Blocks. The golden rule of mechanics
Work and energy mechanical work and powerWhat is work and power in terms of physics? How to calculate them? What are the similarities and differences between the concepts of "work" and "power" in life and in physics? Simple mechanisms What is " Golden Rule» mechanics? Are there golden rules in life? What mechanisms are used to facilitate work? How to calculate the coefficient useful action?Energy What are the similarities and differences between the physical concept of "mechanical energy" and the common concept of "energy"? What are the types of mechanical energy? What examples of the transformation of one type of energy into another do you know?
Mechanical work and power1. Mechanical work \u003d product of force on the path.
2. Mechanical work can be performed only when the body moves under the action of a force, and the force must either promote the movement or hinder it.
Work is positive when the force is directed in the direction of motion of the body. Otherwise, the work is negative.
3. Power is the speed of doing work.
Power shows how much work is done per unit of time.
Simple Mechanisms 4. The "golden rule" of mechanics: if, when performing work, they gain in strength several times, then they lose in the distance by the same number of times.
Mechanisms (lever, gate, inclined plane) - devices that allow you to convert force.
5. Lever - solid, which has an axis of rotation.
The rule of equilibrium for a lever is this: the lever is in equilibrium when the moment of force rotating it clockwise is equal to the moment of force rotating the lever counterclockwise.
Arm of the force = distance from the axis of rotation to the straight line along which the force acts.
Moment of force = product of force on her shoulder.
6. A block is a wheel with a groove into which a cable (chain, belt, rope) is passed.
The immovable block only changes the direction of the force, while the movable block still gives a twofold gain in strength.
7. Coefficient of performance (COP) = the ratio of useful work to full.
When using the perfect mechanism full work always more than helpful. In other words, the efficiency is always less than 100%.
Energy 8. Energy is the ability to do work.
The greater the energy of the body, the more work it can do. When work is done, the energy of the body decreases.
9. Kinetic energy is the energy of movement of a body or system of bodies.
The greater the mass and the greater the speed of a given body, the greater its kinetic energy.
10. Potential energy- this is the energy of interaction of bodies (or parts of one body) depending on their relative position.
The potential energy of a body of mass m raised to a height h is equal to the product mgh.
11. Mechanical energy can be transferred from one form to another.
The golden rule of mechanics
On a gate or on a spire, it is possible, therefore, with a small force to set in motion a significant load. But the speed of this movement in such cases is small - less than the speed with which the force applied to the gate moves.
Consider the last spire example: in one full turn, the end of the pole where the force is applied describes a path of length
2? 3.14? 350 = 2200 cm.
In the meantime, the shaft will also make one revolution, winding around itself a piece of rope, with a length
2? 3.14? 21 = 130 cm.
Consequently, the load will be pulled up by only 130 cm. The force has traveled 2,200 cm, and the load in the same time is only 130 cm, i.e., almost 17 times less. If you compare the amount of load (500 kg) with the amount of force applied to the capstan (30 kg), then make sure that the same relationship exists between them:
500: 30 = about 17.
You see that the path of the load is as many times less than the path of the force, how many times this force is less than the load. In other words: how many times it is gained in strength, how many times it is lost in speed.
Rice. 17. Explanation of the golden rule of mechanics
This rule applies not only to a gate or a spire, but also to a lever, and to any machine in general (it has long been called the "golden rule of mechanics").
Consider, for example, the lever discussed on p. 51. Here it is gained in strength 3 times, but on the other hand, while the long arm of the lever (see Fig. 17) describes a large arc with its end MN, the end of the short arm describes a three times smaller arc OR. Consequently, in this case, the path traveled by the load is also less than the path traveled at the same time by the force by 3 times - as many times as this force is less than the load.
Now it will become clear to you why in some cases it is beneficial to use leverage in reverse: acting great strength on a short arm to move a small load at the end long shoulder. What is the benefit of doing so? After all, we are losing strength here! Of course, but we win in the same amount of time in speed. And when we need more speed, we get it at this price. Such levers represent the bones of our hands (Fig. 18): in them the muscle is attached to the short arm of the lever of the 2nd kind and sets the hand in rapid motion.
Rice. 18. Our hand is a lever. What kind of?
In this case, the loss of strength is rewarded with a gain in speed. We would be extremely slow creatures if the bones of our skeleton were arranged like levers, gaining in strength and, therefore, losing in speed.
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(block, lever, gate, etc.), a wonderful feature of these machines was found. It turned out that all movements in simple mechanisms have a certain connection with the forces that the machine develops. It should be noted that the ratio of displacements of the 2 ends of a simple mechanism, to which forces are applied, is always the opposite of the ratio of forces that are applied to these ends.
