DETERMINING THE SPEED OF THE MOUNTING CHUCK USING A BALLISTIC TURNING PENDULUM
Objective:study of conservation laws using the example of a ballistic torsion pendulum.
Devices and accessories: ballistic torsion pendulum, set of mounting chucks, millisecond watch unit.
Description of the experimental setup
A general view of the ballistic pendulum is shown in the figure. Base 1 equipped with adjustable legs 2 to level the instrument. The column is fixed at the base 3 on which the upper 4 , bottom 5 and middle 6 brackets. A firing device is attached to the middle bracket 7 , as well as a transparent screen with an angular scale applied to it 8 and photoelectric sensor 9 ... Brackets 4 and 5 have clamps for fastening steel wire 10 , on which a pendulum is suspended, consisting of two bowls filled with plasticine 11 , two transported loads 12 , two rods 13 , walker 14 .
Work order
1. Having removed the transparent screen, place the weights at a distance r1 from the axis of rotation.
3. Insert the cartridge into the spring device.
4. Push the cartridge out of the spring assembly.
6. Turn on the time counter (on the panel, the meter indicators light up "0").
7. Deflect the pendulum at an angle φ1, and then let it go.
8. Press the STOP button, when the counter shows nine oscillations, record the time of ten complete oscillations t1. Calculate the oscillation period T1. Enter the data in table No. 1, repeat paragraphs 7.8 four more times.
9. Place the weights at a distance r2. Carry out steps 2-8 for distances r2.
10. Calculate the speed for five measurements using the formula:
11. Estimate the absolute error in calculating the speed by analyzing the five values \u200b\u200bof the speed (Table 1).
r \u003d 0.12 m, m \u003d 3.5 g, M \u003d 0.193 kg.
Table # 1
| Experience number | r1 \u003d 0.09 m | r2 \u003d 0.02 m | |||||||
| φ1 | t1 | T1 | φ2 | t2 | T2 | V | |||
| hail. | glad. | from | hail. | glad. | from | m / s | |||
| 1. | |||||||||
| 2. | |||||||||
| 3. | |||||||||
| 4. | |||||||||
| 5. |
Calculated part
test questions
Formulate the law of conservation of angular momentum.
The moment of impulse of the "cartridge-pendulum" system about the axis is preserved:
Formulate the law of conservation of energy.
When the pendulum oscillates, the kinetic energy of the rotational motion of the system turns into a potential elastically deformed wire during torsion:
Write the equation of motion of a rigid body around a fixed axis
4. What is a torsion pendulum and how is the period of its oscillation determined?
A torsion pendulum is a massive steel rod rigidly attached to a vertical wire. At the ends of the rod there are bowls with plasticine, which allows the cartridge to "stick" to the pendulum. Also on the rod there are two identical weights that can move along the rod relative to its axis of rotation. This makes it possible to change the moment of inertia of the pendulum. A "walker" is rigidly fixed to the pendulum, which allows photoelectric sensors to count the number of its total oscillations.Torsional vibrations are caused by elastic forces arising in the wire when it is twisted. In this case, the period of oscillation of the pendulum:
5. How else can you define the speed of the mounting chuck in this work?
This article is part of the topic equation of a line in a plane. Here we will analyze from all sides: we start with the proof of the theorem, which defines the form of the general equation of the straight line, then we consider the incomplete general equation of the straight line, give examples of incomplete equations of the straight line with graphic illustrations, in conclusion we will focus on the transition from the general equation of the straight line to other types of the equation of this straight line and give detailed solutions to typical problems for the compilation of the general equation of a straight line.
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The general equation of the straight line - basic information.
Let's analyze this algorithm when solving an example.
Example.
Write the parametric equation of a straight line, which is given by the general equation of a straight line 
.
Decision.
First, we bring the original general equation of the straight line to the canonical equation of the straight line:
Now we take the left and right sides of the resulting equation equal to the parameter. We have 
Answer:
From the general equation of the straight line, it is possible to obtain the equation of the straight line with the slope coefficient only when. What do you need to do to transition? First, in the left-hand general equation, leave only the term in the straight line, the rest of the terms must be transferred to the right-hand side with the opposite sign: 
... Second, divide both sides of the resulting equality by the number B, which is different from zero, 
... And that's all.
Example.
