Presentation on the topic "Energy. Kinetic and potential energy. Derivation of the law of conservation of mechanical energy"
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Energy. Kinetic and potential energy. Derivation of the law of conservation of mechanical energy
A ball of mass 100 g flying at a speed of 1.5 m/s is caught on the fly. With what average force does the ball act on the hand if its speed decreases to zero in 0.03 s.
From a boat of mass 240 kg, moving without a rower at a speed of 1 m / s, a load of mass 80 kg fell out. What was the speed of the boat?
In water from a depth of 5 m, a stone with a volume of 0.6 m 3 is raised to the surface. The density of the stone is 2500 kg/m 3 . find a job lifting a stone.
If a body or system of bodies can do work, then they say that they have energy.
ENERGY IS SIGNED: E ENERGY IS MEASURED: J
Mechanical energy is a physical quantity that characterizes the ability of a body to do work. Mechanical energy Kinetic (capable of moving) Potential (power)
Kinetic energy is the energy of a moving body.
Potential energy is the energy of interaction.
Potential energy of elastic deformation.
Law of energy conservation. In a closed system in which conservative forces act, energy does not arise from anywhere and does not disappear anywhere, but only passes from one form to another.
h E p= max E k=0 En=0 Ek= max En=Ek En Ek
A=-(E p -E p 0) (1) A=-(E to -E to 0) (2) E to 0 + E p 0 = E to + E p E=E to + E p - full mechanical energy
Helmholtz Hermann Ludwig Ferdinand (1821-1824)
In physics, conservative forces (potential forces) are forces whose work does not depend on the shape of the trajectory (depends only on the initial and final points of application of forces). This implies the following definition: conservative forces are those forces whose work along any closed trajectory is equal to 0.
Types of impacts Absolutely elastic impact Absolutely inelastic impact Elastic impact Inelastic impact
Mechanical energy is not converted into internal energy. All mechanical energy is converted into internal energy. A small part of the mechanical energy is converted into internal energy. Almost all mechanical energy is converted into internal energy.
Task number 1. With what initial speed should the ball be thrown down from a height h so that it bounces to a height 2h? Assume that the impact is perfectly elastic. Given: h Find: Solution: h 2h Epo+Eko En Ek
Epo + Eco Ek Ep
Task number 2. A sled with a rider with a total mass of 100 kg is moving down a mountain 8 m high and 100 m long.
Given: m=100 kg h=8 m L=100 m Find: Fc- ? Solution: Epo Ek+Ac
TOPIC OF THE LESSON: ???
Let's solve the crossword
2? The reason for the change in body speed?
3? The product of the "cause" of the change
the speed per distance traveled is called...?
4? The ability of a body to do work is called...?
MECHANICAL ENERGY
Lesson type. Learning new material.
Objectives for the lesson: To introduce the concept of energy, as the ability of the body to do work; define potential and kinetic energy.
- Updating previously acquired knowledge. Formation of new concepts. Application of new knowledge to solving practical problems.
Metasubject
- Personal: accept and maintain the learning goal and task.
- Regulatory: the ability to set new learning goals and objectives
- Cognitive: formation of ideas about energy, kinetic and potential energies.
- Communicative: the ability to argue one's point of view, group work skills: the ability to listen to the interlocutor, to discuss the questions that have arisen.
- Basic concepts: Energy; kinetic energy; potential energy of a body raised above the Earth; potential energy of an elastically deformed body.
Energy is the work that a body can do when moving from a given state to zero.
The term “energy” was introduced into physics by the English scientist T. Jung in 1807.
Translated from Greek, the word "energy" means action, activity.
Since in mechanics the movement of bodies and their interaction are studied, then
POTENTIAL
KINETIC
motion energy
interaction energy
Kinetic energy
Let us determine the kinetic energy of a body moving at a speed υ
energy is the work that needs to be done to transfer the body from the zero state (υ 0 \u003d 0) to the given one (υ ≠ 0).
Let's transform this expression:
According to Newton's Law
Path with uniformly accelerated motion:
Potential energy
Let us determine the potential energy of the interaction of the body with the Earth at a height h.