The force acting on the right arm of the lever is n times less than the force acting on the left arm. Accordingly, the movement of the right shoulder (s2) is n times greater than the movement of the left shoulder (s1).
For example, if in order to save the magnitude of the force F2 must be n times less than the magnitude of the force F1. In this case, when the lever rotates, the movement s2 of the second end will be n times greater than the movement s1 of its first end. If the block is double, then the same ratio is relevant for it between the forces that are applied to the ropes that are wound around both blocks and keep it in the equilibrium position, and the movements of the rope ends when the block rotates. Since the importance of this provision cannot be overestimated, it has been called very beautifully: the “golden rule of mechanics”.
Using the notation that has been introduced, the golden rule of mechanics can be expressed by the following formula:
or s1*F1= s2*F2.
Subsequently, there was a gradual complication of the types of movements and the nature of the machines that were used in mechanics. It turned out that the golden rule of mechanics does not always retain its relevance in a simple form. However, when the types of machines became more complex, the golden rule of mechanics became more complex at the same time. So, more difficult cases began to fall under his influence. At the same time, it should be noted that the golden rule of mechanics became the basis for the emergence of various ideas about energy and work. Moreover, this rule is the first, simplest formulation that remains relevant for any natural phenomena.
Application of the "golden rule"
This rule remains relevant only in the case of uniform movement of simple machines (or with small accelerations). For example, when a double block rotates, the ends of the ropes move to distances s1 and s2, which are wound on blocks of radii r1 and r2 and are also fastened together. These distances are proportional to the radii r1/r2 = s1/s2.
Thus, in order for the golden rule to be relevant for a double block, the following certain conditions must be met: F1/F2 = r2/r1.
In this case, the forces F1 and F2 will be balanced. Therefore, the machine must either perform or be at rest. However, in order to start a double block, the balance must be disturbed. To do this, to any force, say, to F1, one should add a certain force f. The movement that occurs in the body will be accelerated.
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Collection from the sale of currency
The issue of introducing a fee from such an activity as the sale of cash currency, in terms of the resonance that it causes in any society, can only be compared with elections to the highest authority and the beginning of the functioning of the newly elected parliament. Considering a large number of different opinions of experts regarding this innovation, the National Bank is obliged to actively pursue information work among the people of their state. In this way, he will be able to explain to the people certain rules and concepts that will be useful to every member of society in the future.
Teacher: Dobrynkina O.A.Subject: Physics Grade 7
UMC: Peryshkin A.V. Physics-7-M, Bustard, 2017
Topic Lesson: "Golden Rule of Mechanics"
Section: "Work and power. Energy"
Form of work of students: frontal, individual, work in groups
.Type of lesson: lesson learning new material, lesson research.
Teaching methods:
heuristic, explanatory-illustrative, problematic, practical tasks, solution of a qualitative problem of physical content.The purpose of the lesson: to develop the skills of conducting experiments, to cultivate a sense of collectivism, the ability to work in a group.
Lesson objectives:
educational: in the laboratory to find out the golden rule of mechanics, based on the concepts of work, strength, body weight; to form the ability to explain the cause-and-effect relationships of the manifestation of the golden rule of mechanics; establish experimentally the relationship between the tension thread and the lever;
Generalize and systematize students' knowledge of the golden rule of mechanics
developing: create conditions for the implementation practical tasks. develop Creative skills students; continue to form the ability to conduct experiments and draw conclusions; develop the ability to observe, analyze, compare, summarize and systematize the information offered, to give a complete detailed answer.
educational: arouse interest in subject on the basis of interdisciplinary connections with literature, mathematics, geography, the desire for independent activity in the classroom in order to obtain new knowledge and apply it. Formation of an active life position, a sense of collectivism and mutual assistance, the responsibility of each for the final results.
Formation of UUD:
subject:
understand the meaning of the "golden rule of mechanics";
gain experience research activities in the process self-study"golden rule of mechanics" when working in a group.
use for knowledge of the world various methods(observation, experiment);
personal:
stimulate the ability to have one's own opinions;
understanding the importance of cooperation with the teacher, with classmates, readiness for interaction and mutual understanding;
independently acquire new knowledge and practical skills.
Metasubject:
Regulatory:
setting goals, planning, self-control and evaluation of the results of their activities;
formation of skills to work in a group, to present and defend one's views and beliefs, to lead a discussion;
Conscious definition of the scope of their interests and capabilities.
Skill Mastery joint activities: coordination and coordination of activities with its other participants; objective assessment of one's contribution to the solution of the common tasks of the team.
Cognitive:
Investigate simple practical situations, make assumptions, understand the need to test them in practice;
The ability to distinguish between fact, opinion, proof, hypothesis.
