1. Three straight bars with a length of 2m and uniform mass form a regular triangular frame ABC, with point C suspended on a smooth horizontal rotating shaft, and the whole frame can rotate around the rotating shaft. Rod AB is a guide rail on which the electric toy squirrel can move. As shown in the picture, the squirrel is observed moving on the guide rail, but the frame is stationary. Try to demonstrate what kind of movement squirrels are. 2. There is a horizontal concave mirror with a radius of curvature of 60cm, which is filled with water. Find the focal length of this mirror. The refractive index of water is 4/3. (Assuming that the thickness of water is small relative to the radius of curvature of the mirror) 3, A, B and C are three identical spheres with smooth surfaces. Ball b and ball c are hung from the ceiling by an inextensible 2-meter-long light rope, and the two balls just touch each other. Take the contact point O as the origin to make a rectangular coordinate system Oxyz, the Z axis is vertical upward, and the Ox axis coincides with the connecting line of two balls, as shown in the figure. Now let ball a shoot at balls b and c and collide with them at the same time. Before the collision, the speed direction of ball A was along the positive direction of Y axis, and the speed was 4m/s. After the collision, ball A bounced back to the negative direction of Y axis at the speed of 0.4m/s. Find the maximum displacement of (1)B and C from O point after being hit. (2) Discuss the movement of ball B and ball C for a long time (ignoring the air resistance, take g= 10 m/s 2) 4. As shown in the figure, at x>0, there is an electric field along the positive direction of the X axis, in which the electric field is uneven in the xd region, and the electric field intensity E increases with X, that is, E=bx, B >；; 0 is a known quantity; In the xd region, the electric field is uniform and the field strength is E=bd. At x<0, the distribution of electric field and the spatial distribution of x>0 are symmetrical, but the direction of field strength is along the negative direction of X axis. When x=5d/2, an electron with a charge of -e and a mass of m begins to move along the positive direction of the Y axis with an initial velocity of v0. It is found that: (1) the period of electron motion in X direction; (2) The distance between any two adjacent intersections between the electron trajectory and the Y axis. 5. There are the following experimental facts: the angle of view of the sun from the earth is 32'; The radiation energy per second perpendicular to the connection line between the earth and the sun passing through the earth's surface is 0.135j/(cm2s); Si-Bo constant = 5.67×10-12j/(cm2sk4); When the sun radiates, it actually looks like an ideal black body. (1) To calculate the temperature of the earth's surface, it can be assumed that the temperature of the earth is constant and does not change with time; The earth is an ideal black body and heat conductor, and the latter assumption means that the temperature of every point on the earth's surface is the same; (2) Find the temperature of the sun's surface. (Note: According to Poirot's law, the total heat radiated by an ideal blackbody surface at 1cm2 is T4, which is Poirot's constant, and t is the absolute temperature of the object. 6. Consider a classical atomic model with atomic number Z, ignoring the interaction between electrons. Let an electron e 1 in an atom make a plane uniform circular motion at a distance from the nucleus r0. Suddenly, due to some process, another electron outside was captured into the nucleus. It is assumed that the trapping process is so fast that the velocity of the electron e 1 is completely unaffected and remains in the atomic system. We try to use r0, electron mass m, absolute value of electron charge e and atomic number z to express the quantity (energy, orbital parameters, period) describing the movement of electron e 1 in this case, and compare it with the original movement. 7. Use two sledges to transport a uniform beam with a mass of m and a length of l on horizontal snow, and keep the beam horizontal. The simplified schematic diagram is shown in the figure. The upper end A of each sled is fixedly connected with the end of the transport beam, and the lower end B is in contact with snow, assuming the contact area is very small. A horizontal traction force F acts on the front sled, and the distance from the action point to the snow is expressed by H. It is known that the dynamic friction coefficient between the front sled and the snow is k 1, and that between the rear sled and the snow is k2. Q: Under the condition that both front and rear sledges are in contact with snow, what conditions should H meet to make the light beam move along the snow at a uniform speed? How big should the horizontal traction force F be? The mass of the sled is negligible. 