What is the rule of lever balance. Lever arm. Lever balance. Moment of power. The golden rule of mechanics

Do you know what a block is? This is such a round contraption with a hook, with the help of which at construction sites they lift loads to a height.

Looks like a lever? Hardly. However, the block is also a simple mechanism. Moreover, we can talk about the applicability of the law of equilibrium of the lever to the block. How is this possible? Let's figure it out.

Application of the law of equilibrium

The block is a device that consists of a wheel with a groove through which a cable, rope or chain is passed, as well as a holder with a hook attached to the wheel axle. The block can be fixed or movable. The fixed block has a fixed axle, and it does not move when the load is raised or lowered. The immovable block helps to change the direction of the force. Having thrown a rope over such a block, suspended at the top, we can lift the load up, while ourselves being at the bottom. However, the use of a fixed block does not give us a gain in strength. We can imagine a block as a lever rotating around a fixed support - the axis of the block. Then the radius of the block will be equal to the shoulders applied on both sides of the forces - the traction force of our rope with a load on one side and the gravity of the load on the other. The shoulders will be equal, respectively, there is no gain in strength.

The situation is different with the moving block. The movable block moves along with the load, as if it lies on a rope. In this case, the fulcrum at each moment of time will be at the point of contact of the block with the rope on one side, the load will be applied to the center of the block, where it is attached to the axis, and the traction force will be applied at the point of contact with the rope on the other side of the block . That is, the shoulder of the body weight will be the radius of the block, and the shoulder of the force of our thrust will be the diameter. The diameter, as you know, is twice the radius, respectively, the arms differ in length by a factor of two, and the gain in strength obtained using the movable block is two. In practice, a combination of a fixed block with a movable block is used. An immovable block fixed at the top does not give a gain in strength, but it helps to lift the load while standing below. And the moving block, moving along with the load, doubles the applied force, helping to lift large loads to a height.

The golden rule of mechanics

The question arises: do the devices used give a gain in work? Work is the product of the distance traveled times the applied force. Consider a lever with arms that differ by a factor of two in the length of the arm. This leverage will give us a gain in strength twice, however, twice as much leverage will travel twice as far. That is, despite the gain in strength, the work done will be the same. This is the equality of work when using simple mechanisms: how many times we have a gain in strength, so many times we lose in distance. This rule is called the golden rule of mechanics., and it applies to absolutely all simple mechanisms. Therefore, simple mechanisms facilitate the work of a person, but do not reduce the work done by him. They simply help to translate one type of effort into another, more convenient in a particular situation.

Sections: Physics

Lesson type: learning lesson

Lesson Objectives:

• Educational:
  • familiarity with the use of simple mechanisms in nature and technology;
  • to form the skills of analyzing sources of information;
  • to establish experimentally the rule of equilibrium of the lever;
  • to form the ability of students to conduct experiments (experiments) and draw conclusions from them.
• Developing:
  • develop the ability to observe, analyze, compare, generalize, classify, draw up diagrams, formulate conclusions on the studied material;
  • develop cognitive interest, independence of thinking and intellect;
  • develop competent oral speech;
  • develop practical skills.
• Educational:
  • moral education: love for nature, a sense of comradely mutual assistance, the ethics of group work;
  • education of culture in the organization of educational work.

Basic concepts:

• mechanisms
• lever arm
• shoulder of strength
• block
• gate
• inclined plane
• wedge
• screw

Equipment: computer, presentation, handout (work cards), a lever on a tripod, a set of weights, a laboratory set on the topic "Mechanics, simple mechanisms".

DURING THE CLASSES

I. Organizational stage

1. Greeting.
2. Determination of absentees.
3. Checking the readiness of students for the lesson.
4. Checking the preparedness of the classroom for the lesson.
5. Organization of attention .

II. Homework check step

1. Revealing the fact that homework was done by the whole class.
2. Visual check of tasks in the workbook.
3. Finding out the reasons for the non-fulfillment of the task by individual students.
4. Questions on homework.

III. The stage of preparing students for active and conscious assimilation of new material

“I could turn the Earth with a lever, just give me a fulcrum”

Archimedes

Guess the riddles:

1. Two rings, two ends, and carnations in the middle. ( Scissors)

2. Two sisters rocked - they sought the truth, and when they achieved it, they stopped. ( Scales)

3. Bows, bows - will come home - stretch out. ( Axe)

4. What kind of miracle giant?
Stretches his hand to the clouds
Doing work:
Helps build a house. ( Crane)

- Look again carefully at the answers and call them in one word. "Tool, machine" in Greek means "mechanisms".

Mechanism- from the Greek word "????v?" - tool, building.
Car- from the Latin word " machine" – building.

