The condition for equality of lever arms is not. Lever equilibrium condition

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 competent 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
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.”

PROGRESS OF THE LESSON

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 the 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- 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 to each group in work map. (Appendix 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- 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.
In the picture ( 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 one weight 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.
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... solid, which 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!

Lever is a solid body that has an axis of rotation or support.

Types of levers:

§ lever of the first kind

§ lever of the second type.

Points of application of forces acting on first class lever , lie on both sides of the fulcrum.

First class lever diagram.

t. O – fulcrum of the lever (axis of rotation of the lever);

t. 1 and t. 2 – points of application of forces and, respectively.

Line of action of force – a straight line coinciding with the force vector.

Shoulder of power – the shortest distance from the axis of rotation of the lever to the line of action of the force.

Designation: d.

f 1 – line of force action

f 2 – line of force action

d 1 – force arm

d 2 – force arm

Algorithm for finding the leverage:

a) draw a line of action of the force;

b) lower the perpendicular from the fulcrum or axis of rotation of the lever to the line of action of the force;

c) the length of this perpendicular will be the arm of this force.

Exercise:

Draw the arm of each force:

t. O is the axis of rotation of a solid body.

Lever balance rule (established by Archimedes):

If two forces act on a lever, then it is in equilibrium only when the forces acting on it are inversely proportional to their arms.

Comment: we assume that the friction force and the weight of the lever are equal to zero.

Moment of power.

The forces acting on the lever can cause it to rotate either clockwise or counterclockwise.

moment of force – physical quantity, which characterizes the rotating effect of the force and is equal to the product of the force modulus and the shoulder.

Designation: M

SI unit of torque: 1 newton meter (1 Nm).

1Nm – moment of force in 1N, the arm of which is equal to 1m.

Rule of Moments: A lever is in equilibrium under the action of forces applied to it if the sum of the moments of the forces rotating it clockwise is equal to the sum of the moments of the forces rotating it counterclockwise.

If two forces act on a lever, then the moment rule is formulated as follows: A lever is in equilibrium under the action of two forces if the moment of the force rotating it clockwise is equal to the moment of the force rotating it counterclockwise.

Note: From the rule of moments for the case of two forces applied to the lever, one can obtain the rule of equilibrium of the lever in the form that was discussed in paragraph 38.

, ═> , ═> .

Blocks.

Block – a wheel with a groove having an axis of rotation. The gutter is designed for thread, rope, cable or chain.

There are two types of blocks: fixed and movable.

Fixed block a block is called whose axis does not move when the block operates. Such a block does not move when the rope moves, but only rotates.

Movable block a block is called, the axis of which moves when the block operates.

Since a block is a solid body that has an axis of rotation, i.e., a type of lever, we can apply the lever equilibrium rule to the block. Let's apply this rule, assuming that the friction force and the weight of the block are equal to zero.

Let's consider a stationary block.

The fixed block is a lever of the first kind.

t. O – axis of rotation of the lever.

AO = d 1 – force arm

OB = d 2 – force arm

Moreover, d 1 = d 2 = r, r is the radius of the wheel.

At equilibrium M 1 = M 2

P d 1 = F d 2 ═>

Thus, a stationary block does not provide any gain in strength, it only allows you to change the direction of the force.

Let's consider a moving block.

The moving block is a lever of the second type.

Today in the lesson we will look into the world of mechanics, we will learn to compare and analyze. But first, let’s complete a number of tasks that will help open the mysterious door wider and show all the beauty of such a science as mechanics.

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Municipal budgetary educational institution

Mikheykovskaya Secondary School

Yartsevo district, Smolensk region

Lesson on the topic

“Simple mechanisms.