8. Connect two capacitors with capacitance of C 1 and C2 to the circuit composed of resistor R and power supply, with electromotive force and internal resistance r=R/3, as shown in the figure. Connect connectors 1 and 2, 3 and 4, 5 and 6 respectively. Before connection, the charging capacity of capacitor C2 is Q0; When the capacitor C 1 is turned on, the voltage between the two poles is equal to /2, and the potential of the contact 3 is higher than that of the contact 2, so as to find the electric quantity q0. 1, a ball with a mass of m = 0.2kg is placed on an upright post with a height of h = 5m. A bullet passes through the center of the ball horizontally, with the mass m=0.0 1 kg, the speed v0=500 m/s, and the ball falls on the ground s=20 meters away from the S-pillar. Find out where the bullet falls on the ground. How much kinetic energy of a bullet is converted into heat energy? 2. Throw a rectangular object into an ideal elastic wall. One side of the brick is always parallel to the wall. Its velocity v forms an angle with the normal of the wall, and the friction coefficient of the block against the wall is 0. Find the relationship between reflection angle and incident angle, and draw the function diagram of the relationship. 3. A container with a volume of 2× 10-3m3 contains 1 mol hydrogen and a small amount of water. At the beginning, the pressure in the container was 17atm, then the pressure in the container was heated to 26atm, and the initial and final temperatures of the container and the mass of evaporated water were calculated. The saturated vapor pressure values of water at some temperatures are listed in the table: pressure (× 105Pa) 1 2 3 4 5 6 temperature (0c)100120133152/kloc-. On the rollers, there is a uniform platform with a weight of p, and the center of the table and the distance and center between the two rollers are slightly staggered. The maximum distance between the two rollers is 2L. The friction coefficient between the roller and the table is f, please describe the movement of the table. The answer should be confirmed by calculation. 5. In the plane perpendicular to the uniform magnetic field B, two mutually perpendicular long straight conductor bars are connected into a fixed cross. A rigid square wire frame with a side length of A moves to the left at a constant speed V. During the movement, the wire frame and the conductor bar always keep smooth contact, and the two vertices A and C of the wire frame are always on the horizontal conductor bar in the figure, as shown in the figure. When the wireframe is set at the position of solid line in the figure, the timing starts, and the current passing through the vertical bar in the figure during the movement is marked as i. Try to find out: (1) as a function of time t I(t), and draw the corresponding curve; (2) The direction and magnitude of the external force F needed to keep the wireframe moving at a uniform speed are expressed by F(t) function, and the corresponding curves are drawn. Let the resistance per unit length of conductor bar and wire frame be R and the magnetic induction intensity be B.6.. What we are discussing and studying now are two launch schemes for launching spacecraft outside the solar system in a space research plan. The first is to launch a spacecraft at a speed large enough to make it escape from the solar system directly. The second scheme is to let the spacecraft approach an alien planet and change the direction of the spacecraft with its help to achieve the speed needed to escape from the solar system. Suppose that the spacecraft only moves in the gravitational field of the sun or planet. So whether to move in the gravitational field of the sun or the gravitational field of the planet depends on which field is stronger at that point. (1) Determine the minimum velocity v 1 required for launching spacecraft according to the first scheme and its direction relative to the Earth. (2) Suppose that the spacecraft has been launched in the direction specified in (1), but it has another velocity v2 relative to the Earth. Find the speed of the spacecraft when it passes through the orbit of Mars, that is, the parallel and vertical components relative to this orbit. When the spacecraft crossed the orbit of Mars, Mars was not near this intersection. (3) Let the spacecraft enter the gravitational field of Mars, and try to find the minimum speed required for launching the spacecraft from the Earth to escape from the solar system. Tip: From the result (1), we can know the size and direction of the optimal speed needed for the spacecraft to escape from the solar system after leaving the Martian gravitational field (regardless of the exact position of Mars when crossing the orbit of Mars). Find out the relationship between this optimal speed and the speed component before the spacecraft enters the gravitational field of Mars, that is, the speed component determined in (2). What about