Physical synthesis and induction

First, flexible solution! Force / can be a problem 1 change to find a plastic ball with a weight of G, immersed in the A container, then the support of the bottom of the container to the ball is the cross-sectional area of ​​the upper and lower parts of the ball is S, and S2 There is another liquid inside. It is known that the ratio of liquid density in the two containers A and B is outside: printing = 3: If the ball is taken out from the A container and placed in the B (the liquid does not overflow), when it is still, the liquid pressure at the bottom of the S container is increased. How much is bigger, analysis: This question provides two physical processes experienced by a plastic ball, through the state one to find out the relationship with the office, according to:! B = 3:5, the ratio to the secondary is obtained. The floating and sinking condition of the object is used to judge the floating and sinking condition of the ball in B, and Vsb = hS is grasped to find out how much the liquid level rises. This paves the way for the final increase in the pressure of the liquid received at the bottom of the vessel. Therefore, comparing the size of the suppression and determining the floating and sinking of the ball in S is the bridge and the link between the two physical processes of the ball, and the key to solving the problem.

Solution: When the plastic ball is in the A container, there is G float = G is the ball Jun = ~ (° ball 莒 ball.

When the plastic ball is in the B container, the plastic ball floats on the liquid surface of the B container.

Explanation: When solving the buoyancy problem, it is the key to clear the floating and sinking of the object in the liquid. Only by knowing the floating state of the object can the relationship between V and V* be determined, so that the Archimedes principle formula can be used to solve the problem. Therefore, When solving the buoyancy problem, it is first necessary to determine the floating and sinking state of the object in the liquid according to the known conditions.

2 The overall thinking quickly solves the water in the container, and a small container floats on the water surface. When a solid small plastic ball is placed in a small container, the height of the water surface in the large container rises. If the plastic ball is taken out of the small container and poured into the water of the large container, the liquid level is lowered to find the density of the plastic ball.

Analysis: The solid small plastic ball is placed in a small container floating on the water surface, and the whole is in a floating state, and the total buoyancy is equal to the total gravity.

Put the small ball container out of the water in the large container, the water surface is reduced, reduced, the total buoyancy is reduced, the total buoyancy is less than the total gravity, and the ball sinks until it sinks to the bottom.

To find the density of this plastic ball, we must find out the mass and volume of the ball. The difficulty is to find the volume of the ball with the change of the liquid level twice. The thinking jump is large, and the overall processing method of the joint problem can be adopted.

Put the ball in the water, then the corpse 'float = G capacity + F ball float.

=G capacity = G ball = 7H ball 茗.

There are W balls = /5 water / l | - A: A - one:. E 2 22 II Description: l. The e-knowledge condition in question n is concealed, but it is a prerequisite for analyzing and solving the problem. When solving problems, you must fully exploit and use the hidden conditions in the problem as the golden key to solve the problem. For example, in this problem, the water surface should be excavated, 'V, decrease, buoyancy decrease, and the buoyancy of the ball is less than the a force of the ball. The condition of sinking until sinking to the bottom.

In the changing physical and physical phenomena, the invariable factors should be sought as a bridge and link for solving problems, and then the related physical knowledge and mathematical knowledge should be used for reasoning, induction and calculation. In this question, it is not necessary to set some parameters according to the needs of the division and the solution. These parameters will not bring trouble to the problem solving. On the contrary, it can play a positive role and shorten the solution. Improve the quality of the solution M. As in this question, Vflfe, 3 create the situation, reasonable hypothesis example 3 to verify: the scale value of the density meter is small and large; the scale spacing is sparse.

Analysis: Density juice is an instrument for measuring the density of liquid. It is a sealed glass tube with lead particles at the lower end. The upper end of the cylinder has a scale. When it is placed in the liquid to be tested, it floats on the liquid surface. The scale value of the surface is the density value of the liquid to be tested, and the unit is gram/cm. It proves that the gravity of the density meter itself is constant, no matter which liquid it floats in, the buoyancy is equal to the gravity it receives, ie Put it in a liquid with a high density, and discharge the liquid volume less. The more the cylinder part of the densitometer is exposed, the greater the liquid density value of the liquid surface.

