite be located in the sky? Radius of the earth r0 = 6.37×106m ... the acceleration of gravity on the earth's surface g = 9. 80 m/s 2 ..
Verb (abbreviation of verb) (15 minutes) As shown in the figure, two parallel long straight metal thin guide rails KL and PQ are fixed on the same horizontal plane, and the distance between them is L, so the resistance can be ignored; Ab and cd are two thin metal rods with mass m, which are perpendicular to the guide rail, have good contact with the guide rail and can slide along the guide rail without friction. The resistance of the two rods is both R, the midpoint of the rod cd is tied with a light rope, and the other end of the rope bypasses the light crown block to hang an object with a mass of m, regardless of the friction between the pulley and the rotating shaft. The light rope between the pulley and the rod cd is in a horizontal and straight state, parallel to the guide rail. Both the guide rail and the thin metal rod are in a uniform magnetic field. The direction of the magnetic field is perpendicular to the plane of the guide rail, and the magnitude of the magnetic induction intensity is B. Now the two rods and the suspension start to move from rest. When the speeds of ab rod and cd rod reach v 1 and v2 respectively, what is the acceleration of the two rods?
6.( 15) has a goblet, as shown in the figure. The bottom inside the goblet is a convex spherical surface, the center of which is at point C in the glass below vertex O, the radius of the spherical surface is R = 1.50cm, and the distance from O to the goblet plane is 8.0cm ... In the center of the bottom of the goblet, point P is close to a picture, and the distance from point O is 6.3cm .. However, if you pour wine and look at the bottom of the goblet from your mouth, it will be. The refractive index of glass and wine is known. This paper tries to explain this phenomenon through analysis, calculation and demonstration.
7.( 15 minutes) As shown in the figure, B is a smooth hemispherical bowl with a mass of mB and a radius of R, which is placed on a smooth horizontal desktop. A is a slender straight rod with mass mA, which is constrained in the vertical direction by a fixed smooth sleeve C, and A can move up and down freely. The mass relationship between the bowl and the rod is mB =2mA ... First, hold the rod A so that its lower end is just on the hemisphere of the bowl. A and b start moving. Let the position of the A-bar be represented by Q, which is the included angle between the connecting line between the ball center O of the bowl surface and the contact point between the lower end of the A-bar and the spherical surface and the vertical direction. Find the velocity of a and b (expressed as a function of q).
8.( 17 minutes) In the circuit shown in the figure, the internal resistance of each power supply is zero, and two points B and C are connected to an infinite combination circuit consisting of a1.0 Ω resistor and a 2.0 Ω resistor on the right. Find the amount of charge on the electrode plate connected with the capacitor 10μF in the figure.
9.( 18) As shown in the figure, the crown blocks B and C and the moving pulley D form a pulley block, and the friction between each pulley and the rotating shaft and the mass of the pulley are ignored. On the moving pulley D, a weight tray A is suspended, and weights 2 and 3 are suspended at both ends of an inextensible light line passing through the pulley block. Tie a compressed lamp spring with a lamp wire (vertical wire passing through the spring in the picture). There is a weight 1 at the upper end (the two do not stick together). It is known that the mass of the three weights and the weight plate are all m, the stiffness coefficient of the spring is k, and the compression amount is l0, so the whole system is static. Now, the lamp wire tied to the spring suddenly burns, the spring stretches, and the weight 1 is pushed upward until the weight 1 is separated from the spring. Suppose the weight is 65438.
Author: 59.48.43. Reply to this speech.
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3 Reply: Physics Olympiad Initial Examination Questions
In △CA P', sine theorems are as follows
(9)
Yes (10)
Considering the paraxial ray, it can be obtained from (9) and (10).
( 1 1)
Have again
( 12)
Substituting the above types into the data, we can get
( 13)
It can be seen that when the wine is not poured, the real image of the scene on the picture is 7.9cm from the mouth of the cup to the O point, and the distance from the O to the plane of the mouth of the cup is 8.0cm. When the human eye looks at the bottom of the cup from the mouth of the cup, the real image is too close to the human eye to see the scene on the picture.
2. After pouring wine, the media on both sides of the convex spherical surface at the bottom of the cup are glass and wine, and the refractive indexes are n 1 and n2, respectively, as shown in Figure 2. Considering that paraxial light is
( 14)
Substituting the values of n 1 and n2, we can get
( 15)
Compared with equation (6), we can see that
( 16)
As can be seen from the above formula and Figure 2, the refraction line will intersect with the OP extension line, which is a virtual image of point P, and the picture will become a virtual image at this position. Can be obtained by calculation.
( 17)
Have again
( 18)
Substitute the above categories into the data.
=13cm (19)
You can see that the scene on the picture becomes a virtual image at p', which is 13cm. Away from the O point, that is, 2 1 cm from the cup mouth. Although the virtual image will be pulled closer to the mouth of the cup due to the refraction of the plane of the wine, it is still far enough away from the mouth of the cup, so when people look at the bottom of the cup from the mouth of the cup, they can see the virtual image of the scene on the screen.
