Formula for the equilibrium condition of a lever. Simple mechanisms: lever, balance of forces on the lever. II. Homework check stage

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

Physical 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:

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.

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 for 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 tools, 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)

Summarizing.

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 a person uses in everyday life, writing them down in a table:

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. An immovable support in our in this case 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 an unliftable with bare hands cargo. 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.

§ 35. MOMENT OF FORCE. LEVER EQUILIBRIUM CONDITIONS

A lever is the simplest and not the most ancient mechanism that a person uses. Scissors, wire cutters, a shovel, a door, an oar, a steering wheel and a gear shift knob in a car all operate on the principle of a lever. Already during the construction of the Egyptian pyramids, stones weighing ten tons were lifted using levers.

Lever arm. Leverage rule

A lever is a rod that can rotate around a fixed axis. Axis O, perpendicular to the plane of Figure 35.2. The right arm of a lever of length l 2 is acted upon by a force F 2 , and the left arm of a lever of length l 1 is acted by a force F 1 The lengths of the lever arms l 1 and l 2 are measured from the axis of rotation O to the corresponding lines of force F 1 and F 2 .

Let the forces F 1 and F 2 be such that the lever does not rotate. Experiments show that in this case the following condition is satisfied:

F 1 ∙ l 1 = F 2 ∙ l 2 . (35.1)

Let's rewrite this equality differently:

F 1 /F 2 =l 2 /l 1. (35.2)

The meaning of expression (35.2) is as follows: how many times is the shoulder l 2 longer than the shoulder l 1, the same number of times the magnitude of the force F 1 is greater than the magnitude of the force F 2 This statement is called the rule of leverage, and the ratio F 1 / F 2 is the gain in strength.

While we gain in strength, we lose in distance, since we have to lower our right shoulder a lot in order to slightly raise the left end of the lever arm.

But the boat's oars are fixed in the rowlocks so that we pull the short arm of the lever, applying significant force, but we get a gain in speed at the end of the long arm (Fig. 35.3).

If the forces F 1 and F 2 are equal in magnitude and direction, then the lever will be in equilibrium provided that l 1 = l 2, that is, the axis of rotation is in the middle. Of course, in this case we will not get any gain in strength. The car's steering wheel is even more interesting (Fig. 35.4).

Rice. 35.1. Tool

Rice. 35.2. Lever arm

Rice. 35.3. Oars give you a speed boost

Rice. 35.4. How many levers do you see in this photo?

Moment of power. Lever equilibrium condition

The force arm l is the shortest distance from the axis of rotation to the line of action of the force. In the case (Fig. 35.5), when the line of action of force F forms an acute angle with wrench, the arm of the force l is less than the arm l 2 in the case (Fig. 35.6), where the force acts perpendicular to the key.

Rice. 35.5. Leverage l less

The product of force F and arm length l is called the moment of force and is denoted by the letter M:

M = F ∙ l. (35.3)

The moment of force is measured in Nm. In the case (Fig. 35.6), it is easier to rotate the nut, because the moment of force with which we act on the key is greater.

From relation (35.1) it follows that in the case when two forces act on the lever (Fig. 35.2), the condition for the absence of rotation of the lever is that the torque of the force that tries to rotate it clockwise (F 2 ∙ l 2) should equal to the moment of force that tries to rotate the lever counterclockwise (F 1 ∙ l 1).

If more than two forces act on a lever, the rule for equilibrium of the lever sounds like this: the lever does not rotate around a fixed axis if the sum of the moments of all forces rotating the body clockwise is equal to the sum of the moments of all forces rotating it counterclockwise.

If the moments of forces are balanced, the lever rotates in the direction in which the larger moment rotates it.

Example 35.1

A load weighing 200 g is suspended from the left arm of a lever 15 cm long. At what distance from the axis of rotation must a load of 150 g be suspended so that the lever is in equilibrium?

Rice. 35.6. Shoulder l is larger

Solution: The moment of the first burden (Fig. 35.7) is equal to: M 1 = m 1 g ∙ l 1.

Moment of the second load: M 2 = m 2 g ∙ l 2.

According to the lever equilibrium rule:

M 1 = M 2, or m 1 ∙ l 1 = m 2 g ∙ l 2.

Hence: l 2 = .

Calculations: l 2 = = 20 cm.

Answer: The length of the right arm of the lever in the equilibrium position is 20 cm.

Equipment: light and fairly strong wire approximately 15 cm long, paper clips, ruler, thread.

Progress. Place a loop of thread on the wire. Approximately in the middle of the wire, tighten the loop tightly. Then hang the wire on a thread (attaching the thread, say, table lamp). Balance the wire by moving the loop.

Load the lever on both sides of the center with chains of different numbers of paper clips and achieve balance (Fig. 35.8). Measure the lengths of the arms l 1 and l 2 with an accuracy of 0.1 cm. We will measure the force in “paper clips”. Record your results in a table.

Rice. 35.8. Lever Equilibrium Study

Compare the values ​​of A and B. Draw a conclusion.

Interesting to know.

*Problems with accurate weighing.

The lever is used in scales, and the accuracy of weighing depends on how accurately the length of the arms matches.

Modern analytical balances can weigh to the nearest ten-millionth of a gram, or 0.1 microgram (Fig. 35.9). Moreover, there are two types of such scales: some for weighing light loads, others - heavy ones. You can see the first type in a pharmacy, jewelry workshop or chemical laboratory.

Large load scales can weigh loads up to a ton, but are still very sensitive. If you step on such a weight and then exhale the air from your lungs, it will react.

Ultramicrobalances measure mass with an accuracy of 5 ∙ 10 -11 g (five hundred-billionths of a gram!)

