The balance condition of arm and lever is an important concept and law in junior high school physics, which has been fully reflected in the examination papers of senior high school entrance examination in recent years. In order to improve students' understanding, the author classifies some questions about leverage in the examination papers of senior high school entrance examinations in various cities in Jiangsu Province in recent years, and analyzes, answers and comments them.

I. Conceptual issues

Example 1. A person's forearm can be regarded as a lever. Pull the spring obliquely upward by hand, with the elbow joint O as the fulcrum, the force F 1 generated by muscle contraction acts on point A, and the resistance F2 acts on point B. Try to draw the force arms L 1 and l2 of F 1 and F2 on the diagram 1 respectively.

Figure 1

Analysis: The distance from the fulcrum to the action line of dynamic (resistance) force is called the dynamic (resistance) force arm. When looking for the moment arm, we should first find out the position of the fulcrum, then draw the line of action of the force along the direction of force and resistance, and then draw the moment arm with the line of action of these forces as the fulcrum.

Solution: (Figure omitted).

Comments: Check whether students understand the important concept of arm of force.

Second, explore the lever balance condition test questions

Example 2. (Zhenjiang Examination) In the experiment of studying the lever balance condition, Zhang Hua found that the lever is not in the horizontal balance position (as shown in Figure 2).

Figure 2

(1) Zhang Hua should adjust the nut to _ _ _ _ _ _ _ _ (choose "left" or "right") to balance the lever in the horizontal position.

(2) Please help Zhang Hua to design and draw a table and record the experimental data, so that Zhang Hua can study the lever balance conditions.

Analysis: In order to eliminate the influence of the weight of the lever on the balance, the gravity line of the lever should pass through the fulcrum. Therefore, before hooking the lever, the nuts at both ends of the lever must be adjusted to keep the lever balanced in the horizontal position.

In order to analyze the experimental data and study the lever balance, the experimental data should be recorded in the table, and the simple table design is the ability that junior high school graduates should have.

Solution:

(1) Right

(2) The design table is roughly as follows:

or

Comments: Check whether students have done experiments to explore the conditions of lever balance. It's hard to do this if they haven't done the experiment.

Third, use leverage to balance the conditions.

Example 3. (Xuzhou exam questions) A pole AB is long 1m, and its fulcrum is 0.4m away from the B end. Now, as shown in Figure 3, an object G 1 with a weight of 200N is hung at the A end. If you want to balance the lever, you should hang a multiple object G2 at the B end.

Figure 3

Analysis: A force and a force arm acting on the lever can be directly found out from the problem, and the other force arm can also be calculated. According to the lever balance condition, it is easy to find another force.

Solution: According to F 1l 1=F2l2, G2=300N is calculated. Note: the corresponding arm of G 1 is not1m.

Comments: Check whether candidates (1) understand the conditions of leverage balance;

(2) Whether the lever balance condition can be applied to solve the lever balance problem.

Example 4. (Xuzhou Examination) In Figure 4, the polished rod OA can rotate around the O point, and the object G with the length of OA of 1.8m and a weight of 120N is hung at the B point with a rope, which is 0.6m away from the O point. As shown in Figure 5, to balance the position of OA, the minimum force on the A point is _ _ _ _ _ _ _ _ _.

Figure 4

Figure 5

Analysis: The moment arm l2 of the resistance F2 acting on the lever point B is OB', not OB. If the force acting on the lever point A is F 1 and the power arm is l 1, according to the lever balance condition, it is F 1l 1=F2l2. Since F2 and l2 are constants, in order to minimize the power F 1 acting on the lever A, the power arm l 1 must be maximized. It can be seen that only l 1=OA is the largest.

Solution:. According to the lever balance condition F 1L 1 = the minimum force acting on point a, the graph of this force is shown in Figure 5.

Comments: graphic methods to check students' understanding, resistance, force arm, resistance arm, lever balance condition and force.

Four. Application of lever test questions

Example 5. All kinds of scissors are paired levers. What kind of scissors are best for cutting hard objects? ()

Analysis: In order to cut hard objects, according to the lever balance condition F 1l 1=F2l2, the power arm must be used, that is, the labor-saving lever.

Solution: You should choose B scissors. When cutting hard objects, according to the lever balance condition F 1l 1=F2l2, the power arm, that is, the labor-saving lever, must be used.

Solution: You should choose B scissors.

Verb (abbreviation of verb) has the feature of "change"

Example 6. (Xuzhou City Examination) As shown in Figure 6, a weight G is hung at point B on the lever OA, and the A end is hung under the small circle E with a string, and the length AE of the string is equal to the radius of the arc. At this time, the lever is just in a horizontal state, and the point A coincides with the center of the arc ring CED. When the E-ring gradually slides clockwise from point C to point D, the force acting on the A end by the lifting rope will be ().

Figure 6

A. remain unchanged

B. Gradually increase

C. From big to small, and then from small to big

D. from small to large, and then from big to small.

Analysis: Because the force F 1 exerted by the string on the A end of the horizontal rod always goes up along the string, the direction of the force F 1 changes during the process of the E ring sliding clockwise from point C to point E and point D along the arc CED, resulting in the arm of force F 1 changing from small to large and then to small. In this process, the resistance F2 (equal to g) and the resistance arm l2 (.

Solution: Choose (c) the answer.