Energy is the work that needs to be done to transfer the body from the zero state (h 0 \u003d 0) to the given one (h).
Energy is the work that needs to be done to transfer the body from the zero state (h 0 =0) to the given state (h).
We define the work of the force F:
Derive the formula yourself
Let's check:
potential energy:
We met two types of mechanical energy
KINETIC
POTENTIAL
motion energy
interaction energy
However, in general case A body can have both kinetic and potential energy at the same time.
called
full mechanical energy
This concept was introduced in 1847 by the German scientist G. Helmholtz.
Study of the free fall of bodies
(in the absence of friction and resistance forces) shows that any decrease in one type of energy leads to an increase in another type of energy.
LAW OF CONSERVATION MECHANICAL ENERGY
Denote the initial energy of the body
And the final
Then the law of conservation of energy can be written as
Suppose that at the beginning of the movement the body speed was equal to υ 0, and the height h 0, then:
And at the end of the movement, the speed of the body became equal to υ, and the height h, then:
The total mechanical energy of the body, which is not affected by the forces of friction and resistance, remains unchanged in the process of motion.
example
A stone of mass 2 kg flies with a speed of 10 m/s. What is the kinetic energy of the stone?
Kinetic energy of the stone
Answer: 100 J.
A brick of mass 4 kg lies at a height of 5 m from the ground. What is the potential energy of the brick?
Potential energy of a brick
Substitute the numerical values of the quantities and calculate:
Answer: 200 J.
Which of these moving bodies has more kinetic energy?
By the plane
In what places of the river - at the source or at the mouth - does each cubic meter of water have more potential energy?
Justify the answer.
Waterfall in the tropics
Which of the two planes has more potential energy?
At the top
Test
1. The energy that a body possesses as a result of its movement is called ... energy.
- potential
- kinetic
- Do not know
1) potential
2) kinetic
3) I don't know
- Raise the helicopter higher;
- Lower the helicopter;
- Land the helicopter on the ground.
- Only kinetic;
- Only potential;
- No;
- Do not know.
Test check.
1 . The energy possessed by a body as a result of its motion is called ... energy.
- potential
- kinetic
- do not know
2. The energy of a compressed spring is an example of... energy.
1) potential
2) kinetic
3) I don't know
3. Two balls of the same size, wooden and lead, at the moment of falling to the ground had the same speed "". Do they have the same kinetic energy?
1) The lead ball had a lot of energy.
2) The wooden sha had great energy
3) The same, since their speeds and sizes are the same
- Lower the helicopter;
- Raise the helicopter higher;
- Increase helicopter speed;
- Reduce helicopter speed;
- Land the helicopter on the ground.
- Only kinetic;
- Only potential;
- Potential and kinetic;
- No;
- Do not know.
The robbers took money and documents from the victim, stripped him to the naked and, deciding that there was nothing more to take from him, threw him from the bridge into the river. What did the victim have halfway to cold water?
Answer: potential energy, gradually turning into kinetic energy.
Homework:
- Read § 14.15
- Learn the basic concepts, formulas, definitions.
- Prepare a short summary
§ 16 to level I,
abstract presentation on the topic
Mechanical work and energy:
- KINETIC ENERGY
- AND MECHANICAL WORK
- WORK BY GRAVITY AND POTENTIAL ENERGY
- LAW OF CONSERVATION OF MECHANICAL ENERGY
- Let's start the path to another conservation law.
- It is necessary to introduce several new concepts so that they do not seem to you to have fallen "from the ceiling", but reflect the living thought of people who for the first time pointed out the usefulness and meaning of new concepts.
- Let's start.
- Let's solve the problem using Newton's laws: a body of mass m moves with acceleration under action of three forces shown in the figure. Determine the speed at the end of the path S.
- F1 + F2 + F3 = m × a,
- in the projection on the OX axis:
- F1cos - F3 = m×а
- F1cos - F3 = m × (υ²–υо²)
- F1S cos - F3S = mυ² –mυо²
- F1S cos - F3S = m²– mυо²
- Let's discuss the result.
