Topic 4 mechanical energy and its conservation law

Course arrangement: 2 hours

Teaching objective: 1. Deeply understand the concepts of work and work, master the relationship between gravity work and the change of gravity potential energy, and skillfully apply kinetic energy theorem to solve related problems.

2. Apply the law of conservation of mechanical energy to solve practical problems and improve the ability to analyze and solve practical problems.

Emphasis of this lecture: kinetic energy theorem, law of conservation of mechanical energy and its application.

Difficulties in this lecture: 1. Kinetic energy and kinetic energy theorem

2. The law of conservation of mechanical energy and its application

First, the interpretation of the syllabus.

The test sites involved in this topic are: work and work, kinetic energy and kinetic energy theorem, gravitational work and gravitational potential energy, functional relationship, law of conservation of mechanical energy and its application.

The syllabus requires that all the test sites in this part are Class II, that is, to understand the exact meaning of the listed knowledge and its connection with other knowledge, to describe and explain it, and to use it in the process of analyzing, synthesizing, reasoning and judging practical problems.

Functional relationship has always been the "top priority" of the college entrance examination, and it is also a hot and difficult point in the college entrance examination. The problems involved in this part are not only comprehensive and weighty, but also often have the finale of the college entrance examination. The kinetic energy theorem and the conservation law of mechanical energy are the most studied. This part of knowledge is easy to associate with Newton's law of motion, circular motion, and the motion of charged particles in electric and magnetic fields. The general process is complex, difficult and requires high ability. The knowledge of this test center often examines the ability of candidates to transform physical problems into mathematical problems through analysis and reasoning, and then use mathematical knowledge to solve physical problems. Therefore, when reviewing, we should pay attention to the understanding and mastery of basic concepts and laws, and strengthen the ability to establish physical models and use mathematical knowledge to solve physical problems.

Second, the proposition trend

The content involved in this topic is the continuation and deepening of dynamics content, which is the focus of senior high school physics and the hot spot of college entrance examination. We should accurately understand the meaning of work and right, and master the judgment methods of positive work and negative work; In order to deeply understand the condition of conservation of mechanical energy, we can use the functional relationship to solve the comprehensive problem about energy change.

Third, the detailed analysis of examples.

Example 1 An athlete with a mass of m jumps from a squat state. After the center of gravity rises H, his body straightens out and just leaves the ground at the speed of V. In the process,

A. what did he do to him?

B.what did he do to him?

C. what did he do to him?

D. the work done by the ground to him is zero

Analysis: the displacement of the ground to the human force is zero, so the work is zero.

Answer: D.

Reflection after the question: This question examines the concept of work. College entrance examination questions have a reputation, which is easy to enter and difficult to start. Is there any work on the ground? If no work is done, where does kinetic energy come from? The college entrance examination questions integrate the examination of basic laws and concepts into familiar and unfamiliar situations.

Swing is a popular fitness and entertainment activity. People who can swing can swing higher and higher without the help of others, while those who can't swing can never swing. To make the swing swing higher and higher, the reasonable way is:

A. When swinging down from a height, the body quickly squats, and when swinging up from the lowest point, the body quickly stands up.

B keep your body upright when you swing from a height, and squat down quickly when you swing up from the lowest point.

C. whether you are swinging down from a height or swinging up from the lowest point, you should keep squatting.

D. Whether you swing from a height or from the lowest point, keep your body upright.

Analysis: When swinging down from a height, the body quickly squats, and gravity does work on the human body, and the potential energy of gravity is converted into kinetic energy. When swinging upward from the lowest point, the body quickly stands up, overcomes gravity to do work, and physical energy is converted into mechanical energy, which increases mechanical energy. Therefore, option A is correct.

Answer: a.

Reflection after the question: this question involves the knowledge of work and energy transformation and conservation. Swing is a popular sport, but some people may not seriously understand the physical laws. The college entrance examination tends to grasp the exam materials that people are more familiar with and easy to ignore to make propositions. This question examines the analytical reasoning ability of candidates.

Example 3 A ball with a mass of m is tied with a light rope with a length of L and moves in a circle in a vertical plane. During the movement, the ball is subject to air resistance. It is known that the light rope is pulled by 7mg when the ball passes through the lowest point, and it can just pass through the highest point after half a week, so the work done by the ball to overcome air resistance in this process is ().

A.mgL/4 B.mgL/3 C.mgL/2 Design Company

Analysis: According to Newton's law of motion, when the ball passes through the lowest point, it is 7mg-mg=mv 12/L, and the condition that the ball can just pass through the highest point is that gravity provides centripetal force, that is, mg=mv22/L, which is obtained from the kinetic energy theorem, and mv12-mv22/2 = 2mgl-wf. Solve the above problems.

Answer: C.

Reflection after the question: this question involves many aspects of knowledge such as work and energy, Newton's law of motion, circular motion, centripetal force and so on. Candidates are required to analyze the situation that the rope pulls the ball to the highest point in a circular motion, which reflects the examination of candidates' comprehensive analysis ability. The combination of functional relationship and circular motion has a high repetition rate in college entrance examinations over the years.

