We see that with the help of simple mechanisms you can get a gain in power. Do simple mechanisms give a win in the work?

Calculate the work done by the force F when lifting a load using an inclined plane (see Fig. 1):

   \\ (~ A_F = Fl. \\)

Substitute the found values ​​of the force \\ (~ F = mg \\ frac hl \\) and get

   \\ (~ A_F = mg \\ frac hl l = mgh. \\)

So the job A  F is equal to the work that needs to be done to evenly lift the load to a height hwithout using an inclined plane.

Does not give a win in the work and lever. Indeed, if a balanced lever (Fig. 6) is set in motion, then the points of application of forces F  1 and F  2 at the same time make different movements Δ r  1 and Δ r  2 In this case (we consider the angle α   turning the lever small) Δ r 1 = l 1 α , Δ r 2 = l 2 α   Therefore, these forces will do the work. A 1 = F  1 Δ r 1 = F 1 l 1 α   and A 2 = F  2 Δ r 2 = F 2 l 2 α . Because F 1 l 1 = F 2 l  2, then A 1 = A 2 .

When using a fixed block, we see that the applied forces F  and mg  the paths traveled by the points of application of forces when lifting a load are also the same, and therefore the work is the same.

That by means of the mobile block to lift freight on height h, you need the end of the rope to which the force is applied F, move to 2 h. Consequently, A 1 = mgh  and \\ (~ A_2 = F \\ cdot 2h = \\ frac (mg) (2) 2h = mgh \\).

Thus, getting a win in force twice, lose twice in moving, therefore, the movable unit does not give a win in work.

The centuries-old practice has shown that none of the simple mechanisms gives a gain in work.

Even the ancient scholars formulated a rule (the "golden rule of mechanics") applied to all mechanisms: how many times we win in strength, how many times we lose in distance.

When considering simple mechanisms, we do not take into account friction, as well as the weight of the mechanisms themselves. In real conditions, this must be taken into account. Therefore, part of the work is done by force F  on the movement of individual parts of the mechanism and against the friction force. Work on lifting cargo A  p (useful work) will be less than full work BUT  (work done by force F).

The effectiveness of the mechanism is characterized by the coefficient of efficiency (efficiency of the mechanism):

Efficiency - a physical quantity equal to the ratio of useful work A  p for all work expended BUT:

   \\ (~ \\ eta = \\ frac (A_p) (A) \\ cdot 100%. \\)

Literature

Aksenovich L. A. Physics in secondary school: Theory. Tasks. Tests: Textbook. allowance for institutions providing obsch. environments, education / L.A. Aksenovich, N.N.Rakina, K.S. Farino; Ed. K.S. Farino. - Minsk: Adukatsyya i Vyhvanna, 2004. - C. 75-76.

The simple mechanisms considered by us are used in work when it is necessary to balance another force by the action of one force.

The question naturally arises:  giving a gain in power or on the road, do simple mechanisms of scoring not give in the work? The answer to this question can be obtained from experience.

Having balanced on the lever two forces of F1 and F2 of some kind different in magnitude (Fig. 170), they set the lever in motion. It turns out that at the same time and the same time, the point of application of a smaller force F2 travels the larger path s2, and the point of application of a larger force F1 is smaller ways1. MeasuringThese paths and power modules find that the lengths of the paths traversed by the points of application of forces on the lever are inversely proportional to the forces:

Thus, acting on the long arm of the lever, we win in strength, but at the same time as many times, we lose in the length of the path.

The work of force on the path is work. Our experiments show that the work done at both ends of the lever, equal to each other:

So, when using the lever, no gain in work is obtained.

Using the lever, we can win either in strength or in distance. If we apply force to a long arm, then we will win in strength, but in so much same time we lose in the distance. Acting on the short lever arm, we will win in the distance, but we will lose in force the same time.

There is a legend that Archimedes, delighted with the discovery of the rule of lever, exclaimed: “Give me a fulcrum and I will raise the Earth!”

Of course, Archimedes could not cope with such a task, even if he was given a fulcrum and a lever of the desired length. For lifting Land just 1 cm long lever shoulder should  It would describe an arc of great length. It would take millions of years to move the long end of the lever along this path, for example at a speed of 1 m / s.

Does not give a win in the work and the type of lever - fixed block which is easy  make sure on experience. The paths traversed by the points of application of the forces P and F are the same, the forces are the same, and therefore the work is the same.