- The influence of all forces on the change ΔΕk can be described in a unified way if we introduce the value A=Fs cosα, called mechanical work:
- A1= F1S cos,
- A2= F2S cos 90°=0,
- A3 = F3S cos180°=F3S,
- and together A1 + A2 + A3= Ek Eko
- or: the change in the kinetic energy of the body is equal to the work of the forces acting on the body.
- The resulting expression is the kinetic energy theorem: ΣA=ΔΕk.
- =1J
- [A]=1J
- Note that Ek and A are scalars!
- Let's consolidate the information about the new concepts.
- Which of the bodies has more kinetic energy: a calmly walking person or a flying bullet?
- The speed of the car has doubled (tripled). How many times has its kinetic energy changed?
- Under which of the following movements does the kinetic energy of bodies change: RPD, RUD, RDO?
- Express the kinetic energy in terms of the momentum modulus of the body and the momentum modulus in terms of the kinetic energy.
- 3) RUD υ=υ0+at υ
- (modulus of speed increases), m = const
- .
- Body momentum modulus:
- Kinetic energy:
- Work is a scalar quantity, expressed as a number. A 0, if 0≤90°; A0, if 90° ≤ 180°.
- If a force acts on a body at an angle of 90° to the direction of the instantaneous velocity, say, the force of gravity when the satellite moves in a circular orbit or the force of elasticity when the body rotates on a thread. A=Fs cos90°=0.
- According to the theorem 0 = Ek – Eko Ek = Eko the force does not change the speed!!!
- Let's also remember the momentum: are there any bodies in the figure that have the same momentum?
- The numbers in the circles mean the masses of the bodies, the numbers next to the vector are the speeds of the bodies. All quantities (masses and velocities) are expressed in SI units.
- IMPULSE - VECTOR!
- Indicate with an arrow the direction of speed so that:
- A1 0, A2 0, A3 0;
- А1 0, А2 0, А3 =0;
- А1 0, А2 0, А3 =0;
- A1 0, A2 0, A3 0.
- Is such a combination of signs of work possible, for which it is generally impossible to choose the direction of velocity?
- In which of the following cases is the work of the resultant positive, negative, equal to zero:
- The bus departs from the stop, moves evenly and in a straight line, turns at a constant modulo speed, approaches the stop;
- You are going down the hill; ride on a carousel, on a swing?
- The concept of kinetic energy was introduced for the first time by the Dutch physicist and mathematician Christian Huygens, who was called great by I. Newton himself. Studying the collisions of elastic balls, Huygens came to the conclusion: “When two bodies collide, the sum of the products of their magnitudes by the squares of their velocities remains unchanged before and after the impact” (“values” - read “mass”). From the modern standpoint, Huygens' discovery is nothing more than a special case of the manifestation of the law of conservation of energy. Huygens, a handsome man from an old family in which "talents, nobility and wealth were hereditary", not only for the first time determined kinetic energy, but also pointed out the vector nature of the impulse. He invented the pendulum clock, performed a number of brilliant works in mathematics and astronomy. "A finely disciplined genius...respecting his abilities and striving to use them to the fullest."
- In everyday life, we constantly need to change the direction and modulus of speed of various bodies (movement of fingers, eyelids, etc.). To change the speed module, it is necessary to perform mechanical work: A=ΔΕk. This work is done by your muscles.
- Consider the most common phenomenon - climbing stairs. You stand on a step, put your foot on the next one, strain your muscles, there is a support reaction that compensates for the force, the force does positive work А0, the speed of your body increases: ΔΕk 0, you go up one step. At the same time, gravity does negative work, since \u003d 180 °. The work of the muscle tension force should be at least a little, but more than the work of gravity (modulo), otherwise it will not be possible to increase Εk.
- AA, otherwise it will not be possible to increase the kinetic energy Ek = A + A, (A 0). Since the movement of the torso under the action of these forces is the same, it is clear that , and
What is ENERGY? In our life we often encounter the concept of energy. Cars and airplanes, diesel locomotives and motor ships operate by consuming the energy of burning fuel. People, in order to live and work, replenish their energy reserves with the help of food ... So what is energy?
