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

A fixed point is called a fulcrum.

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

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

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

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

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

Let's put experience

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

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

Rice. 25.2. Experiments to find the equilibrium condition of a lever

Lever equilibrium condition. The distance from the fulcrum to the straight line along which the force acts is called the arm of this force. Let us denote by F 1 and F 2 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 arms of these forces:

F 1 /F 2 = l 2 /l 1.

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

You can study the equilibrium condition of a lever experimentally in laboratory work № 11.

Do you know what a block is? This is a round thing with a hook that is used to lift loads to heights on construction sites.

Does it look 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 clip with a hook attached to the wheel axle. The block can be fixed or movable. A fixed block has a fixed axis and does not move when lifting or lowering a load. Not moving block helps change the direction of force. By throwing a rope over such a block, suspended at the top, we can lift the load upward, while ourselves being below. However, using a fixed block does not give us any gain in strength. We can imagine a block in the form of a lever rotating around a fixed support - the axis of the block. Then the radius of the block will be equal to the arms applied on both sides of the forces - the traction force of our rope with a load on one side and the gravitational force of the load on the other. The shoulders will be equal, so there is no gain in strength.

The situation is different with a moving block. The moving block moves along with the load, as if it were lying 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 impact of 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 is known, is twice the radius; accordingly, the arms differ in length by two times, and the gain in strength obtained with the help of a movable block is equal to two. In practice, a combination of a fixed block and a movable block is used. Pinned at the top fixed block does not give a gain in strength, but it helps to lift a 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 provide benefits in operation? Work is the product of the distance traveled and the force applied. Consider a lever with arms that differ by a factor of two in arm length. This lever will give us a gain in strength twice as large, however, twice as much leverage will travel twice as far. That is, despite the gain in strength, perfect work will be the same. This is the equality of work when using simple mechanisms: the number of times we gain in strength, the number of 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 make a person’s work easier, but do not reduce the work he does. They simply help translate one type of effort into another, more convenient in a particular situation.

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 power.

Lever equilibrium condition: the lever is in equilibrium if the forces applied to the lever F 1 And F 2 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 = 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 it is fulfilled « Golden Rule» mechanics (if friction and mass of the lever can be neglected).

By applying some force to a long lever, you can use the other end of the lever to lift a load whose weight greatly exceeds this force. This means that by using leverage, a gain in power can be achieved. When using leverage, a gain in power is necessarily accompanied by an equal loss along the way.

Moment of power. Rule of Moments

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

Rule of Moments: A lever is in equilibrium if the sum of the moments of forces tending to rotate the lever in one direction is equal to the sum of the moments of forces tending to rotate it in the opposite direction. This rule is valid for any rigid body capable of rotating around a fixed axis.

The moment of force characterizes the rotating action of the force. This action depends on both the force and its leverage. 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 using a screwdriver with a wider handle, etc.

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

Sections: Physics

Lesson type: lesson in learning new material

Lesson objectives:

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

Basic concepts:

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

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

DURING THE CLASSES

I. Organizational stage

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

II. Homework check stage

1. Revealing that the whole class has completed homework.
2. Visual check of tasks in the workbook.
3. Finding out the reasons for the failure of individual students to complete the task.
4. Questions about 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 a stud in the middle. ( Scissors)

2. Two sisters were swinging - they were seeking the truth, and when they achieved it, they stopped. ( Scales)

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

4. What kind of miracle giant is this?
Reaches his hand to the clouds
Does work:
Helps build a house. ( Crane)

– Look carefully at the answers again and name them in one word. “Weapon, machine” translated from Greek means “mechanisms.”

Mechanism– from Greek word"????v?" – weapon, construction.
Car– from the Latin word “ machina" – construction.

– 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 your notebooks, write down the date and topic of the lesson: “ Simple mechanisms. Conditions for the equilibrium of a lever."
– What goal should we set for you today in class...

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, were said by Archimedes more than 2000 years ago. But people still remember them and pass them on 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 a lever was our distant prehistoric ancestor, who used a stick to move heavy stones in search of edible roots or small animals hiding under the roots. Yes, yes, after all, an ordinary stick that has a fulcrum around which it can be rotated is a 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 had no idea about the law of leverage, but they already knew well that a lever in skillful hands turns a heavy load into a light one.
Lever arm- is an integral part of almost every modern car, machine, mechanism. An excavator digs a ditch - its iron “arm” with a bucket acts as a lever. The driver changes the speed of the car using the gear shift lever. The pharmacist hangs the powders on very precise pharmacy scales; the main part of these scales is the lever.
When 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 an inclined plane.
2nd examines the lever.
The 3rd is studying the block.
The 4th is studying the gate.
The 5th studies the wedge.
6th studies the screw.

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

Based on the students' answers, we draw up a diagram. ( Appendix 2 )

– What mechanisms did you get acquainted with...
– What are simple mechanisms used for? ...

Lever arm- a rigid body capable of rotating around a fixed support. In practice, the role of a lever can be played by a stick, board, crowbar, etc.
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 lowered from the fulcrum to the line of action of the force).
Typically, the forces applied to the lever can be considered the weight of the bodies. We will call one of the forces the resistance force, the other the driving force.
On the image ( Appendix 4 ) you see an equal-arm lever, which is used to balance forces. An example of such a use of leverage is a scale. What do you think will happen if one of the forces doubles?
That's right, the scales will be out of balance (I show it on ordinary scales).
Do you think there is a way to balance greater power with lesser power?

Guys, I suggest you in the course mini-experiment derive the equilibrium condition for the lever.

Experiment

There are laboratory levers on the tables. Let's find out together when the lever will be in equilibrium.
To do this, hang it on a hook with right side one weight 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.
• As many times as the strength has increased, so many times has the shoulder decreased,

- Let's formulate lever balance rule:

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

– Now try to write this rule mathematically, i.e. the formula:

F 1 l 1 = F 2 l 2 => F 1 / F 2 = l 2 / l 1

The rule of lever equilibrium was established by Archimedes.
From this rule it follows that a smaller force can be used to balance a larger force using a lever.

Relaxation: Close your eyes and cover them with your palms. Imagine a sheet of white paper and try to mentally write your first and last name on it. Place a period at the end of the entry. Now forget about the letters and remember only the period. It should appear to you to be moving from side to side with a slow, gentle rocking motion. You have relaxed... remove your palms, open your eyes, you and I are returning to the real world full of strength and energy.

V. Stage of consolidation of new knowledge

1. Continue the sentence...

• Lever is... a rigid body that can rotate around a fixed support
• The lever is in balance if... the forces acting on it are inversely proportional to the arms of these forces.
• Leverage of power 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 mechanisms include... lever and its varieties: – wedge, screw; inclined plane and its varieties: wedge, screw.
• Simple mechanisms are needed for... in order to gain power

2. Fill out the table (by yourself):

Find simple mechanisms in devices

No.	Device name	Simple mechanisms
1	scissors
2	meat grinder
3	saw
4	ladder
5	bolt
6	pliers,
7	scales
8	axe
9	jack
10	mechanical drill
11	pen sewing machine, bicycle pedal or handbrake, piano keys
12	chisel, knife, nail, needle.

MUTUAL CONTROL

Transfer the assessment after mutual control to the self-assessment card.

Was Archimedes right?

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

VI. 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 students worked especially diligently (grades).

2. Homework

Everyone: § 55-56
For those interested: create a crossword puzzle on the topic “Simple mechanisms at my home”
Individually: prepare messages or presentations “Levers in wildlife”, “The power of our hands”.

- Class is over! Goodbye, all the best to you!