Golden Rule. A. Golden Rule Message Equal Work When Used

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

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We have already examined some simple mechanisms. Some studied in great detail (lever, block), others just mentioned. We must have already realized 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 human actions more convenient.
  But we know such a physical quantity as work. The question naturally arises: what is the gain in work we get using simple mechanisms? The answer is discouraging: no. Not a single simple mechanism of gain in work gives.
  In paragraph sixty-two, this conclusion is reached by calculation. This is first done for leverage. Then the output extends to the fixed block, then to the moving one.
  Simple mechanisms apply. To win in strength or in distance. You can’t get a win in either. Winning in one, you lose in the other. This is the "golden rule" of mechanics. It was known to people even in antiquity. Now you will know him.

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

We calculate the work that the force F does when lifting the load using an inclined plane:

Substitute the found strength values

and get

Thus, the work is equal to the work that needs to be done to uniformly raise the load to a height h, without using an inclined plane.

Does not give a gain in work and leverage. Indeed, if the balanced lever (Fig. 1) is set in motion, then the points of application of forces and at the same time will make different movements and. At the same time (we consider the angle of rotation of the lever small)

Consequently, these forces will do the work.

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

In order to raise the load to a height h using a movable block, it is necessary to move the end of the rope, to which the force F is applied, to move 2h. Consequently, and

Thus, receiving a gain in force twice, they lose twice in the movement, therefore, the mobile unit does not give a gain in work.

Centuries-old practice has shown that not one of the simple mechanisms gives a gain in work.

Even ancient scientists formulated a rule (the “golden rule of mechanics"), applied to all mechanisms: how many times we win in strength, so 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 performed by force F to move the individual parts of the mechanism and against the friction force. The work of lifting the load (useful work) will be less than the full work A (the work that the force F does).

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

The question naturally arises:  giving a gain in strength or in transit, do simple mechanisms of gain in work also not give? The answer to this question can be obtained from experience.

By balancing on the lever two any forces F1 and F2 which are different in absolute value (Fig. 170), the lever is set in motion. It turns out that at the same time, the point of application of a smaller force F2 passes the larger path s2, and the point of application of a larger force F1 lesser ways1. By measuring, these paths and force moduli 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 lose the same length of time along the path.

The product of power on the path is work. Our experiments show that work performed at both ends of a lever equal to each other:

So, when using the lever of gain in work do not get.

Using the lever, we can win either in strength or in distance. If we apply force to the long shoulder, then we will win in force, but in so much let's lose in the distance. Acting by force on the short arm of the lever, we will win in distance, but we will lose in strength as many times.

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

Of course, Archimedes could not have cope with such a task, even if he had been given a fulcrum and a lever of the required length. For lifting Earth only 1 cm long shoulder of the lever should It would describe an arc of enormous 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 gain in work and a kind of lever - fixed block, what is easy  make sure from 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 done with the help of a movable unit. To raise the load to a height h using a movable unit, 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 strength of 2 times, they lose 2 times in transit, and therefore the mobile unit does not give a gain in work.

Centuries-old practice has shown that none of the mechanisms gives a gain in work. Various mechanisms are used in order to depending on working conditions  win in power or on the go.

Already ancient scholars knew the rule that applies to all mechanisms: how many times we win in strength, so many times we lose in distance. This rule was 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 traveled by the points of application of forces on the lever, and these forces? 3. Is it possible gain with a lever  plans are accepted? What are they losing then? 4. How many times do they lose on the way using a movable unit to lift goods? 5. What is the “golden rule” of mechanics?

Exercises.

1. With the help of a movable block, the load was raised to a height of 1.5 m. How long was the free end of the rope extended?
2. Using a movable unit, the load was lifted to a height of 7 m. What work did the worker perform 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 unit and the friction force should not be taken into account.)
3. How to apply a block to win in the distance?
4. How can fixed and movable blocks be connected to each other to gain a 4-fold gain in strength? 6 times?

The task.

Prove that the law of equality of work (the "golden rule" of mechanics) applies to a hydraulic machine. Do not take into account friction between the pistons and the walls of the vessels.

Indication Use Figure 132 for proof. When a small piston, under the action of force F1, falls down a distance h1, it displaces a certain volume of liquid. The volume of liquid under the large piston increases by the same amount, which at the same time rises to a height h2.

Problem solving on the topic: Equality of work when using simple mechanisms. The Golden Rule of Mechanics

LESSON OBJECTIVES:Actualize knowledge on the topic "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 force, and on the other hand, allow you to change the direction of motion of the body under the action of force;

To cultivate an intellectual culture in bringing students to an understanding of the basic rule of simple mechanisms; - to form the ability to generalize known data on the basis of highlighting the main;

Form elements of creative search based on the reception of generalization.

During the classes

1.Organizational moment

2.Checking homework

Front poll:

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 he serving for?

4. What is the shoulder of power? A moment of strength?

5.Formulate the condition of balance of the lever?

6. Formulate the "golden rule of mechanics"

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

8. Is it possible with the help of a lever, having a fulcrum, to overturn the Earth. Justify the answer.

3 problem solving

A task:   The length of the smaller arm is 5 cm, the larger is 30 cm. A force of 12H acts on the smaller arm. What force must be applied to the larger shoulder to balance the lever? Find a power gain?

Given: C: Decision:

l 1 \u003d 5 cm 0.05 m 1) We write the condition for the balance of the lever:

l 2 \u003d 30 c m 0.3m

F 1 \u003d 12 N Express from it F 2:

F 2 \u003d?


F 1 / F 2 \u003d? 2) Find the gain in strength, i.e.

.

Answer:   F 2 \u003d 2H, F 1 / F 2 \u003d 6H.

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

Test yourself (Answer: 0.75m)

Solve the problem according to the model:  At the ends of the lever there are forces 25N and 150N. The distance from the fulcrum to the greater force is 3 cm. Determine the length of the lever, if under the influence of these forces it is in equilibrium?

Test yourself (Answer: 0.21m)

A task:   Using a lever, a load of 200 kg was lifted. To what height was the load raised if the force acting on the long arm of the lever did 400 J.

Let's make an explanatory drawing:



l 2

Given: C: Decision:

m 1 \u003d 200kg 1) Mathematically write the “golden rule” of mechanics: A 1 \u003d A 2

A 2 \u003d 400 J 2) By definition, work Is the product of the force acting along the motion

h \u003d? body, on the path that the body goes through this force. Then:

And 1 \u003d F 1 · h 1

Express from this formula h 1:



3) To find F 1, we use the formula to find the gravity of the cargo:

F 1 \u003d F weight \u003d m 1 g \u003d 200kg10N / kg \u003d 2000N

4) Given that A 1 \u003d A 2, we calculate h 1:



Answer:   h 1 \u003d 0.2 N.

Solve the problem according to the model:  Using a lever, a little door was lifted weighing 0.84 kN, acting on a long arm with a force of 30N. At the same time, 26J mechanical work was performed. To what height was the door raised, and how large is the distance by which the end of the long arm of the lever has moved?

Test yourself (Answer: 3.1 cm high; 8.7 cm high) (at home)

Homework Think up a problem on a studied topic and solve it. Pov steam 47