Put it in a liquid with a small density. If the cylinder portion of the densitometer is exposed less, the liquid density value of the liquid surface will be smaller.

Therefore, the engraved density of the juice is the upper and lower.

Let the mass M be, "the density meter is placed in a liquid of /5, and the liquid level is at the position where it is.

Immersion fr: The volume in the liquid is V, then the cross-sectional area of ​​the pgVu闽 cylinder portion is taken as: V is the minimum inscription.

In the liquid of +Ap), since the Vw is put into the liquid of the (p-Ap) due to the Vw, the volume of the multi-immersion S in the cylinder portion is (p-Ap)g (V0) due to ft*t. +hhS)=mg.3 will be the first generation of the human type 2, and the solution will be solved by the first generation of the human type 3.

(Such as).

Therefore, the density of the densitometer is densely spaced.

Exercise 1. Fill in the blanks and put a wooden block in the water. The volume of the exposed water surface is 2.4X丨 (T5m3, the exposed water surface is cut off and then placed in the water. The volume of the exposed water surface is 1.6x15m. 3. The whole solid metal balls of the wooden blocks A and B are equal in mass, and their densities are 5x13 kg/m3 and 1x13 kg/m3 respectively. The armor is hung under the armor scale and the ball is hung. Under the spring balance of the B spring, and let both balls be fully immersed in water. At this time, the ratio of buoyancy of the two balls of A and B is the ratio of the volume of the aluminum to the volume of the cavity of the aluminum basin. V empty = . (= = 2.7x g / m 1) a piece of wood. Two times under the action of object B and object C, can stay under the water. The following statement is correct ().

In both cases, the buoyancy of A is equal to that of B. The quality of B is greater than that of A. (D) The density of B is greater than the density of A. 5. When the plastic ball and the wooden ball are connected to the water by a string, the wood The volume of the ball exposed to the water surface is its own volume. When the string is cut, the plastic ball sinks to the bottom, and the volume of the wooden ball exposed to the water surface is its own volume. At this time, the plastic ball is supported by the bottom of the pool. ,Such as. If the ratio of the volume of the plastic ball to the wooden ball is 13 kg/m3 0)) After the rope is cut, the total buoyancy of the two objects is different. 2F is hooked with the spring object, and then the object is submerged in water and alcohol. The spring scales are 8 cattle and 10 cattle, respectively. If the spring balance is used to hook the object, and then the object is immersed in water and alcohol, the spring scales are 5 cattle and 7 cows respectively. The correctness of the following statements is () * the volume of the two objects The density of two objects, A and B, must be the same. The buoyancy of two objects in A and B must be equal. The gravity of the object must be the same as the gravity of the object. The two overflow cups are filled with A and B respectively. Two kinds of liquids, now the same solid balls A and B are placed in the two overflow cups respectively. As a result, the A ball sinks in the nail liquid, and 20 grams of the liquid is overflowed. The S ball floats on the liquid surface of the liquid B, overflowing. B liquid 30 grams. Then the ratio of the density of the two liquids A and B is P ().

It is S, the height is /t, and the square of the square block is a, the gravity is G, and the water of the weight G is poured into the container, and the pressure of the block on the bottom of the container is exactly zero. Then the depth of the water in the *8 container is ().

For example, there is a cylindrical container and a cylindrical metal block of sufficient length, the cross-sectional area Ss: Ss = 3:1, the container contains water, the metal block is suspended under a thin wire, and the metal block is slowly placed. People in the water. Q: If the metal block is immersed in water to a depth of 15 cm, the pressure at the bottom of the container is increased. If the rope just touches the water surface from the bottom of the metal block to the lower side of the water L:: - 22 cm, the bottom of the container Under the pressure increase of water, 13 kg / m 3 and chemistry = 4 X 103 kg / m 3 of two materials made of equal mass, the hollow part of the ball is also equal in volume, hollow ball and B, will be released in the water Just can be suspended. It is also required to put the ball into the water, and the volume of the exposed water surface accounts for a few parts of the whole volume. The uniform cylindrical container contains an appropriate amount of water, and a wooden block is placed in the water. When the wooden block is stationary, the container The pressure at the bottom is 1200 Pa when it is not placed in the wood. If the wood is partially immersed in water and then the wood is placed in the water to stand still, the pressure at the bottom of the container is increased by 400 Pa when the wood is placed. Find the density of the wood block (g = 10 N / k).