When weighing on precise scales many problems arise:

a) No matter how hard you try, the arms of the rocker arm are still not equal.

b) The scales, although small, differ in mass.

c) Starting from a certain threshold of accuracy, the weight begins to react to the force of the air, which is very small for bodies of ordinary sizes.

d) When placing the scales in a vacuum, this disadvantage can be eliminated, but when weighing very small masses, the impacts of air molecules begin to be felt, which cannot be completely pumped out by any pump.

Rice. 35.9. Modern analytical balances

Two ways to improve the accuracy of unequal-arm scales.

1. Taring method. Removing the load using a bulk substance such as sand. Then we remove the weight and weigh out the sand. Obviously, the mass of the weights is equal to the true mass of the load.

2. Alternate weighing method. We weigh the load on a scale, which is located, for example, on an arm of length l 1. Let the mass of the weights, which leads to balancing of the scales, be equal to m 2. Then we weigh the same load in another bowl, which is located on an arm of length l 2. We get a slightly different mass of weights m 1. But in both cases the real mass of the load is m. In both weighings the following condition was met: m ∙ l 1 =m 2 ∙ l 2 and m ∙ l 2 = m 1 ∙ l 1 . Solving the system of these equations, we get: m = .

Topic for research

35.1. Construct a scale that can weigh a grain of sand and describe the problems you encountered in completing this task.

Let's sum it up

The force arm l is the shortest distance from the axis of rotation to the line of action of the force.

The moment of force is the product of force by the arm: M = F ∙ l.

The lever does not rotate if the sum of the moments of forces that rotate the body clockwise is equal to the sum of the moments of all forces that rotate it counterclockwise.

Exercise 35

1. In what case does leverage give a gain in strength?

2. In which case is it easier to tighten the nut: fig. 35.5 or 35.6?

3. Why door knob maximum distance from the axis of rotation?

4. Why can you lift a larger load with an arm bent at the elbow than with an outstretched arm?

5. Long rod It is easier to hold it horizontally by holding it by the middle than by the end. Why?

6. By applying a force of 5 N to a lever arm 80 cm long, we want to balance the force of 20 N. What should be the length of the second arm?

7. Let us assume that the forces (Fig. 35.4) are equal in magnitude. Why don't they balance?

8. Can an object be balanced on a scale so that over time the balance is disrupted by itself, without external influences?

9. There are 9 coins, one of them is counterfeit. She is heavier than others. Suggest a procedure by which a counterfeit coin can be unambiguously detected in a minimum number of weighings. There are no weights for weighing.

10. Why does a load whose mass is less than the sensitivity threshold of the scales not disturb their equilibrium?

11. Why is precision weighing carried out in a vacuum?

12. In what case will the accuracy of weighing on a lever scale not depend on the action of the Archimedes force?

13. How is the length of the lever arm determined?

14. How is the moment of force calculated?

15. Formulate the rules for lever equilibrium.

16. What is the gain in power in the case of leverage?

17. Why does the rower grab the short arm of the lever?

18. How many levers can be seen in Fig. 35.4?

19. Which balances are called analytical?

20. Explain the meaning of formula (35.2).

3 history of science. The story has reached our times about how the king of Syracuse, Hiero, ordered the construction of a large three-deck ship - a trireme (Fig. 35.10). But when the ship was ready, it turned out that it could not be moved even with the efforts of all the inhabitants of the island. Archimedes came up with a mechanism consisting of levers and allowed one person to launch the ship. The Roman historian Vitruvius spoke about this event.

Even before our era, people began to use levers in construction. For example, in the picture you see the use of leverage in the construction of the pyramids in Egypt. A lever is a rigid body that can rotate around a certain axis. A lever is not necessarily a long and thin object. For example, a wheel is also a lever, since it is a rigid body rotating around an axis.

Let us introduce two more definitions. The line of action of a force is a straight line passing through the force vector. We call the shortest distance from the axis of the lever to the line of action of the force the shoulder of the force. From your geometry course, you know that the shortest distance from a point to a line is the perpendicular distance to this line.

Let us illustrate these definitions with an example. In the picture on the left, the lever is the pedal. The axis of its rotation passes through point O. Two forces are applied to the pedal: F1 is the force with which the foot presses on the pedal and F2 is the elastic force of the tensioned cable attached to the pedal. Drawing through vector F1 the line of force action (shown blue), and by lowering a perpendicular from point O onto it, we get the segment OA - the arm of force F1.

With force F2 the situation is even simpler: the line of its action need not be drawn, since the vector of this force is located more successfully. Dropping a perpendicular from point O to the line of action of force F2, we obtain segment OB—the arm of this force.

With the help of a lever, a small force can balance a large force. Consider, for example, lifting a bucket from a well. The lever is a well gate - a log with a curved handle attached to it. The axis of rotation of the gate passes through the log. The lesser force is the force of the person's hand, and the greater force is the force with which the bucket and the hanging part of the chain are pulled down.

The drawing on the left shows the gate diagram. You can see that the arm of greater force is segment OB, and the arm of lesser force is segment OA. It is clearly seen that OA > OB. In other words, the lower-strength arm is larger than the higher-strength arm. This pattern is true not only for the gate, but also for any other lever. In more general view it sounds like this:

When a lever is in equilibrium, the arm of the smaller force is as many times larger than the arm of the larger force, how many times the larger force is greater than the smaller one.

Let's illustrate this rule using a school lever with weights. Take a look at the picture. In the first lever, the arm of the left force is 2 times greater than the arm of the right force, therefore, the right force is twice as great as the left force. On the second lever, the shoulder of the right force is 1.5 times greater than the shoulder of the left force, that is, the same number of times as the left force is greater than the right force.

So, when two forces are in balance on a lever, the larger of them always has a smaller leverage and vice versa.