As shown in the figure, the left end of a light spring is fixed to the left end of a long wooden board M, and the right end is connected to a small wooden block M, ignoring the friction between M and the ground. At first, both M and M were stationary. Now, constant horizontal forces F 1 and F2 with equal magnitude and opposite directions are applied to M and M simultaneously. It is assumed that the deformation of the spring does not exceed its elastic limit during the whole movement after two objects start to move. For the system consisting of m, m and spring ()

A. due to the great reversal of F 1 and F2, the mechanical energy of the system is conserved.

B when the spring force is equal to F 1 and F2, the kinetic energy of m and m is maximum.

C. Since the sizes of F 1 and F2 are unchanged, M and M have been doing uniform acceleration respectively.

D. Because F 1 and F2 can do positive work, the mechanical energy of the system has been increasing.

Analysis: Because the sum of the work done by F 1 and F2 on the system is not zero, the mechanical energy of the system is not conserved and A is wrong; When the spring force is equal to F 1 and F2, the velocity reaches the maximum, so their kinetic energy is the largest, and B is correct; Because the elastic force is changing, the resultant force on m and m is also changing, and it will not accelerate evenly, so c is wrong; Because F 1 and F2 do positive work on the system first, when the speed of the two masses drops to zero, the spring force is greater than F 1 and F2. After that, the two masses move towards each other again, and F 1 and F2 do negative work on the system, so the mechanical energy of the system begins to decrease, and D is wrong.

Answer: B.

Reflection after the question: This question involves more knowledge about the conservation conditions of spring, work and mechanical energy, and the relationship between force and motion. The topic situation is complex, and the ability of candidates to understand, analyze and solve problems is comprehensively investigated. In recent years, the combination of functional relationship and spring has appeared more in the college entrance examination, so we should pay attention to it in review.

Example 5 As shown in the figure, an object with a mass of m is placed on a smooth horizontal surface, one end of the rope passes through the crown block and is fixed on the object, and the other end moves vertically downward at a constant speed v0 under the action of force F, and the angle between the object and the horizontal direction is 45? 0? In this process, the work done by the tension in the rope to the object is

mv02

C.mv02 D.mv02

Analysis: The object starts to move from rest, and the work done by the tension in the rope to the object is equal to the increased kinetic energy of the object. The object moves until the angle between the rope and the horizontal is α=45? 0? The rate at 2 o'clock is set to V, with: vcos45? 0? 2=v0, then: v=v0, then the work done by the tension of the rope on the object is W=

Answer: B.

Reflection after the question: this question involves the synthesis and decomposition of motion, the theorem of work and kinetic energy and many other knowledge. Candidates are required to deeply understand the meaning of kinetic energy theorem and be able to calculate instantaneous velocity by using the decomposition law of vectors. The topic requires high ability of candidates.

Example 6 As shown in the figure, balls A and B with a mass of m are connected by a thin line with a length of L and placed on a smooth horizontal desktop with a height of H (L > 2h), and ball A is next to the table. Release two balls from a static state. If ball A and ball B don't rebound after landing, the following statement is correct.

The acceleration of the ball before landing is

B.the speed at which the ball reaches the table is

The horizontal distance between C. A and B landings is H.

D. the work that rope l does to ball b is as follows

Analysis: Before the ball A landed, the acceleration of the whole ball was calculated according to Newton's second law, and A was correct; From the release of ball A to the landing, according to the conservation of mechanical energy, there are:, and the solution is: Neither ball will rebound after landing, so the horizontal distance between A and B is △s=vt=, B is wrong and C is right. The work done by the rope L to the ball B is equal to the kinetic energy obtained by the ball B, W=, D is correct.

Answer: ACD

Reflection after the question: this question involves many aspects of knowledge such as the conservation of mechanical energy, Newton's second law, flat throwing motion, kinetic energy theorem and so on. There are many processes and complex scenes, which require candidates to choose the research object reasonably, analyze the physical process correctly and fully examine the comprehensive application ability of candidates.

Example 7 As shown in the figure, the height of the top of the smooth ramp is h from the horizontal plane, and the small piece A with the mass of m slides down from the top of the ramp, and there is no mechanical energy loss when entering the slideway on the horizontal plane. In order to brake, one end of the light spring is fixed on the wall at the extension line M of the horizontal slide, and the other end is just at the end point O of the slide. It is known that in the OM section, the dynamic friction coefficient between block A and the horizontal plane is μ, ignoring the friction in other places, and the acceleration of gravity is g, so find:

The speed at which the (1) box slides to the o point;

(2) the elastic potential energy of the spring at the maximum compression d (let the elastic potential energy be zero when the spring is at the original length)

(3) If Block A can be bounced back to the ramp, what is the maximum height it can rise?

Analysis: (1) is derived from the law of conservation of mechanical energy.

(2) The work done by the slider A to overcome friction on the horizontal slide is

According to the law of conservation of energy