Wang liantao
(Department of Physics, Dalian University, Dalian 1 16622)
Is the law of conservation of momentum one of the basic laws of physics? 6? 8. Use it
Solve some variable force problems, such as strike, collision, explosion and
It is more convenient to change the quality problem. Solution of Newton's second law
Solving such problems often shows helplessness, but many scholars have realized it.
Students lack a deep understanding of some basic concepts of this law.
When applying this law, some of the same mistakes often occur.
We divide these errors into two categories and give the methods to avoid them.
Wrong method.
one
Consistency of frame of reference
The law of conservation of momentum is to study the relationship between momentum changes of objects.
The relationship between the magnitude and direction of the momentum of an object depends on the description.
The size and direction of body speed. Describe the speed at which an object moves.
Degrees must be based on the choice of reference system. Therefore, in application dynamics
The law of conservation of quantity studies an object system composed of several objects, each of which
The momentum of an object must be in the same reference frame.
Example: A person with a mass of 70kg stands on a boat, and the boat and the boat are in harmony.
Male * * * Weight m: 200 kg. The boat is still on the water, man.
From the bow to the stern at a constant speed, the distance S=4 meters.
If the resistance of water to the ship is negligible, please ask someone to take the water too far.
How far?
Many students can easily answer this question:
Let the human speed be l=.
'
The speed of the ship is 2 =(Z is the distance traveled by the ship).
Because it is not affected by external forces in the horizontal direction, it is
Momentum is conserved in the horizontal plane, so there is
M l-(m-m) v2: 0
Because 1 takes the ship as the frame of reference and 2 takes the water as the reference.
According to the system display. For different reference systems, the law of conservation of momentum does not hold.
So the above equation is wrong.
The correct solution should be:
Suppose the speed of people to the ship is.
The speed of the ship to the water is 2,
Shang Yun's
'
Solution? 6? 8 ka
= 5)
r & ltWhen =: ln—
R b e nlsinaeo (1) 丌 ~.z.trltn, "1-
R>R cloud =: l, = an e.
(2)
Inside the solenoid. A magnetic field is a uniform magnetic field along an axis.
Magnetic field, outside the solenoid, the distance between the magnetic field and the solenoid axis is O.
With the increase of line spacing, it is inversely proportional to attenuation.
2 discussion
Referring to fig. 2, the relationship between α and solenoid geometry is as follows:
. n 27rR 1
~/(27 rrn)+ 1 ~/(2 RRR)+ 1
(3)
Substituting (3) into (1) and (2) gives:
& ltr, mu: Some e (4) ~/(27 rrn) 0+ 1'
b-0(r & gt； R) B= 0nl e
(r>r), the results are the same as those given in general textbooks.
This is just an idealized situation, the magnetic field distribution of solenoid.
When n-0, the current flows axially on the solenoid wall.
Dynamic, obtained from (4) and (5):
A F0 (r
1L 2 rr (,>r,? 6? eight
The results are consistent with the magnetic field distribution of a long straight current-carrying hollow cylinder.
When the scale is 1 +0, = 1 E, it is equivalent to infinite length.
Magnetic field of current-carrying straight wire.
From the above analysis, it can be seen that formulas (4) and (5) are used in several special situations.
It is consistent with the corresponding magnetic field current distribution, so it can be considered that
These two formulas are exact solutions of the magnetic field of a long straight close-wound solenoid in the whole space.
Modern physics knowledge
Displacement and deformation
Chen Jide
(Wuhan China Geo University)
Lichuan
Hubei 430074)
Displacement and deformation are two related and different concepts.
Read, deformation is scalar, displacement is vector.
Under the action of external force, the position of each point in the object should be
Change, the change of this position is called displacement. Displacement can be divided into
Rigid displacement and deformation displacement. If any two objects
The relative position of the point has not changed, so the displacement of the object is said at this time.
For rigid displacement, for example, in theoretical mechanics, when the rigid body is translated or
Displacement in the process of rotation is rigid displacement. If any two objects
The relative position of a point has changed, so the position of the object at this time.
Displacement is called deformation displacement, such as the research object in material mechanics.
Volume displacement is deformation displacement related to linear strain or angular strain.
Displacement and deformation are two concepts in mechanics of materials.
Often occur one after another, for example, in axial tension and axial compression.
Deformation is obtained by Hooke's law, but it is often necessary in exercises.
Calculating the displacement of the rod end of the tension-compression bar; In the torsion of an equi-straight circular shaft,
Its deformation is measured by the torsion angle, but the torsion angle itself is
Is angular displacement; In the plane bending of a beam, its deformation should be beam-shaped.
The curvature of the deflection curve, but because the curvature is difficult to measure, it is usually
Deflection and rotation angle are used to reflect the change of beam.
Shape.
In elasticity, deformation and displacement are expressed by geometric equations.
The geometric equation of space problem is
a u a 1L a 1l
e y +
a 1l a u}
ey y +
Artel Nie
e y" +
According to the geometric equation, when the displacement component of a point in the object is completed
When fully determined, the strain component is also fully determined, because the strain
Is the differential form of displacement; But when the strain component is completely determined
The displacement component may not be solved because of this.
In addition to pure deformation displacement, the displacement of an object can also be
Rigid displacement can be included.
The speed of human beings to water is,
According to the principle of velocity synthesis, there are 3= 1-2,
Choosing water as the frame of reference and applying the law of conservation of momentum, there are
My3-(m-ra) 2 = 0
Solve the above two equations.
2 1
Because = VL-V: = VL-ra = Mu Danao
The distance people walk to the water's edge in t time is
s .: = 5= ×4:2-6(
Second, immediacy.
The law of conservation of momentum often studies the momentum of physical systems.
The change of t at a certain moment is the law of conservation of momentum.
Primary Ko=0
The total. Must be both momentum vectors.
This is the instantaneity of the law of momentum conservation. Ignore this.
Will cause fundamental mistakes.
For example:
On the calm water, there is a boat with an elbow.
Supplement (200 years)
The speed is moving at a constant speed. Today, an object with mass ra is used as a phase.
For ship/d, the speed is thrown backwards. Ask the speed of the boat after throwing.
To what extent
For this problem, most students can choose water correctly.
It's a frame of reference. Because there is no force in the horizontal direction, because
You can use the law of conservation of momentum.
I found that students can write the following two equations:
Mv = (Mv=(M —ra) +ra (a u)
Or mv = (m-ra)+ra ('-u).
Which indicates the speed of the ship after the object is thrown. From an observation point of view,
The difference between these two equations is the speed at which an object is thrown into the water.
There is a difference in degree. Obviously, the previous equation is wrong.
The reason is that the "instantaneity" of momentum is ignored because it is
The speed of the ship and the object before the throwing action is completed.
Both, that is, the phase between the object and the ship when the speed of the ship is constant.
Yes, the speed is zero. The speed of the ship changes at the moment when the object is thrown.
Because, at the same time, the object obtains the relative n with the ship.
Speed.
=+u. Used to solve the second equation above.
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