the conservation of energy of spacecraft? (4) Estimate the maximum percentage of energy saving of the second scheme compared with the first scheme. Note: Let all the planets move around the sun in the same plane and in the same direction. Ignore the air resistance, the energy consumed by the earth's rotation and separation from the earth's gravitational field. Data: The speed of the earth's rotation around the sun is 30 km/s, and the ratio of the distance between the earth and the sun to the distance between Mars and the sun is 2/3. (4) The space station with the mass of 1 and the docked spacecraft with the mass of m move around the earth in a circular orbit, and the orbital radius is n times that of radius of the earth R (n= 1.25). At a certain moment, the spacecraft ejected from the space station from the direction of motion, and then moved in an elliptical orbit, with the distance from its farthest point to the center of the earth of 8nR. When asked what the mass ratio is m/M, the spacecraft happened to meet the space station after circling the earth. 2. A spherical glass fish tank with radius r is placed in front of an upright flat mirror. The cylinder wall is very thin, the distance from the mirror center is 3R, and the cylinder is filled with water. The observer looks at the distant fish tank through the center of the ball and perpendicular to the mirror. A small fish swims along the cylinder wall of the nearest point to the mirror at a speed v, and finds the relative speed of the two images of the fish seen by the observer. The refractive index of water is n=4/3. 3. In the circuit shown in the figure, the electromotive force of the power supply is 1= 2= 12 volts, the internal resistance is r 1=2 ohms, r2=2 ohms, the resistance is R 1=6 ohms, R2=4 ohms and R3=8 ohms. Find: (1) total current I and each branch current I 1 and I2; (2) If 2=20 volts, other conditions remain unchanged, can the power supply 1 be charged, and why? 4. There is a wooden board that can rotate around the horizontal axis at the lower end, and the rotation axis is located on a vertical wall, as shown in the figure. At the beginning, the angle between the board and the wall is 150. Put a right cylindrical wooden stick with a cross-sectional radius of R in the included angle, and apply a force F on the outside of the board to keep it balanced. The static friction coefficients between the wooden stick and the wooden board are respectively. If the applied force f decreases slowly, the included angle will slowly open and the stick will fall. When the included angle is 600, which direction does the arrow on the end face of the stick point to? Attached trigonometric function table: A7.50 150 300 600 Sina 0.131.259 0.500 0.866 COSA 0.991.966 0.866 0.500 5. There is an optical picture on a piece of paper (as shown in the picture), because there are only three pictures left after the ink fades. The light source s, the focal point f of the thin lens and the point m on the lens. In addition, a part of the straight line A from the light source S to its image S' remains. From the words on the paper, we can see that the point S is closer to the lens than the point S'. Is it possible to restore this picture? If possible, draw it and determine the focal length of the lens in the picture. 6. A particle is fixed in the middle of a 20 cm long thin rod. The stick stands against the smooth wall, and the lower end of the stick can slide along the ground without friction. The rod is in an unstable equilibrium state. Tilt the pole slightly so that its lower end slides away from the wall. The rod is always in one plane. When the center of the stick touches the ground, it stops immediately. Find the final distance from the center of the pole to the wall. 7. As shown in the figure, next to the infinite linear current, there is a rectangular wire frame with side lengths of A and B respectively, and the wire frame rotates at an angular speed with one of its long sides (parallel to the linear current) as the fixed axis. It is known that the linear current intensity is I, and its distance from the rotating shaft is A+C. When the wire frame turns to what position, the induced electromotive force is the largest? What is the value of this maximum induced electromotive force? 8. The molar ideal gas starts from the initial state (P0, V0), changes to (aP0, V0) through the isobaric process, then changes to (aP0, V0) through the isobaric process, and finally changes to the initial state through the isobaric process, thus going through a cycle. Known. The difference between the highest temperature and the lowest temperature in the cycle is 100K, and R=8.3 1J/mol. K, and calculate the external work of gas in this cycle. 