A solid iron hemisphere of 260 cm 3 and a radius J = 5 cm rests at the bottom of a horizontally placed flat container of water, at which time the bottom of the container is at a depth of 15 cm from the horizontal. The pressure of the water on the spherical part of the hemisphere is kg/m%g = lN/kg) (provided by Xiaoli) 2. The minimum force acting on point B and the force arm of this force on the balance of simple mechanical and work levers (Fig. Medium O is the fulcrum).

The students understood the "balanced conditions of leverage" and the "concept of the arm". When solving the problem, they thought about the "force that acts at the minimum point B".

Solution: According to the concept of the force arm and the knowledge of geometry, we can know that the maximum force of the force acting as the fulcrum and acting on point B is OB. Therefore, when drawing, first connect OB, that is, the maximum force arm made, then OB The vertical line is the action line of the minimum force, and then the FB is separated from the fulcrum O on both sides, and the direction of the heart is judged from the effect. Therefore, the direction should be perpendicular to the OB to the lower left. Such as.

A thin and even lever, put a candle of the same thickness on both sides of the fulcrum, just balanced. If the candle burns at the same speed, then after a period of combustion, the lever ().

The A end sinks (B) The B end sinks (C) is still balanced (D) Can not judge the solution: Because the two candles have the same thickness, different lengths, and the same burning speed, it is conceivable that when burning for a period of time, if the A end candle Just after burning, the B end must not be burned, so the force at the A end is zero, the lever can of course not be balanced, and the B end should sink, so it should be selected (B).

Note: This is the limit method. The limit method is a method of thinking that expands the difference between physical quantities by taking minimum or maximum values, so that the problem can be solved quickly and accurately.

Example 3, such as the device, each pulley weighs 5 cattle, the rope weight and friction are not counted, the object A weighs 60 cattle, C is the spring balance, and a heavy object B is hung on the free end of the rope, the whole device is at rest, at this time the spring balance reading For 50 cattle. Then, what is the weight of the object B, and what is the pressure of the object A on the ground? Analysis: If the B object is directly used for the B object weight, the research object must be converted.

The sub-suspension is on the fixed pulley, so the fixed pulley is taken as the research object first. It is subjected to the vertical upward force as the spring balance pulling force R, and the vertical downward force is the pulling force of the 3 strands of the rope 3GS, and the fixed pulley gravity Gft. When the pulley is stationary, there is KdGB+GftJP. Since the object A is suspended on the movable pulley by the rope, the research object turns to the movable pulley. It is subjected to a vertical upward force of 2 GB for the tension of the two ropes, a vertical downward force of A pulling force F2, and a movable pulley gravity G wheel. Because the moving pulley is stationary, there are 2GB to calculate the pressure of the object A on the ground, and the support force of the ground to A can be obtained. Therefore, the research object is the object A, which is subjected to the vertical upward force as the ground support force F, and the moving pulley Pulling force, the vertical downward force is gravity GA. Because A is stationary, there is a mutual force according to the interaction between objects, and the pressure of A on the ground is F'=F=35 N.

The wheel group moves the object with a gravity of 400 cattle at a constant speed along the horizontal ground. The distance the object moves is 5 meters, and the tension at the rope end is F=30 cattle. The mechanical efficiency of the pulley block is the frictional resistance of the ground to the object.

Solution: (1) Because the number of ropes that the pulley group bears the load is three, that is, "=3, the distance at which the rope end tension moves is three times the moving distance of the object. Since the distance of movement of the object is s'=5 meters, the distance at which the tension of the rope moves is s = 3/= 15 meters. According to the title, (2) is to overcome the frictional resistance of the ground to the object / work done, that is, W useful = / /. Description: The key to solving such problems is to clarify the work done by the rope end pull force F Gong, overcome the frictional resistance of the ground to the object when moving at a constant speed, and the work done is useful. The weight of 400 cattle is an unnecessary condition.