Application of the law of equilibrium

lever to block"

7th grade

Compiled and conducted

Physics teacher of the highest category

Lavnyuzhenkov Sergey Pavlovich

2017

Lesson Objectives (planned learning outcomes):

Personal:

- developing skills to manage one’s educational activities;

Formation of interest in physics in the analysis of physical phenomena;

Formation of motivation by setting cognitive tasks;

Formation of the ability to conduct dialogue on the basis of equal relations and mutual respect;

Development of independence in acquiring new knowledge and practical skills;

Development of attention, memory, logical and creative thinking;

Students' awareness of their knowledge;

Metasubject:

Development of the ability to generate ideas;

Develop the ability to determine goals and objectives of activities;

Conduct an experimental study according to the proposed plan;

Based on the results of the experiment, formulate a conclusion;

Develop communication skills when organizing work;

Independently evaluate and analyze your own activities from the perspective of the results obtained;

Use various sources for information.

Subject:

Forming an idea of simple mechanisms;

Formation of the ability to recognize levers, blocks, inclined planes, gates, wedges;

Do simple mechanisms provide gains in strength?

Formation of the ability to plan and conduct an experiment, and formulate a conclusion based on the results of the experiment.

Lesson progress

Item no.

Teacher activities

Student activity

Notes

Organizational stage

Preparing for the lesson

The stage of repetition and testing of mastery of the material covered

Working with pictures, working in pairs - oral storytelling

According to plan, mutual knowledge testing

Stage of updating knowledge, goal setting

Introduction of the concept of “simple mechanisms”, according to

Organizational and activity stage: assistance and control over the work of students

Working with a textbook, drawing up a diagram

Self-esteem

Fizminutka

Exercise

Organizational and activity stage: practical work, actualization and goal setting

Installation assembly

Introduction of the concept of “leverage”, goal setting

Introduction of the concept of “shoulder strength”

Experimental confirmation of the lever equilibrium rule

Self-esteem

Stage of practical consolidation of acquired knowledge: problem solving

Solve problems

Peer review

Stage of consolidation of the material covered

Answer questions

Teacher:

There are several pictures on the screen:

The Egyptians build a pyramid (lever);

A man lifts water (with the help of a gate) from a well;

People roll a barrel onto a ship (inclined plane);

A man lifts a load (block).

Teacher: What do these people do? (mechanical work)

Plan your story:

1. What conditions are necessary to perform mechanical work?

2. Mechanical work is …………….

3. Symbol mechanical work

4. Work formula...

5. What is the unit of measurement for work?

6. How and after which scientist is it named?

7. In what cases is work positive, negative or zero?

Teacher:

Now let's look at these pictures again and pay attention to how these people do their work?

(people use a long stick, a collar, an inclined plane device, a block)

Teacher: How can you call these devices in one word?

Students: Simple mechanisms

Teacher: Right! Simple mechanisms. What topic do you think we will talk about in class today?

Students: About simple mechanisms.

Teacher: Right. The topic of our lesson will be simple mechanisms (writing the topic of the lesson in a notebook, a slide with the topic of the lesson)

Let's set the goals of the lesson:

Together with children:

Learn what simple mechanisms are;

Consider the types of simple mechanisms;

Lever equilibrium condition.

Teacher: Guys, what do you think simple mechanisms are used for?

Students: They are used to reduce the force we apply, i.e. to transform it.

Teacher: Simple mechanisms are found both in everyday life and in all complex factory machines, etc. Guys, which household appliances and devices have simple mechanisms.

Students: B Lever scales, scissors, meat grinder, knife, axe, saw, etc.

Teacher: What simple mechanism does a crane have?

Students: Lever (boom), blocks.

Teacher: Today we will take a closer look at one of the types of simple mechanisms. It is on the table. What kind of mechanism is this?

Students: This is a lever.

We hang weights on one of the arms of the lever and, using other weights, balance the lever.

Let's see what happened. We see that the shoulders of the weights are different from each other. Let's swing one of the lever arms. What do we see?

Students: After swinging, the lever returns to its equilibrium position.

Teacher: What is a lever?

Students: A lever is a rigid body that can rotate around a fixed axis.

Teacher: When is the lever in balance?

Students:

Option 1: the same number of weights at the same distance from the axis of rotation;

Option 2: more load – less distance from the axis of rotation.