Comments: Test students: (1) Whether they understand the concept of moment arm; (2) Can you understand the lever balance condition? (3) Whether the lever balance condition can be applied to solve the lever problem with "variable" characteristics.

Six. Deformation lever test questions

Example 7. Wheel weight 100N, stuck in the mud pit. As shown in Figure 7, what is the minimum force that needs to be applied at point A to turn the wheel counterclockwise out of the mud pit? Draw a diagram of this force on the diagram.

Figure 7

Analysis: When the wheel rotates counterclockwise, the wheel rotates around the contact point O between the mud pit and the wheel, so the point O is the fulcrum. It can be seen that the wheel is a deformed lever, and the resistance F2 acting on the lever is the weight of the wheel, and the point of action is on the axis of the wheel, and its arm L2 = ob；; The arm l 1 of the minimum force (i.e. power) F 1 applied at point A must be equal to OA. According to the lever balance condition, the magnitude of F 1 can be calculated and the force diagram can be drawn.

Solution: Let the radius of the wheel be r, then. Because, according to the lever balance condition F 1l 1=F2l2, the minimum force f1= 25n acting on point A is obtained; The graph of this force is shown in Figure 8.

Figure 8

Comments: Check whether students can abstract the lever from the real thing, find out the fulcrum of the lever, the resistance and the resistance arm acting on the lever, and then apply the lever balance condition to solve the problem.

7. Comprehensive knowledge test questions

Example 8. (Yangzhou test) As shown in Figure 9, an object with a mass of 10kg is hung on the B end of a light lever, and the A end of the lever is tied to the ground with a string. The angle between the chord and the lever is 30, OA= 1m, OB=0.4m At this time, the lever is balanced in a horizontal position. Now put an object with a mass of 5kg at point O, and use the horizontal pulling force of F= 10N to make the object slide to the left at a constant speed of 0.1m/s. ask

(1) How far is the object from the O point, and the tension of the chord AC is exactly zero?

(2) What is the work and power F does when moving an object?

Figure 9

Analysis: When the object slides to the left with a horizontal pulling force of F= 10N, the object exerts a horizontal sliding friction force on the lever AB, which is equal to 10N. This force can be approximately regarded as passing through the fulcrum o of the lever, which does not affect the balance of the lever. When the tension of the string is zero, there are two forces that affect the lever balance; One is the force F (equal to G) acting on the B end of the lever, and the other is the pressure F 1 exerted on the lever when the object moves to the left of the fulcrum O (equal to the weight of the moving object). Using the lever balance condition, the moving distance of the object can be obtained, and then according to the time when the force acts on the object, the work and work done by the horizontal pulling force can be obtained.

Solution:

Using the lever balance condition F 1l 1=F2l2, it is found that when the tension of the chord AC is zero, the distance from the object to the O point is

Object motion time

Pull work

force

Comments: Test students: (1) whether they have solid basic knowledge, whether they can face many conditions, and exclude redundant conditions (such as the angle between the chord and the lever is 30, OA= 1m, etc.). ) and select useful conditions.

(2) Whether important laws such as lever balance condition, speed formula, work formula and power formula can be comprehensively applied to solve practical problems. Example 9. As shown in figure 10, a light rod OA can rotate around point O, with one end tied with a rope and the other end tied to point C of the vertical wall. A G weight is suspended at the midpoint B of the lever, and the lever is in a horizontal static state. It is known that the length of lever OA is 2l, and the distance from point O to point C is l. (1) Please draw the arm of force F on the diagram; (2) Find the magnitude of the pulling force f; (3) If the maximum pulling force that the rope can bear is 0, how far can the weight be hoisted from point O at most?

Figure 10

Analysis: According to the lever balance condition, the pull force F is required, and its arm DO must be found (as shown in figure 1 1). To sum up, because it is a public angle, there is. As can be seen from the formula, DO can be found as long as the length of AC is found, and AC can be found according to Pythagorean theorem.

Figure 1 1

Find the moment arm DO of the pulling force f, and use the lever balance condition to find out how far the weight can hang from O at most.

Solution: The moment arm of (1) pulling force f is shown in figure 1 1.

(2) in

because

that is

According to the leverage balance condition, there is, so Zhang Liwei.

(3) When the tension on the rope is set, the distance between the lifting point of the heavy object and the O point is,

Comments: Test students: (1) Whether they understand the concept of moment arm;

(2) Whether mathematical tools can be used to solve physical problems;

(3) Whether the lever balance conditions are mastered.

As can be seen from the above questions, in order to answer the lever question, students must have the following qualities:

(1) You can do experiments to study the lever balance conditions, and you can design tables to record the experimental data;

(2) Being able to abstract the lever from the real thing, find the fulcrum of the lever, the force and resistance acting on the lever, and understand the concept of the moment arm, you will find (make) the moment arm correctly;

(3) The force arm and the resistance arm can be calculated with the knowledge of geometry and triangle in mathematics;

(4) Understand the lever balance condition and apply it to solve the lever balance problem;

(5) Have solid mechanical knowledge and be able to answer comprehensive mechanical questions about levers.

About the direction of force: (1) When the force and resistance are on the same side of the fulcrum, the directions of the two forces are opposite; (2) When the force and resistance are on opposite sides of the fulcrum, the directions of the two forces are the same.