A straight line in a rectangular coordinate system Oxy defines the general equation of a straight line. Get the equation of this line with the slope.
Decision.
Let's take the necessary steps:.
Answer:
When a straight line is given by the complete general equation of a straight line, it is easy to obtain the equation of a straight line in segments of the form. To do this, we transfer the number C to the right side of the equality with the opposite sign, divide both sides of the resulting equality by –C, and finally transfer the coefficients for the variables x and y to the denominators: 
A (-3; 4), B (2; 1), C (-1; a). It is known that AB \u003d BC. Find a. 3. The radius of the circle is 6. The center of the circle belongs to the Ox axis and has a positive abscissa. The circle passes through the point (5; 0). Write the equation of the circle. 4. Vector a is codirectional with the vector b (-1; 2) and has the length of the vector c (-3; 4). Find the coordinates of the vector a. Urgently Help please!)
vector a (5; - 9). The answer should be 2x - 3y \u003d 38.
2. With a parallel translation, point A (4: 3) goes to point A1 (5; 4). Write the equation of the curve into which the parabola y \u003d x ^ 2 (in the sense of x squared) - 3x +1 with this movement goes. The answer should be: x ^ 2 - 5x +6.
Please help with questions about geometry (grade 9)! 1) Formulate and prove the lemma on collinear vectors. 2) What does it mean to decompose a vector in twogiven vectors. 3) Formulate and prove a theorem on the expansion of a vector in two non-collinear vectors. 4) Explain how a rectangular coordinate system is introduced. 5) What are coordinate vectors? 6) Formulate and prove an assertion about the expansion of an arbitrary vector in coordinate vectors. 7) What are vector coordinates? 8) Formulate and prove the rules for finding the coordinates of the sum and difference of vectors, as well as the product of a vector by a number according to given coordinates of vectors. 9) What are the radius vectors of a point? Prove that the coordinates of a point are equal to the corresponding coordinates of vectors. 10) Derive formulas for calculating the coordinates of a vector by the coordinates of its beginning and end. 11) Derive formulas for calculating the coordinates of a vector by the coordinates of its ends. 12) Output a formula for calculating the length of a vector by its coordinates. 13) Derive a formula for calculating the distance between two points by their coordinates. 14) Give an example of solving a geometric problem using the coordinate method. 15) What equation is called the equation of this line? Give an example. 16) Derive the equation of a circle of a given radius centered at a given point. 17) Write the equation of a circle of a given radius centered at the origin. 18) Derive the equation of this line in a rectangular coordinate system. 19) Write the equation of lines passing through a given point M0 (X0: Y0) and parallel to the coordinate axes. 20) Write the equation of the coordinate axes. 21) Give examples of the use of the equations of the circle and the line in solving geometric problems.
1) Formulate and prove the lemma on collinear vectors.2) What does it mean to decompose a vector in two given vectors.
3) Formulate and prove a theorem on the expansion of a vector in two non-collinear vectors.
4) Explain how a rectangular coordinate system is introduced.
5) What are coordinate vectors?
6) Formulate and prove an assertion about the expansion of an arbitrary vector in coordinate vectors.
7) What are vector coordinates?
8) Formulate and prove the rules for finding the coordinates of the sum and difference of vectors, as well as the product of a vector by a number at the given coordinates of the vectors.
9) What is the radius vector of a point? Prove that the coordinates of the point are equal to the corresponding coordinates of the vectors.
10) Derive formulas for calculating the coordinates of a vector by the coordinates of its beginning and end.
11) Derive formulas for calculating the coordinates of a vector by the coordinates of its ends.
12) Output a formula for calculating the length of a vector by its coordinates.
13) Derive a formula for calculating the distance between two points by their coordinates.
14) Give an example of solving a geometric problem using the coordinate method.
15) What equation is called the equation of a given line? Give an example.
16) Derive the equation of a circle of a given radius centered at a given point.
17) Write the equation of a circle of a given radius centered at the origin.
18) Derive the equation of this line in a rectangular coordinate system.
19) Write the equation of lines passing through a given point M0 (X0: Y0) and parallel to the coordinate axes.
20) Write the equation of the coordinate axes.
21) Give examples of using the equations of a circle and a line in solving geometric problems.
Please, it is very necessary! Preferably with pictures (where necessary)!