It is possible to measure and compare among themselves the work performed by the mobile unit. That by means of the mobile block to lift freight on height h, you need the end of the rope to which the dynamometer is attached,  as experience shows (Fig. 171), move to 2h. Thus, receiving a gain in force of 2 times, lose 2 times in the way, therefore, the mobile unit does not give a gain in work.

The centuries-old practice has shown that none of the mechanisms gives a gain in work. Apply different mechanisms to depending on working conditions  win in force or in transit.

Even the ancient scientists knew the rule applicable to all mechanisms: how many times we win in strength, how many times we lose in distance. This rule is called the “golden rule” of mechanics.

Questions  1. What is the relationship between the forces acting on the lever and the shoulders of these forces? 2. What is the relationship between the paths covered by the points of application of forces on the lever and these forces? 3. Is it possible get a win with a lever  plans are accepted? What then lose? 4. How many times do they lose on the way, using a mobile unit to lift cargo? 5. What is the “golden rule” of mechanics?

Exercises.

1. With the help of the movable block, the load was lifted to a height of 1.5 m. How long was the free end of the rope extended?
2. With the help of the movable block, the load was raised to a height of 7 m. What kind of work did the worker do when lifting the load, if he applied force to the end of the rope  160 N? What work will the worker do if he lifts this load to a height of 7 m without a block? (The weight of the block, and the friction force is not taken into account.)
3. How to apply a block to win in the distance?
4. How can fixed and moving blocks be combined with each other in order to get a 4-fold gain in strength? 6 times?

The task.

Prove that the law of equality of work (the “golden rule” of mechanics) is applicable to a hydraulic machine. Disregard friction between the pistons and vessel walls.

Note. Use for the proof of figure 132. When a small piston under the action of a force F1 drops down to a distance h1 it displaces some volume of fluid. At the same amount increases the volume of fluid under a large piston, which in this case rises to a height h2.

§ 62. Equality of work when using simple mechanisms. The Golden Rule of Mechanics - Physics Grade 7 (Peryshkin)

Short description:

We have already reviewed a few simple mechanisms. Some studied in great detail (lever, block), others just mentioned. We must have already understood that all simple mechanisms make life easier for a person. They either give a gain in strength, or allow you to change the direction of the force, thereby making a person’s actions more convenient.
  But we know such a physical quantity as work. The question naturally arises: how much do we benefit from using simple mechanisms? The answer is discouraging: no. None of the simple mechanism of winning in the work does not.
  Paragraph sixty-two comes to this conclusion by calculation. First it is done for a lever. Then the output spreads to the fixed block, then to the movable one.
  Simple mechanisms apply. To get a gain in strength or in distance. It is impossible to get a win in both. Winning one, you lose the other. This is the "golden rule" of mechanics. It was known to people even in antiquity. Now you will know him too.

Problem solving on the topic: Equality of work when using simple mechanisms. "The golden rule of mechanics"

LESSON OBJECTIVES:Update knowledge on the subject of “Simple Mechanisms” and learn the general position for all varieties of simple mechanisms, which is called the “golden rule” of mechanics.

Prove that the simple mechanisms used in the work, give a gain in strength, and on the other hand, allow you to change the direction of body movement under the action of force;

To cultivate an intellectual culture in leading students to an understanding of the basic rule of simple mechanisms: - to form the ability to summarize known data based on the selection of the main thing;

Generate elements of creative search based on the method of generalization.

During the classes

1.Organization moment

2. Check homework

Front-end survey:

1. What devices are called simple mechanisms, what are they for?

2. What you know the simplest mechanisms give examples?

3.What is a lever? What is it for?

4. What is called the shoulder of power? Moment of power?

5. Formulate the equilibrium condition of the lever?

6. Formulate the “golden rule of mechanics”

7. Why do the door handle is attached not to the middle of the door, and at its edge.

8. Is it possible to turn the Earth with a lever, having a fulcrum? Justify the answer.

3. Solving tasks

Task:   The length of the smaller lever arm is 5 cm, the larger one is 30 cm. The force of 12N acts on the smaller arm. What force must be applied to a larger shoulder to balance the lever? Find the win in force?

Given: Si: Decision:

l 1 = 5 cm 0.05 m 1) We write the equilibrium condition of the lever:

l 2 = 30 cm 0.3m

F 1 = 12 N Express from it F 2:

F 2 =?