For example: A body raised relative to the surface of the Earth has potential energy, because. energy depends on the relative position of this body and the Earth and their mutual attraction. The water, which is raised by the dam of the power plant, sinking down, drives the turbines of the power plant. When a spring is stretched or compressed, work is done. In this case, the individual parts of the spring change position relative to each other.
quality tasks. 1. Which of the two bodies has more potential energy: a brick lying on the surface of the earth, or a brick located in the wall of the house at the level of the second floor? 2. Which of the two bodies has more potential energy - a steel ball or a lead ball of the same size lying on the balcony of the fifth floor? 3. Under what condition will two bodies raised to different heights have the same potential energy? 4. At athletics competitions, athletes push the shot. Men - a core weighing 7 kg, women - a core weighing 4 kg. Which nucleus has more kinetic energy at the same flight speed? 5. Which of the two bodies has more kinetic energy: the one that moves at a speed of 10 m / s, or the one that moves at a speed of 20 m / s? 6. What is the physical meaning of the Finnish proverb “What you spend going uphill, you will return on the way down”? To the table of contents
Challenges for ingenuity. 1. Two identical barrels were loaded onto a car. One barrel was loaded using an inclined plane, and the second was lifted vertically. Are the potential energies of the barrels on the car equal? 2. When does the car consume more fuel: when driving at a steady pace or when driving with stops? 3. Can potential energy be negative? Give examples. To the table of contents
Test. 1. Which of the following units is a unit of kinetic energy? A) N C) J B) Pa D) W 2. What mechanical energy does a stretched or compressed spring have? A) Kinetic B) Potential C) Does not have mechanical energy 3. Energy, which is determined by the position of interacting bodies or parts of the same body, is called ... A) potential energy. B) kinetic energy. 4. The notebook is on the table. What mechanical energy does it have relative to the floor? A) Kinetic B) Potential C) Has no mechanical energy 5. What does the kinetic energy of a body depend on? A) On the mass and speed of the body. B) On the speed of the body. C) From the height above the Earth's surface and body weight. 6. The energy possessed by the body as a result of its movement is called ... A) potential energy. B) kinetic energy. 7. What does the potential energy of a body raised above the ground depend on? A) On the mass and speed of the body. B) On the speed of the body. C) From the height above the Earth's surface and body weight. 8. What is the mechanical energy of a car moving on the road? A) Kinetic B) Potential C) Has no mechanical energy
slide 1
LAW OF CONSERVATION OF MECHANICAL ENERGY. Completed by: teacher MOU - Secondary School No. 1 Tide L. A. G. Asino.slide 2
A physical quantity characterizing the process during which the force F deforms or moves the body. This quantity is used to measure the change in the energy of systems. The performance of work can lead to a change in the location of bodies (work to move, work to approach bodies) serves to overcome friction forces or cause acceleration of bodies (work to accelerate). Unit: 1 H m (one newton * meter) 1 H m = 1 W s (one watt * second) = = 1 J (joule) 1 J is equal to the work that is expended to move the point of application of a force of 1 N 1 m in the direction of moving the point.
slide 3
A physical quantity that characterizes the speed of mechanical work. P - power A - work, t - time. Unit: 1 H m/s (one newton * meter per second) 1 H m/s=1J/s=1W 1 W is the power that is expended when the point of application of a force of 1 H moves 1 within 1 s m in the direction of movement of the body.
slide 4
A physical quantity that characterizes the ratio between the useful and expended part of mechanical work, energy or power. useful work, useful power useful energy consumed energy consumed power consumed energy
slide 5
Energy is a scalar physical quantity that characterizes the ability of a body to do work. The useful work of any device is always less than the work expended. The efficiency of the device is always less than 1. The efficiency is always expressed in decimal fractions or as a percentage.
slide 6
Kinetic energy is the energy that a body possesses as a result of its movement (characterizes a moving body). 1) In the chosen reference system: - if the body is not moving -- - if the body is moving, then
Slide 7
The potential energy of a body raised above the Earth is the energy of the interaction of the body with the Earth. Potential energy is a relative value, because it depends on the choice of the zero level (where).