Teacher: What is this relationship called in mathematics?

Students: Inversely proportional.

Teacher: With what force do the weights act on the lever?

Students: The weight of the body due to the gravity of the Earth. P=F cord = F

Teacher: This rule was established by Archimedes in the 3rd century BC.

Task: Using a crowbar, a worker lifts a box weighing 120 kg. What force does he apply to the larger arm of the lever if the length of this arm is 1.2 m, and the smaller arm is 0.3 m. What will be the gain in force? (Answer: Strength gain is 4)

Problem solving (independently with subsequent mutual verification).

1. The first force is equal to 10 N, and the shoulder of this force is 100 cm. What is the value of the second force if its shoulder is 10 cm? (Answer: 100 N)

2. A worker using a lever lifts a load weighing 1000 N, while he applies a force of 500 N. What is the arm of the greater force if the arm of the lesser force is 100 cm? (Answer: 50 cm)

Summing up.

What mechanisms are called simple?

What types of simple mechanisms do you know?

What is a lever?

What is leverage?

What is the rule for lever equilibrium?

What is the significance of simple mechanisms in human life?

2. List the simple mechanisms that you find at home and those that people use in everyday life, recording them in the table:

A simple mechanism in everyday life, in technology	Type of simple mechanism

3. Additionally. Prepare a report about one simple mechanism used in everyday life and technology.

Reflection.

Complete the sentences:

now I know…………………………………………………………..

I realized that…………………………………………………………………………………

I can……………………………………………………………………………………….

I can find (compare, analyze, etc.) …………………….

I did it myself correctly………………………………...

I applied the studied material in a specific life situation………….

I liked (didn’t like) the lesson …………………………………

Since ancient times, people have been using various auxiliary devices to make their work easier. How often, when we need to move a very heavy object, we take a stick or pole as an assistant. This is an example of a simple mechanism - a lever.

Application of simple mechanisms

There are many types of simple mechanisms. This is a lever, a block, a wedge, and many others. In physics, simple mechanisms are devices used to convert force. An inclined plane that helps to roll or pull heavy objects up is also a simple mechanism. The use of simple mechanisms is very common both in production and in everyday life. Most often, simple mechanisms are used to gain strength, that is, to increase the force acting on the body several times.

A lever in physics is a simple mechanism

One of the simplest and most common mechanisms, which is studied in physics in the seventh grade, is the lever. In physics, a lever is a rigid body capable of rotating around a fixed support.

There are two types of levers. For a lever of the first kind, the fulcrum is located between the lines of action of the applied forces. For a second-class lever, the fulcrum is located on one side of them. That is, if we are trying to move a heavy object with a crowbar, then the lever of the first kind is a situation when we place a block under the crowbar, pressing down on the free end of the crowbar. In this case, our fixed support will be a block, and the applied forces are located on both sides of it. And the lever of the second kind is when we, putting the edge of the crowbar under the weight, pull the crowbar up, thus trying to turn the object over. Here the fulcrum is located at the point where the crowbar rests on the ground, and the applied forces are located on one side of the fulcrum.

Law of balance of forces on a lever

Using a lever, we can gain strength and lift a load that is too heavy to lift with our bare hands. The distance from the fulcrum to the point of application of force is called the shoulder of force. Moreover, You can calculate the balance of forces on the lever using the following formula:

F1/ F2 = l2 / l1,

where F1 and F2 are the forces acting on the lever,
and l2 and l1 are the shoulders of these forces.

This is the law of lever equilibrium, which states: a lever is in equilibrium when the forces acting on it are inversely proportional to the arms of these forces. This law was established by Archimedes back in the third century BC. It follows from this that a smaller force can balance a larger one. To do this, it is necessary that the shoulder of lesser force be larger than the shoulder of greater force. And the gain in force obtained with the help of a lever is determined by the ratio of the arms of the applied forces.

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

A fixed point is called a fulcrum.

A familiar 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 loads have different weights, 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 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.