Exercise 21, multiple-choice questions (there are four options in the following sub-questions, only one of which meets the meaning of the question) 1. For example, regardless of the friction and the gravity of the pulley, both objects A and B are at rest. If the P end of the rope is moved to the left for a certain distance and then fixed, and the rope is long enough, then ().

After the object rises for a certain distance, the static balance of the object is lowered by a certain distance, and the static balance of the object does not rise or fall, but still maintains the balance in the original position. The object continues to rise until it is blocked by the fixed pulley. 2. For example, the "straight rod can be Rotate around the axis O, hang a heavy object at the midpoint of the straight rod, apply a force F that always maintains a horizontal direction at the other end of the rod, and force the F to slowly raise the straight rod from the vertical position to the horizontal position. The change in F size is () balanced. Immerse the iron in the liquid of the density to be measured, and move the scale to read the density of the liquid directly on the rod. In the following statement, the fault is that the scale zero of the density scale is on the scale of the A point scale on the left side of the smaller scale. The scale of the density scale is at the right point of point A. To lift the weight G, use the lever* Always maintain a vertical force F to make the lever! Q* is slowly shifted from the vertical position to the horizontal position I. In this process, the lever 1=1I is labor-saving first, then the laborious first is laborious, then the labor-saving oil drum is wrapped around a few turns of the rope, and a horizontal force F is applied at the leading end of the rope to make the oil drum Rolled horizontally for a week. In this process, the work done by the pull force F is ().

Second, multiple-choice questions (the following sub-questions have four options, at least one of which meets the meaning of the question). The buoyancy of 000 cattle rises vertically at a constant speed. If you add 10 kg of objects to the load, the balloon will fall vertically at a constant speed. Let the buoyancy and resistance of the balloon rise and fall unchanged, take g = 10 Ng. The following judgments are correct: () * (A) The combined force received when the balloon rises is greater than the resultant force when the balloon is lowered (1)) The gravity received when the balloon rises is 950 cattle CC) The resistance received by the balloon when rising and falling is 50. When the balloon is lowered, the movement state has been changing. One person uses the same pulley block to raise the weight of the object weighing 1 000 and 2000 cattle by 5 meters at a constant speed. The moving pulley weighs 200 cattle, and the weight and friction are not counted. Then in the above two situations (.).

The mechanical efficiency of the pulley block is not equal. The extra work done by the person equals the distance of the free end of the rope. The error in the following statement is ().

The greater the motor power, the more work the motor has. The lower the motor power, the slower the work. The more the motor works, the higher the mechanical efficiency. The motor power and efficiency are two different concept sprinklers running at a constant speed on a horizontal road, and constantly sprinkling water during driving. In the process, the sprinkler () (D) mechanical vehicle that does not change at a constant speed of 36 km / h, does 3.6 X 105 joules of work in 1 minute, and the resistance it receives is heavy. 2 times. Then the gravity of the car is a cow.

A hard and even hard rod AB is hung. When the weight G of 100 cattle is hung at A, the hard rod is just balanced, and the gravity of the hard rod itself is a cow.

=200 cattle pulling the object A at a speed of 3 meters / speed on the horizontal ground at a constant speed, the object B movement force is the cow, the pulling force F is 3, the bottom of the oil barrel is round, the diameter is 60cm, the height is 80cm, full The oil weighs 1 000 cows and is placed on a level surface. If you want to push the oil drum down (no slip between the barrel and the ground), you need at least the thrust of the cow.