Slide 8
Potential energy of an elastically deformed body. - energy of interaction of body parts. - - body rigidity; - elongation. Ep depends on the deformation: , - the greater the deformation, the Ep - if the body is not deformed, Ep = 0
Slide 9
Potential energy is the energy possessed by objects at rest. Kinetic energy is the energy of a body acquired during movement. THERE ARE TWO KINDS OF MECHANICAL ENERGY: KINETIC AND POTENTIAL, WHICH CAN TURN INTO EACH OTHER.
slide 10
transformation potential energy into kinetic. THROWING UP THE BALL, WE GIVE IT THE ENERGY OF MOTION - KINETIC ENERGY. WHEN UP, THE BALL STOPS AND THEN STARTS TO FALL. AT THE MOMENT OF STOPPING (AT THE HIGH POINT) ALL KINETIC ENERGY TURNS FULLY INTO POTENTIAL. WHEN THE BODY MOVES DOWN, THE REVERSE PROCESS HAPPENS.
slide 11
The law of conservation of mechanical energy - total mechanical energy The total mechanical energy of a body or a closed system of bodies that are not affected by friction forces remains constant. The law of conservation of total mechanical energy is a special case of the universal law of conservation and transformation of energy. The energy of the body never disappears and does not appear again: it only changes from one form to another.
slide 12
CONVERSATION 1. What is called energy? 2. In what units is energy expressed in SI? 3. What energy is called potential kinetic energy? 4. Give examples of the use of the potential energy of bodies raised above the Earth's surface. 5. What is the relationship between changes in the potential and kinetic energy of the same body?
slide 13
6. Formulate the law of conservation of total mechanical energy. 7. Describe an experiment in which you can trace the transition of kinetic energy into potential energy and vice versa. 8. Why is the law of conservation of mechanical energy violated under the action of friction force? 9. Formulate the universal law of conservation and transformation of energy. 10. Why are perpetual motion machines inoperable?
slide 14
REMEMBER: AFTER THE IMPACT OF THE LEAD BALL ON THE LEAD PLATE, THE STATE OF THESE BODIES CHANGED - THEY DEFORMED AND HEATED. IF THE STATE OF THE BODIES HAS CHANGED, THEN THE ENERGY OF THE PARTICLES OF WHICH THE BODIES COMPOSE HAS CHANGED. WHEN HEATING THE BODY, THE SPEED OF MOVEMENT OF MOLECULES INCREASES AND THEREFORE, THE KINETIC ENERGY INCREASES. WHEN THE BODY HAS DEFORMED, THE LOCATION OF ITS MOLECULES HAS CHANGED AND THEIR POTENTIAL ENERGY HAS CHANGED. THE KINETIC ENERGY OF ALL MOLECULES OF WHICH THE BODY COMPOSES AND THE POTENTIAL ENERGY OF THEIR INTERACTION CONTAIN THE INTERNAL ENERGY OF THE BODY
slide 15
CONCLUSION: MECHANICAL AND INTERNAL ENERGY CAN TRANSFER FROM ONE BODY TO ANOTHER. THIS IS FAIR FOR ALL THERMAL PROCESSES. DURING HEAT TRANSFER, A MORE HOT BODY GIVES ENERGY, AND A LESS HOT BODY RECEIVES ENERGY. IN THE TRANSITION OF ENERGY FROM ONE BODY TO ANOTHER OR IN THE TRANSFORMATION OF ONE TYPE OF ENERGY INTO ANOTHER, ENERGY IS CONSERVED
slide 16
THE STUDY OF THE PHENOMENA OF THE TRANSFORMATION OF ONE TYPE OF ENERGY INTO ANOTHER LEAD TO THE DISCOVERY OF ONE OF THE MAIN LAWS OF NATURE - THE LAW OF CONSERVATION AND TRANSFORMATION OF ENERGY IN ALL PHENOMENA OCCURING IN NATURE, ENERGY DOES NOT APPEAR AND DISAPPEAR. IT ONLY TRANSFORMS FROM ONE KIND TO ANOTHER, AND ITS VALUE IS KEPT.