Scoring standard:
The score of this question is 15. Give 5 points to those who get the formula (13) and 2 points to those who can't see it. Find the formula (19), give 5 points, and give 3 points for "seeing".
Seven, according to the conditions, if observed from the ground reference system, then at any moment, A moves in the vertical direction, let its speed be vA, and B moves in the horizontal direction, let its speed be VB. If you take B as the reference system, then the rod A stays in the vertical direction, and its contact point with the bowl moves in a circle with radius R, and the direction of speed is tangent to the circle. Let its speed be VA and the speed of the rod relative to the ground be
( 1)
(2)
therefore
(3)
conservation of energy
(4)
Pass (3) and (4).
(5)
(6)
Scoring standard:
The score of this question is (15). (1) and (2) each have 3 points, (4) has 5 points, and (5) and (6) each have 2 points.
8. Let the equivalent resistance of the infinite combination circuit on the right of B and C be 0, then the circuit with current in the drawing can be simplified to the circuit in Figure 1. The circuit on the right side of B and C can also be simplified as the circuit in Figure 2, where is the equivalent resistance of the circuit on the right side of the dotted line. Because the circuit structure on the right side of B and C is the same, it is an infinite combination circuit, so there is
( 1)
It can be obtained from series and parallel resistance formulas.
(2)
It is derived from formula (1) and formula (2).
solve
(3)
The current in the loop shown in figure 1
(4)
The current is clockwise.
Let the capacitances of the three capacitors in the circuit be C 1, C2 and C3 respectively, and the charges on the plates of each capacitor are Q 1, Q2 and Q3 respectively, with polarities as shown in Figure 3. Because of the conservation of charges, the algebraic sum of charges on the three plates should be zero in the dotted box, that is,
(5)
Potential difference between point a and point e
(6)
Have again
(7)
Potential difference between two points b and e
(8)
Have again
(9)
According to formulas (5), (6), (7), (8) and (9), by substituting the values of C 1, C2 and C3, we can get.
( 10)
That is, the plate of capacitor C3 connected to point E is negatively charged, and the charge amount is.
Scoring standard:
The score of this question is 17. Formula (3) gives 3 points, formula (4) gives 1 minute, formulas (5), (6), (7), (8), (9) and (10) give 2 points, indicating that the charge on the investigated board is negative, and then give 65.
9. Let the time from broken wire burning to weight 1 separating from spring be Dt. During this period, the stress of each weight and weight plate is shown in figure 1. In the figure, f represents the elastic force of the spring at any time in Dt time, t represents the tension in the light rope passing through the pulley block at that time, mg represents gravity, and T0 represents the tension of the rope hanging the pallet. There are some because the mass of d is ignored.
( 1)
At any moment of time Dt, the weight 1 moves upward, the pallet moves downward, and the weights 2 and 3 rise upward, but the speeds of the weights 2 and 3 and the pallet are the same. When the weight 1 leaves the spring, the speed of the weight 1 is v 1, and the speeds of the weights 2 and 3 and the pallet are v2, which are determined by the following formula.
(2)
(3)
(4)
(5)
Where IF, Img, IT and The magnitude of impulses f, mg, t and T0 representing the internal force of d t time respectively. Note that the formula (1) has
(6)
According to (2), (3), (4), (5) and (6)
(7)
During the extension of the spring, the upper end of the spring moves upward with the weight 1 and the lower end moves downward with the tray. Dl 1 indicates the distance that the upper end of the spring moves upward in Dt time, and Dl2 indicates the distance that the lower end moves downward. Because the speed of the pallet is 1/3 of the speed of the heavy object, it can be found at any time during the extension of the spring.
(8)
otherwise
(9)
In the process of spring elongation, mechanical energy is conserved, and the reduction of spring elastic potential energy is equal to the increase of system kinetic energy and gravity potential energy, that is, there are
( 10)
Pass (7), (8), (9), (10)
( 1 1)
After the weight 1 is released from the spring, the weight is thrown upward, and the time to rise to the maximum height is t 1, including
( 12)
The forces on the weights 2 and 3 and the pallet are shown in Figure 2 to show the magnitude of acceleration, including
( 13)
( 14)
( 15)
( 16)
Pass (14), (15) and (16).
( 17)
The acceleration of the pallet is upward, and the initial speed v2 is downward. It is assumed that the pallet speed becomes zero and exists after the lapse of time t2.
( 18)
From formulas (7), (12), (17) and (18).
( 19)
That is to say, the time from the separation of the weight 1 from the spring to zero speed is equal to the time from the tray to zero speed. According to the symmetry, when the weight returns to the separation position, the tray also returns to the separation position, that is, after t 1, the weight meets the spring.
(20)
By (1 1), (12), (20)
(2 1)
Scoring standard:
The score of this question is 18. Formula (7) gives 5 points, formula (1 1) gives 5 points, and formulas (17), (19), (20) and (2 1) give 2 points.