Information and communication:
Reflect verbally the results of their activities;
The development of monologue and dialogic speech, the ability to express one's thoughts and the ability to listen to the interlocutor, understand his point of view, recognize the right of another person to a different opinion;
Form of organization learning activities students: frontal, individual, work in groups.
Applied technologies: problem-based learning technology, ICT, health-saving technologies.
Planned results:
Subject:
know the "golden rule of mechanics", the movable and fixed block, the ratio of forces acting on the blockBe able to: experimentally find out the "golden rule of mechanics".
Personal
: job satisfaction in the lesson, cooperation skills in different situations, the ability not to create conflicts and find ways out of controversial situations.Metasubject
: literature, mathematics, historyBasic concepts: work, force, mechanism, lever, conditions, the golden rule of mechanics.
Equipment:
*
laboratory vessels with fresh and sea water; a set of bodies of different densities; potato tuber; a piece of plasticine and a plasticine boat.* computer, projector, virtual laboratory.
*computer presentation of the lesson in the program
Smart"Golden Rule of Mechanics", table.Lesson structure:
organizational stage. 2 minutes.
Knowledge update. 5 minutes.
Formation of the topic of the lesson, setting goals 3 min.
Exploring a new topic. 10 min.
Primary fixation of the material. 3 min.
Lesson results. 3 min.
Homework 2 minutes.
Reflection. 2 minutes.
During the classes
Organizational stage
Organization of the beginning of the lesson. Greeting, identifying absentees, checking the readiness of students for the lesson, the readiness of visual aids.
Teacher: Hello!
Dear seventh graders!
I'm very happy
Enter your friendly class
And for me already a reward
Attention of your smart eyes.
I know that everyone in the class is a genius
But without effort, talent is not for the future
From your knowledge and skills
We will write a lesson together.
2. Stage updating knowledge
Teacher. We continue to master the mysterious, mysterious country called Physics. What does physics study?
Student. Physics is the science of nature.
Teacher. Yes, Man has long tried to explain the inexplicable, to see the invisible, to hear the inaudible. Looking around him, he thought about nature and tried to solve the riddles that she put before him.
Teacher: today, as in other physics lessons, you will act as theorists, researchers, practitioners. Today we will have to unravel another of the mysteries of nature. But for this you will need the knowledge gained in the previous lessons.
Teacher: To begin with, I suggest that you be a little theoretician and recall the formulas studied in previous physics lessons. please collect the formulas presented on the interactive board.
A=F*h, A=mgh, F1/F2=l2/l1, M=F*l
(pin the formulas on the board)
We remembered that with you the formulas will still be useful to us, and now I suggest you solve a crossword puzzle,
The action of one body on another. (force)
The value is directly proportional to the applied force and the distance traveled (work)
As they are called, movements are associated with a change in the position of bodies relative to each other (mechanical)
What is the name of the device that serves to transform the force (mechanism)
The value describing the ratio of work to the time for which it was completed? (power)
What is the name of the block whose axis is fixed and when lifting loads, it does not rise or fall? (fixed)
What is the name of physical quantity equal to the ratio of the force acting perpendicular to the surface area. (pressure)
Pressure Teacher: Guys, look, what keyword did we get?
Student: Archimedes
Photos of Archimedes
Teacher: Who is ARCHIMEDES? Which of his discoveries have you already studied?
Students: Gravity, Archimedean force
Archimedes said:
"Give me a foothold and I will lift the Earth"But proved it Ancient Greek scholar Heron of Alexandria, who lived inIcentury AD, although legend attributes this to Archimedes.
3. Stage updating knowledge. 1 minute.
U: Guys now, carefully look at the screen. What do you see in the pictures?
What time period do you think the events depicted in the pictures belong to?
W: And in these photographs, what time do you think? What do they show? What do you think these two frames have in common?
W: Indeed, simple mechanisms were used in antiquity, and found wide application Nowadays.
What do you think, if simple mechanisms are used to obtain a gain in strength, let's think about whether simple mechanisms give a gain in work?
STUDENT ANSWERS
Teacher: Today we will try to answer these questions.
4. Formation of the topic of the lesson, setting goals 2 min.
Teacher: Let's open notebooks and write down the topic of our lesson "The Golden Rule of Mechanics". Guys, what are the goals of our lesson?
Teacher: Find out the golden rule of mechanics
Teacher: develop experimentation skills
Teacher: to cultivate a sense of collectivism, the ability to work in a group.
Teacher: So guys, the topic is defined, the goals are set.
We begin to walk towards our goal in the footsteps of Archimedes. Do you know how Archimedes came to his discovery?Student experiences.
Teacher: So we will now try to conduct an experiment to clarify the golden rule of mechanics
Each group has equipment and cards on the table.
task. Without wasting a minute, we complete the task in pairs, helping each other. Having completed the task, we can answer the main question.Task for practitioners:
The first practical task.