F 1 / F 2 =? 2) Find the gain in power, that is

.

Answer:   F 2 = 2H, F 1 / F 2 = 6H.

According to the model solve the problem:The 300H force acts on the smaller lever arm, and 20N - on the larger arm. The length of the smaller shoulder is 5 cm. Determine the length of the larger shoulder. Make a drawing.

Check yourself (Answer: 0.75m)

According to the model solve the problem:  At the ends of the lever act forces 25N and 150N. The distance from the fulcrum to a greater force of 3 cm. Determine the length of the lever, if under the action of these forces it is in equilibrium?

Test yourself (Answer: 0.21m)

Task:   With the help of a lever, a weight of 200 kg was lifted. How high the load was, if the force acting on the long arm of the lever made 400 j.

Let's make an explanatory picture:

l 2

Given: Si: Decision:

m 1 = 200 kg 1) Let us write the mathematical rule of mechanics: А 1 = А 2

A 2 = 400 J 2) By definition, job  - the product of the force acting along the movement

h =? body, the path that the body takes under the influence of this force. Then:

And 1 = F 1 · h 1

Express from this formula h 1:

3) To find F 1, we use the formula for finding the force of gravity of the load:

F 1 = F strands = m 1 g = 200 kg · 10N / kg = 2000N

4) Given that A 1 = A 2, we calculate h 1:

Answer:   h 1 = 0,2 N.

According to the model solve the problem:  With the help of a lever, the door weighing 0.84 kN was lifted slightly, acting on a long arm with a force of 30N. In this case, the mechanical work was done 26J. At what height was the door raised, and how large is the distance that the end of the long arm of the lever moved?

Test yourself (Answer: to a height of 3.1 cm; 8.7 cm) (at home)

Homework Think of a problem on the topic being studied and solve it. Pov par 47

Equality of work when using simple mechanisms. The “golden rule” of mechanics.

• Physics teacher Puchkova SA
• MBOU Sukhovskaya SOSH

• Devices that transform forces are called mechanisms.

•   lever (block, gate),
•   inclined plane (wedge, screw).

• Application

•   The rule of the lever underlies the actions of various kinds of tools used in everyday life and technology where a gain in strength or path is required.

• A fixed block is a block whose axis is fixed and does not rise and fall when lifting loads.

• A movable block is a block whose axis rises and falls with the load. He gives a power gain of 2 times.

• In practice, use a combination of a movable unit with a fixed. Fixed block is used for convenience. He does not win in strength, but changes the direction of the force.

• Building

• The medicine

• Screw

•   Simple mechanisms used in ancient times.

• Using

• goal

•   In order to supply water from the lower level of a river or canal to the upper one, for example, to another canal through which it will flow further "by itself", a simple but very effective technical device was invented - shaduf. He looks like a crane - a long lever with a counterweight.

•   The Greeks tried to reduce the amount of manual labor using construction equipment. In the 6th century BC, they invented two cranes: for lifting small and heavier loads. According to the images found by archaeologists among the ruins of one of the ancient cities, it was possible to establish how he acted. The wheel of a huge crane was rotated by five people, at the same time, two were driving the load from the bottom and two from above.

•   Simple mechanisms are used mainly in order to get a gain in strength, i.e. increase the force acting on the body several times.

• question

• Will do

•   The paths traversed by the points of application of forces on the lever are inversely proportional to the forces.

• h1 / h2 = F2 / F1

•   Acting on the long arm of the lever, we win in strength, but at the same time we lose the same amount on the way.

•   Using the lever
•   we can win either in force,
• either in the distance.

•   The legend about Archimedes says that he admired the discovery of the rule of the lever, he exclaimed: “Give me a fulcrum and I will turn the Earth over”

• V = 30 000 km / s
• t = 10 million years

• Moving unit does not win in work

• How many times winning in strengthso many times losing in the distance

• The “golden rule” of mechanics applies to all mechanisms.

• Types of mechanisms

• 1. With the help of a movable block, the load was lifted to a height of 1.5 m. For how long was the free end of the rope extended?
• 1.5 m 0.75 m 3 m
• 2. With the help of a movable block, the load was lifted to a height of 7 m. What work did the worker do when lifting the load, if he applied a force of 160 N to the end of the rope? What work will he do if he lifts this load to a height of 5 m?

• Right!

• Mistake!!!