1. The train road is located between two cliffs far apart. The walls of the cliff are vertical and parallel to each other, and the track and the cliff are vertical. On a certain section of the road, there happened to be a locomotive running. The locomotive moving at a constant speed keeps whistling. The speed of the train is V, the frequency of whistling is F, and the speed of sound in the atmosphere is V. How often does the echo return to the locomotive? 2. The conductor made of superconducting material with a diameter of 1mm is a ring with a radius of 5cm. The ring is in superconductor state, and the current in the ring is 100A. One year later, it is found that the change of current in the ring is less than 10 6A. Try to estimate the upper limit of the order of magnitude of resistivity of this superconductor material. Tip: After the current I is applied to the ring with radius r, the magnetic induction intensity in the center of the ring is 3. A rope is fixed at the end of the rigid vertical rod, and a small ball is tied to the rope to make the ball move around the circle in the horizontal plane. The trajectory of the rope is a conical surface with an opening angle of 2a. The above system starts with a stationary elevator, and at a certain moment, the elevator begins to land. Suppose the rope is thin, light and soft, old and unable to pull. Please describe the movement of the ball before and during the landing of the elevator. 4. Let the balloon volume be constant, which is 1. 1m3. The volume of balloon skin can be ignored, and its mass is 0. 187Kg. When the outside air temperature is 200℃ and the normal outside air pressure is1.013x105pa, the balloon starts to lift off, and the outside air density is 1.2Kg/m3. (1) What is the temperature of the hot air inside the balloon to make the balloon just float? (2) First tie the balloon to the ground and heat the air in the balloon to a stable temperature of 1 10℃. What is the rope tension at this time? (3) Assume that the lower end of the balloon is tied (the air density in the balloon remains unchanged). When the internal air is kept at a stable temperature of 100℃, the balloon rises to an isothermal atmosphere of 20℃, and the ground pressure is1.013×105pa. Under these conditions, how high can the balloon rise? (4) When it rises to the height h in question (3), pull the balloon away from the equilibrium position 10cm in the vertical direction and then release it. Try to reason qualitatively what kind of movement the balloon will make. It is pointed out that there is a relationship between the atmospheric pressure p at height h and the atmospheric pressure P0 at zero height, in which the atmospheric density at zero height decreases exponentially (or the density decreases) with the increase of height when the height changes little, which can be approximately regarded as a linear function of height. 5. There is a transparent optical material. The refractive index of many parallel thin layers with slightly different refractive indexes and thickness of d=0 1mm is nk, and its numerical values are NK = N0-kV, n0= 1.4 142, and v=0.0025. Today, a ray PO is aimed at point O with an incident angle of 300. 6. On one side of the straight track of the cycling track, there is an inclined plane with an inclination angle of, the length of the straight track is L, and the height of the upper end of the inclined plane is H. As shown in the figure, the athlete starts from point A and ends at point A'. Athletes can choose a straight line AA' or a route along the symmetrical broken line AMA''. If the starting speed of the bicycle is v0, the driving force of the athlete is equal to the resistance, and the lateral friction between the wheel and the ground is enough to prevent the wheel from slipping, which route should the athlete take to achieve better results? 7. As shown in the figure, there is a car with a magnet on the infinitely smooth guide rail, with the N pole of the magnet at the bottom and the S pole at the top. The end face of the magnet is a square with a side length of A (assuming that the magnetic field is all concentrated on the end face and the magnetic induction intensity is B). A series of short metal bars are welded between two guide rails. The distance between two adjacent metal bars is equal to the length of the metal bars and both are equal to A. The resistance of each metal bar and the resistance of each small section of the guide rail are R. What is the inclination of the guide rail that makes the magnet move down along the guide rail at a uniform speed V? (The magnetic field can be considered as a uniform magnetic field) 8. The mass of platform A is m, supported by a spring with a stiffness coefficient of k, and the mass of small object B is also m, which is freely placed in the center of the platform. Now press down the spring with the force of F=mg (still within the elastic limit of the spring), remove the external force when the system is at rest, and calculate the maximum heights of (1)A and B respectively. (2) Please describe the movements of A and B after removing the external force.