Check in practice whether the inclined plane gives a gain in work?
For this:
Determine the weight of the load using a dynamometer
Measure the height of the inclined plane
h using a measuring tape.Find work to lift the body vertically.
(BUT 1 = P* h )Determine the force using a dynamometer
F , which must be applied to lift the load on an inclined plane.Determine the length
l inclined plane with a measuring tape.Find a job lifting a load up an incline
(BUT 2 = F*l)Fill the table:
Body weight, RInclined plane height,
hWork, BUT 1
applied force,
FInclined plane length,
lWork, BUT 2
Make a conclusion by answering the question: Does the inclined plane give a gain in work?
Teacher:
Conclusion: The inclined plane does not give a gain in work.The second practical task.
Check in practice whether a fixed block gives a gain in work.
Use the fixed block to lift a 1N load to the highest possible height.
l
(BUT
1 = P * l)Attach a dynamometer to the thread, lifting the load, determine the applied force
FUse a ruler to determine the length
l 1 stretched thread.Calculate the perfect work.
(BUT 2 = F *l 1 )Repeat the experiment with two weights.
Fill the table:
Compare the results obtained, draw conclusions: does a fixed block give a gain in work?
Conclusion: A fixed block does not give a gain in the work of a fixed block. Getting a gain in strength, we lose on the way.
The third practical task.
CARD 2
Purpose: to find out if leverage gives a gain in work.
Equipment: tripod, clutch, lever, 2 hooks, 3 weights of 100 g each, dynamometer, measuring tape.
Work order:
1. Balance the lever in a horizontal position.
2. Measure the weight of two weights
F1 using a dynamometer. write down F 1 \u003d ___ N.2. Hang on the left shoulder of the lever at a distance of 6 cm from the axis of rotation two weights
F 1 (picture 1).3. Balance the lever by hanging one weight on the right arm of the lever. Write down the force with which one weight acts on the right arm of the lever F 2 \u003d ___ N.
4. Measure the distance h from the table surface to the point of application of forces. write down
h = ____ cm = ______ m.
5. Deviate the lever at some angle from the vertical plane (Figure 2).
6. Measure the paths taken by the force application points F 1 and F 2 as the difference between the distances from the table surface after and before the lever deflection:
s 1 \u003d h 1 - h \u003d ____ cm - ____ cm \u003d ____ cm \u003d _______ m;
s 2 \u003d h - h 2 \u003d _____ cm - ____ cm \u003d ____ cm \u003d _____ m.
7. Calculate the work done by the force of gravity of two loads A one . Write down A 1 \u003d _____J.
8. Calculate the work done by the force of gravity of one load A 2. Write A 2 \u003d ______ f.
9. Fill in the table.
F1,s 1 , m
Force F 2 , N
The path traveled by the point of application of force F 2,
s2, m
The work of the force F 1,
The work of the force F 2,
10. Answer the questions:
Does a simple mechanism give strength?
Does a simple mechanism win along the way?
Does a simple mechanism work better?
11. Draw a conclusion.
General conclusion: The golden rule of mechanics: “How many times we win in strength, so many times we lose on the road”
Physical education minute
Guys, now I suggest you not only relax, but also consolidate the studied material. If you win in strength or ways you get up differently
1. increased strength by 5N
2. Reduced height
3.reduced way
4. Increased weight
5.increased speed
6. Reduced force by 3N
Teacher: Now guys, we will stay with you a little theorists and solve the following problems.
Task number 1.
A load weighing 245 N was evenly lifted to a height of 6 cm using a lever, while a force of 50 N was applied to the other end of the lever, the point of application of this force dropped by 30 cm. Find the work of the forces applied to the ends of the lever, make a comparison.
Solution:useful work
A1=mg*h1
full work
А2=F*h2
Task number 2.
A bucket of sand weighing 24.5 kg is lifted with a fixed block to a height of 10 meters. Acting on a rope with a force of 250 N, it was pulled out 9.8 meters.
Find the work of each force, make a comparison.
Solution:
Ap=mgh=24.5*10*10=2450J Az=Fh=250*10=2500J
Well done
Guys, tell me, can we now answer the question that was posed at the beginning of the lesson?
Homework, item 62.Conduct a mini study on the topic: Does the “Golden Rule” of mechanics apply to a hydraulic machine or not?
Grading a lesson.
Reflection.
Tell me guys, did you like working together in a group?
Shake hands and say thank you
The guys in front of you are the ranks of sailors. Choose the rank that will tell us how much you liked the lesson and whether you learned this topic lesson.
Thank you guys for the lesson, I really enjoyed working with you today.
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