For example, a uniform metal rod has a mass of 7* kilograms and a length of Z meters. One end of the metal rod is suspended at point O and can be rotated around point O. Now use a horizontal rightward force on the other end of the rod to slowly move from the vertical position to the dotted line in the figure. In this process, under the action of the horizontal force group, the object A advances at a constant speed of 2 meters along the horizontal ground at a speed of 0.2 m. It is known that the object A weighs 300 cattle and the pulling force F has a power of 12 watts, excluding the weight of the rope and the pulley. Then, the pulling force F 16 is 6, and the object weighing 10 cattle on the pulley A is a fixed point (ground). When the pulley A rises upwards at a constant speed under the action of the force F, the speed of the pulley A is twice the speed at which the weight W rises, and the force F should be a cow. Schematic diagram of the force and force arm (pulley A and rope weight and friction are not counted).

18. A child weighing 400 cattle stood on the ground and wanted to use the pulley block to evenly mention the object of 1300 cattle to the height of 10 meters. The selected rope can only withstand 300 cattle. The total weight of the movable pulley is 100 cattle. (Excluding friction and rope weight) Please help him design a simple pulley block; calculate how much power it actually saves, how much pressure the child has on the ground, how long the rope is pulled by the child, the diameter is 100cm, and the mass is 40 kg. A uniform cylinder, placed on a level surface, leaning against a 10 cm high step. In order to make it roll on this step, then at which point on the edge of the cylinder and in which direction, when the force is applied, the cylinder can be just off the ground with minimum force, mark this point on the figure, and draw the force The direction of the force is determined (the cylinder is in contact with the step at point A).

Use the pulley block as shown in Figure 9 to raise the weight at a constant speed, and all friction is not counted. When the weight of the extract is G = 320 N, the rope end pull force is F=200 N. Find the mechanical efficiency of the pulley block at this time. If the weight of the extracted material is increased to G 420 cattle and the lifting height is 2 meters, how much work is done on the rope end tension, = 12 kg. Under the action of F, the object A is 0.4 m. The speed is uniform linear motion on the horizontal plane, the spring scale is 12 four, and the drawing title is 17, such as 7. When the lever is balanced, draw the A point in the horizontal direction, ignore the friction between the pulley and the rope, and the pulley and spring æž°And the gravity of the rope, and the rope is long enough. Seeking: the amount of friction between the object A and the horizontal plane; the magnitude of the pulling force F; the movement of the object A for 10 seconds, the pulling force F and the gravity of the object A; the power of the pulling force F.

22. Use a pulley consisting of a movable pulley and a fixed pulley with a weight of G to raise a weight at a constant speed, regardless of the gravity of the rope and the friction on the pulley. At this time, the mechanical efficiency of the pulley block is 75%. It is equal to the rated current of the electrical appliance. Otherwise, the varistor is easy to be burned. After changing to the new moving pulley of the lightweight material with the weight of G2, it will be improved.

1 When this weight is heavy, the mechanical efficiency of the pulley block is increased to 85%. The gravity of the new moving pulley is how many times the gravity of the original moving pulley. (Ignore the friction and the weight of the rope) The force of the cow can make the cylinder just leave the ground, such as 1. Times (voiced by Wen Shu) III. Electrical Comprehensive Problem 1 The power supply voltage is 220 volts. If the appliance marked with *220V, 800W* can work under the voltage of 110V to 220V (the resistance value of the appliance is constant), ask: To use the appliance to meet the requirements of use, what kind of electrical appliance should be connected in the circuit, how to connect What is the maximum power consumed by this appliance? Analysis: This question examines both the basic knowledge and the ability method.

