3.
H.minimum h. h.:
1) kinetic energy ball maximum
2) The potential energy of the spring is minimal
3) The potential energy of the ball interaction with the earth is maximum
Decision:
h., the ball changes the direction of his movement. It ceases to rise and begins to descend, so the speed of it at this point is zero, and therefore the kinetic energy is minimal. On the other hand, at this point, the ball is at the maximum height above the surface of the Earth, therefore, the potential energy of the interaction of the ball with the earth is maximum.
Note
It should be noted that the potential energy of the springs is minimal when the spring is not stretched. If you simply hang the cargo to the ceiling on the spring, the spring stretches, and when hesitations, the cargo will fluctuate around this new "stretched" equilibrium position. Therefore, if it turns out that h. exactly coincides with the long non-deformed spring, then at this point the spring will not stretch. Consequently, with this condition, item 2 will also be faithful.
4.
The cargo fluctuates on the spring suspended vertically to the ceiling, while the maximum distance from the ceiling to the cargo center is H, minimal h.. At the point removed from the ceiling at the distance h.:
1) kinetic energy ball maximum
2) kinetic energy ball minimal
3) the potential energy of the spring is maximum
4) The potential energy of the interaction of the ball with the earth is minimal
Decision:
At the point removed from the ceiling at the distance h., the ball changes the direction of his movement. It ceases to rise and begins to descend, so the speed of it at this point is zero, and therefore the kinetic energy is minimal. Approval 3 and 4 refer to the key position when it is removed from the ceiling for distance H.. At this point, the spring is stretched as much as possible, and the ball is on minimum distance from the earth.
5.
The load fluctuates on the spring suspended vertically to the ceiling, while the maximum distance from the ceiling to the center of cargo is equal H.minimum h.. The position of the equilibrium of the cargo is from the ceiling at a distance:
1) h.
2) H.
3) (H + H) / 2
4) (H-H) / 2
Decision:
The spring pendulum makes harmonic oscillations around its equilibrium position. Let A. - amplitude of oscillations, and x. - The desired distance from the ceiling to the equilibrium position. Then
,
Where do you find that
6.
The ball varies on the spring, suspended vertically to the ceiling, while the maximum distance from the ceiling to the ball center is equal H.minimum h.. At the point removed from the ceiling at the distance H.Maximum:
1) kinetic energy ball
2) Potential Spring Energy
3) Potential Energy Energy Energy Energy
4) The sum of the kinetic energy of the ball and the interaction of the ball with the earth
Decision:
At the point removed from the ceiling at the distance H., the ball changes the direction of his movement. It ceases to descend and begins to rise, so the speed of it at this point is zero, and therefore the kinetic energy is minimal. At the same time, the ball is at the minimum distance from the Earth, therefore, the potential energy of interaction with the Earth is also minimal. Spring, on the contrary, it turns out in this position as stretched as much as possible. Thus, the statement 2 is true.
7.
The oscillatory movement of the body is set by the equation: 
,
Where a \u003d 5 cm, b \u003d 3 s -1. What is the amplitude of oscillations?
Decision:
General view of the law of change over time the coordinates of the fluctuations in the body has
,
Where x MAX - amplitude of oscillations. Comparing with conclude that the amplitude of oscillations is equal x max \u003d a \u003d 5 cm
8. A cargo suspended on the spring of 400 N / m rigidity, performs free harmonic oscillations. What should be the rigidity of the spring so that the frequency of the oscillations of this cargo has increased by 2 times?
Answer: N / m.Decision:
The frequency of fluctuations of the spring pendulum is associated with the rigidity of the spring and the weight of the cargo by the ratio
Consequently, with a constant weight of the cargo to increase the frequency of oscillations, it is necessary to increase the rigidity of the spring 4 times. Thus, the rigidity of the spring must be equal to
9.
The figure shows the dependence of the amplitude of the established pendulum oscillations from the frequency of the forcing force (resonant curve). 
What is equal to the amplitude of the oscillations of this pendulum during resonance.
Decision:
The resonance is the phenomenon of a sharp increase in the amplitude of the forced oscillations when the frequency of the forcing force is approached to its own frequency of the pendulum. From the graph, it can be seen that the resonance occurs when the frequency of the forcing force in 1 Hz is found, the amplitude of the pendulum oscillations is 10 cm.
10.
A massive ball suspended on the spring makes harmonic oscillations along the vertical straight line. To increase the period of oscillations 2 times, enough bulb mass
1) increase by 4 times
2) reduce 4 times
3) increase by 2 times
4) reduce 2 times
Energy interaction tel. Potential energy body in itself cannot have. Determined by the force acting on the body from another body. Since the interacting bodies are equal, then potential energy There are only interacting bodies.
A. = FS. = mG. (h 1. - h 2.).
Now consider the movement of the body on the inclined plane. When moving the body down the inclined plane of gravity makes work
A. = mgSCOSα..
From the figure it is clear that s.cOSα. = h., hence
BUT = mG.h..
It turns out that the work of gravity does not depend on the body movement trajectory.
Equality A. = mG. (h 1. - h 2.) can be written as A. = - (mG.h. 2 - MG. h. 1 ).
That is, the work of gravity when moving the body mass m. From the point h 1. exactly h 2. on any trajectory is equal to change some physical quantity mGH with the opposite sign.