- It turns out that an ordinary stick is the simplest mechanism. Who knows what it's called?
- Let's formulate the topic of the lesson together: ....
– Open notebooks, write down the date and the topic of the lesson: “Simple mechanisms. Lever equilibrium conditions.
- What is the goal we should set with you today in the lesson ...

IV. Stage of assimilation of new knowledge

“I could turn the Earth with a lever, just give me a fulcrum” - these words, which are the epigraph of our lesson, Archimedes said more than 2000 years ago. And people still remember them and pass from mouth to mouth. Why? Was Archimedes right?

- Levers began to be used by people in ancient times.
What do you think they are for?
- Of course, to make it easier to work.
- The first person to use the lever was our distant prehistoric ancestor, who moved heavy stones with a stick in search of edible roots or small animals hiding under the roots. Yes, yes, because an ordinary stick that has a fulcrum around which it can be turned is the real lever.
There is a lot of evidence that in ancient countries - Babylon, Egypt, Greece - builders widely used levers when lifting and transporting statues, columns and huge stones. At that time they did not know about the law of the lever, but they already knew well that the lever in capable hands turns a heavy load into a light one.
Lever arm- is an integral part of almost every modern machine, machine tool, mechanism. The excavator digs a ditch - its iron "arm" with a bucket acts as a lever. The driver changes the speed of the car using the gearshift lever. The pharmacist hangs the powders on a very precise pharmacy scales, the main part of these scales is the lever.
Digging up beds in the garden, the shovel in our hands also becomes a lever. All kinds of rocker arms, handles and gates are all levers.

- Let's get acquainted with simple mechanisms.

The class is divided into six experimental groups:

1st studies the inclined plane.
2nd examines the lever.
3rd is studying the block.
4th examines the gate.
5th is studying the wedge.
6th examines the screw.

The work is carried out according to the description proposed to each group in the work card. ( Annex 1 )

We draw up a diagram based on the answers of the students. ( Appendix 2 )

- What mechanisms did you get acquainted with ...
What are simple machines for? …

Lever arm- a rigid body capable of rotating around a fixed support. In practice, a stick, board, crowbar, etc. can play the role of a lever.
The lever has a fulcrum and a shoulder. Shoulder- this is the shortest distance from the fulcrum to the line of action of the force (i.e., the perpendicular dropped from the fulcrum to the line of action of the force).
Usually, the forces applied to the lever can be considered the weight of the bodies. One of the forces we will call the force of resistance, the other - the driving force.
On the image ( Appendix 4 ) you see an equal-arm lever that is used to balance forces. An example of such an application of a lever is a scale. What do you think will happen if one of the forces is doubled?
That's right, the scales will go out of balance (I show on ordinary scales).
Do you think there is a way to balance the greater power with the lesser?

Guys, I suggest you during mini experiment derive the equilibrium condition for the lever.

Experiment

There are laboratory levers on the tables. Let's find out together with you when the lever will be in balance.
To do this, hang one load on the hook on the right side at a distance of 15 cm from the axis.

• Balance the lever with one weight. Measure your left shoulder.
• Balance the lever, but with two weights. Measure your left shoulder.
• Balance the lever, but with three weights. Measure your left shoulder.
• Balance the lever, but with four weights. Measure your left shoulder.

– What conclusions can be drawn:

• Where there is more strength, there is less leverage.
• How many times the strength has increased, how many times the shoulder has decreased,

- Let's formulate lever balance rule:

The lever is in equilibrium when the forces acting on it are inversely proportional to the shoulders of these forces.

- And now try to write down this rule mathematically, that is, the formula:

F 1 l 1 = F 2 l 2 => F 1 / F 2 \u003d l 2 / l 1

The rule of equilibrium for a lever was established by Archimedes.
From this rule follows that a smaller force can be balanced by a leverage of a larger force.

Relaxation: Close your eyes and cover them with your palms. Imagine a sheet of white paper and try to mentally write your name and surname on it. Put a period at the end of the entry. Now forget about the letters and remember only the dot. It should appear to you as moving from side to side in slow, gentle wiggles. You are relaxed… remove your palms, open your eyes, we are returning to the real world full of strength and energy.

V. Stage of consolidation of new knowledge

1. Continue the phrase ...

• The lever is... solid, which can rotate around a fixed support
• The lever is in balance if... the forces acting on it are inversely proportional to the shoulders of these forces.
• The arm of strength is... the shortest distance from the fulcrum to the line of action of the force (i.e., the perpendicular dropped from the fulcrum to the line of action of the force).
• Strength is measured in...
• The leverage is measured in...
• Simple machines are... lever and its varieties: - wedge, screw; inclined plane and its varieties: wedge, screw.
• Simple mechanisms are needed for ... in order to get a gain in strength

2. Fill in the table (on your own):

Find simple mechanisms in devices

MUTUAL CONTROL

Transfer the assessment after peer review to the self-assessment chart.