For the first question, you only need to have the knowledge of series voltage division, it is not difficult to know that you can use the electric appliance to work at 110V to 220V. Just connect the electric appliance in series with a sliding varistor with suitable resistance. The key is to consider the sliding varistor. Specifications (resistance range, maximum current that can withstand). When the appliance is operated at 110V, the voltage obtained by the varistor is also 110V, and the resistance of the connected circuit should be equal to the resistance of the electrical appliance, which is the maximum resistance of the varistor. When the appliance is operated at 220V, the voltage obtained by the varistor is zero, and the resistance of the circuit is also zero. The current in the circuit reaches the maximum, which is the rated current of the appliance. This current does not pass through the varistor, but considering that the current through it will approach this current before the resistance of the varistor becomes zero, so the maximum current that the varistor can withstand the second question should be considered when the supply voltage is constant and the resistance A constant varistor in series with a series of appliances, in the process of increasing resistance, how the power consumed changes, this problem can not be solved by the usual method. Because the resistance i' of the varistor increases, the voltage across it (T also increases with it, and the current through it decreases. If used (/wide or wide = wide 2K' for analysis, the public two The factors are both increased and the other decreases. The change of P' cannot be determined. If the analysis is performed with =g, the numerator and denominator are both enlarged, and the change of H p' is still uncertain. Some students adopt In the end-value method, the power consumed by the varistor is zero when the resistance is zero, and the power consumed by the varistor is considered to be the maximum when the resistance is maximum. It is not appropriate to solve the problem, even if the answer is correct, it is coincidental. Students expect that the power consumed by the varistor in this scenario implies an extreme value, which should be analyzed by the extreme value method. Since the resistance, voltage and current of the varistor are simultaneously changed, the function of the extremum is usually only one. Variables, therefore, when using columnar analysis, make full use of the relationship between physical quantities, and list the functional formulas with only one variable.

Let the power supply voltage be I/, the resistance of the electrical appliance is the ruler, and the value of =J2 is fixed. The mathematical proposition "the product of two positive numbers is a fixed value. If and only if the two positive numbers are equal, their sum has a minimum. It can be seen that the value of P' is the largest only when =*, iT = i. This makes us realize the law of power consumption of the series varistor: when the resistance of the varistor connected circuit is equal to the resistance of the electric appliance with constant resistance in series with it, the varistor consumes the most power.

The electric current of the electric appliance is female. Therefore, a sliding rheostat with a resistance range of 060.5 ohms and capable of withstanding 3.64 amps should be connected in series.

(2) When the resistance of the sliding varistor connected to the circuit is JT Europe, the voltage is divided by 000:=3.6\16 Jiao: The corpse "calculates the corpse value.

According to the calculation of i, the value of the person is replaced by the body, and the C7S can be calculated.

One circuit is separately entered. The following relationship is incorrect ().

The sliding value of the large value of 100 ohms is connected in series with the ~b~ resistor, and it is connected to the voltage! 7 on the circuit. If the following Jr 11 U=6 volts, no matter how the slide P is moved, the total power in the circuit will not exceed 2 watts if U>6 volts, and the bulb and the varistor will not be damaged, no matter how the slider P is moved, the circuit The total power must be greater than 2 watts. When the slide P is moved to a certain position, the electric power of L and only can be equal to the fixed resistance of the ohms and the number of wires. They are respectively associated with the relevant binding posts labeled A, B, and C in the dashed box. Connection, after testing, found that the resistance between terminal A and B, B and C, C and A is 10 ohms. According to the test results, draw the connection of the resistance wires between the binding posts in the dotted line box.

Bubble, the known lamp and L3 resistance are only, = 10 ohms, i3 = 25 ohms. When the power supply voltage is measured after connecting the circuit, it is found that the length of the wire connecting the voltmeter is not enough. Therefore, he uses the voltmeter to connect to the two points A and C and finds that the reading is 15 volts. When the two points are connected to B and D, the reading is 20 Volt. At this time, the power supply voltage is how many volts, the ratio of the ratio is 2:1. When S, closed, S2 is disconnected, the slide of the sliding varistor only emits light at the midpoint. The sliding piece P is moved from the midpoint to the 6th end, and the ratio of the voltmeter to the number is 3:5. The sliding piece is not moved at the 6th end, the Si is disconnected, the S2 is closed, and the L2 is also normally illuminated. Find: the ratio of the rated voltage of 1 and L2; S2 is closed, S, when disconnected, the ratio of the power consumed by the sliding varistor when P moves from 6 to the midpoint.

15. In order to control the temperature of a simple hatchery factory, 3 sets of *220V300W* electric heaters were purchased, the power supply voltage was 220V, the wire was appropriate, and 3 switches were used.

Using the above equipment, design a circuit to make the circuit have three gears; demonstrate the design.

1. 1.2.422.1 Table 22 in the serial number 2, * reading (provided by Li Shuwen, Tianjin Xinhua Middle School)

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