The physical quantity equal to the product of body weight on the fluency acceleration module and to the height to which the body is raised above the surface of the Earth is called the potential energy of the body.
Potential energy is denoted through E R.. E R. = mGH, hence:
A. = - (E. R 2 - E. R 1 ).
The body can possess both positive and negative energy. Body mass m. at a depth h. From the surface of the Earth has negative potential energy: E R. = - mGH.
Consider the potential energy of the elastified body.
Attach to the spring with rigidity k. Bar, stretch the spring and let go of the bar. Under the action of the strength of elasticity, the stretched spring will drive the bar and move it for a while. We calculate the work of the strength of the spring of the spring from some initial value x 1 to finite x 2.
The strength of elasticity in the process of deformation of the spring changes. To find the work of the elastic force, you can take the product of the average value of the power module and the move module:
BUT = F U.Sh.(x 1 - x 2).
Since the strength of the elasticity is proportional to the deformation of the spring, the average value of its module is equal
Substituting this expression in the work formula, we get:
The physical value equal to half the product of the hardness of the body into the square of its deformation is called potential energy Elastified Body:
From where it follows that A. = - (E P2. - E P1.).
Like a magnitude mGH, potential energythe elastified-deformed body depends on the coordinates, since x. 1 I. x. 2 is the extension of the spring and at the same time - the coordinates of the end of the spring. Therefore, we can say that the potential energy in all cases depends on the coordinates.
Denoting "action". You can call an energetic person who moves, creates a certain job, can create, act. Also, energy has vehicles created by people, live and dead nature. But it is in ordinary life. In addition, there is a strict science of physics that determined and denoted many types of energy - electrical, magnetic, atomic, etc. However, now it will be about the potential energy that cannot be considered in the detachment from the kinetic one.
Kinetic energy
This energy, according to the ideas of mechanics, have all the bodies that interact with each other. And in this case we are talking about the movement of tel.
Potential energy
A \u003d fs \u003d ft * h \u003d mgh, or Ep \u003d Mgh, where:
EP - Potential Body Energy,
m - body weight,
h - body height above the ground surface,
g - Acceleration of free fall.
Two types of potential energy
In potential energy, two types differ:
1. Energy with a mutual arrangement of tel. Such energy has a hanging stone. Interestingly, the potential energy has conventional firewood or coal. They contain not oxidized carbon, which can oxidize. If you say easier, burnt firewood can potentially heat the water.
2. Elderly elastic deformation. For example, here you can bring an elastic harness, compressed spring or system "bone-muscle-ligaments".
Potential and kinetic energy are interrelated. They can go into each other. For example, if you throw a stone up, when moving first it has kinetic energy. When it reaches a certain point, then for a moment there is a cast and get potential energy, and then the gravity pulls it down and the kinetic energy will appear again.
Any body always has energy. If there is a movement, it is obvious: there is a speed or acceleration, which, multiplied by the mass, gives the desired result. However, in the case when the body is motionless, it, if neither paradoxical, can also be characterized as possessing energy.
So, it occurs when moving, potential - with the interaction of several tel. If everything is more and less obvious from the first, then often the force arising between two fixed objects remains beyond the understanding.
It is well known that the planet Earth affects all the bodies on its surface at the expense, that is, it attracts any item with a certain force. When moving the subject, changing its height, there is also a change in energy indicators. Immediately at the time of lifting the body has acceleration. However, at the highest point when the subject (even in a fraction of a second) is immobile, it has potential energy. The thing is that he is still pulling the field of the Earth, with which the body interacts.
Speaking otherwise, potential energy arises always due to the interaction of several objects forming the system, regardless of the size of the items themselves. At the same time, by default, one of them is represented by our planet.
Potential energy - The value depending on the mass of the subject and height to which it is raised. International designation - Latin letters EP. as follows:
Where m is a mass, G - acceleration H - height.
It is important to consider in more detail the elevation parameter, since it often becomes the reason for solving problems and understand the value of the value under consideration. The fact is that any vertical movement of the body has its own initial and end point. For the correct location of the potential energy of interaction bodies, it is important to know the initial height. If it is not specified, then its value is zero, that is, coincides with the surface of the Earth. In the case, if known as the initial point of reference and the final height, it is necessary to find the difference between them. The resulting number and will be the desired H.
It is also important to note that the potential energy of the system may have a negative value. Suppose we have already raised the body above the ground level, it became, it has a height that is called initial. When it sinks it, the formula will look like:
Obviously, H1 is greater than H2, therefore, the value will be negative, which will give the entire formula a minus sign.
It is curious that the potential energy is higher than the farther from the surface of the Earth the body is located. In order to better understand this fact, we think: the higher you need to raise the body above the ground, the thoroughly perfect work. The higher the value of the work of any strength, the fact that the energy is more invested. Potential energy, in other words, is the energy of the possibility.
Similarly, it is possible to measure the energy of the interaction of bodies when stretching the subject.
As part of the topic under consideration, it is necessary to separately discuss the interaction of the charged particle and electric field. In such a system, the potential energy of charge will be given. Consider this fact. For any charge, which is within the electrical field, the power of the same name operates. Moving the particle occurs due to the work produced by this force. Considering that the actual charge and (more precisely speaking, the body that created it) is a system, we also obtain the potential energy movement energy within the specified field. Since this type of energy is a special case, he was assigned the name of the electrostatic.