Was Archimedes right?

Archimedes was sure that there is no such heavy load that a person would not lift - you just need to use the lever.
And yet Archimedes exaggerated the possibilities of man. If Archimedes knew how huge the mass of the Earth is, he would probably have refrained from the exclamation attributed to him by legend: “Give me a point of support, and I will lift the Earth!”. After all, in order to move the earth by only 1 cm, the hand of Archimedes would have to travel a distance of 10 18 km. It turns out that in order to move the Earth by a millimeter, the long arm of the lever must be greater than the short arm of 100,000,000,000 trillion. once! The end of this shoulder would have traveled 1,000,000 trillion. kilometers (approx.). And such a journey would take a man many millions of years!.. But this is the topic of another lesson.

VI. The stage of information to students about homework, instructions on how to complete it

1. Summing up: what new things were learned in the lesson, how the class worked, which of the students worked especially diligently (grades).

2. Homework

To all: § 55-56
For those who wish: make a crossword puzzle on the topic “Simple mechanisms in my house”
Individually: prepare messages or a presentation "Leverage in wildlife", "The strength of our hands".

- Lesson completed! Goodbye, all the best to you!

A lever is a rigid body that can rotate around a fixed point. The fixed point is called fulcrum. The distance from the fulcrum to the line of action of the force is called shoulder this strength.

Lever equilibrium condition: the lever is in equilibrium if the forces applied to the lever F1 And F2 tend to rotate it in opposite directions, and the modules of forces are inversely proportional to the shoulders of these forces: F1/F2 = l 2 /l 1 This rule was established by Archimedes. According to legend, he exclaimed: Give me a foothold and I will lift the earth .

For the lever, "golden rule" of mechanics (if friction and mass of the lever can be neglected).

By applying some force to a long lever, it is possible to lift a load with the other end of the lever, the weight of which far exceeds this force. This means that by using leverage, you can get a gain in strength. When using leverage, gain in strength is necessarily accompanied by the same loss in the way.

Moment of power. moment rule

The product of the force modulus and its arm is called moment of force.M = Fl , where M is the moment of force, F is the force, l is the arm of the force.

moment rule: A lever is in equilibrium if the sum of the moments of forces seeking to rotate the lever in one direction is equal to the sum of the moments of forces seeking to rotate it in the opposite direction. This rule is true for any rigid body that can rotate about a fixed axis.

The moment of force characterizes the rotating action of the force. This action depends on both strength and her shoulder. That is why, for example, when wanting to open a door, they try to apply force as far as possible from the axis of rotation. With the help of a small force, a significant moment is created, and the door opens. It is much more difficult to open it by applying pressure near the hinges. For the same reason, it is easier to unscrew the nut with a longer wrench, the screw is easier to remove with a screwdriver with a wider handle, etc.

The SI unit of moment of force is newton meter (1 N*m). This is a moment of force 1 N, having a shoulder of 1 m.

A lever is a rigid body that can rotate around a fixed point.

The fixed point is called the fulcrum.

A well-known example of a lever is a swing (Fig. 25.1).

When two people on a swing balance each other? Let's start with observations. Of course, you have noticed that two people on a swing balance each other if they have approximately the same weight and are approximately the same distance from the fulcrum (Fig. 25.1, a).

Rice. 25.1. Seesaw equilibrium condition: a - people of equal weight balance each other when they sit at equal distances from the fulcrum; b - people different weight balance each other out when the heavier one sits closer to the fulcrum

If these two are very different in weight, they balance each other only on the condition that the heavier one sits much closer to the fulcrum (Fig. 25.1, b).

Let us now pass from observations to experiments: let us find experimentally the conditions for the equilibrium of the lever.

Let's put experience

Experience shows that loads of equal weight balance the lever if they are suspended at the same distance from the fulcrum (Fig. 25.2, a).

If the goods have different weight, then the lever is in equilibrium when the heavier load is so many times closer to the fulcrum, how many times its weight is greater than the weight of the light load (Fig. 25.2, b, c).

Rice. 25.2. Experiments on finding the equilibrium condition of the lever

Lever equilibrium condition. The distance from the fulcrum to the straight line along which the force acts is called the shoulder of this force. Let F 1 and F 2 denote the forces acting on the lever from the side of the loads (see diagrams on the right side of Fig. 25.2). Let us denote the shoulders of these forces as l 1 and l 2 , respectively. Our experiments have shown that the lever is in equilibrium if the forces F 1 and F 2 applied to the lever tend to rotate it in opposite directions, and the modules of the forces are inversely proportional to the shoulders of these forces:

F 1 / F 2 \u003d l 2 / l 1.

This condition for the equilibrium of a lever was established experimentally by Archimedes in the 3rd century BC. e.

You can learn the equilibrium condition of a lever by experience in laboratory work № 11.