LABORATORY WORK No. 5
DETERMINATION OF MOMENTS OF INERTIA OF BODIES OF ARBITRARY FORM
1 Purpose of the work
Determination of the moment of inertia of mathematical and physical pendulums.
2 List of devices and accessories
Experimental setup for determining the moments of inertia of mathematical and physical pendulums, ruler.
1-physical pendulum,
2-mathematical pendulum,
4-place thread attachment,
5-vertical rack,
6-base,
3 Theoretical part
A mathematical pendulum is a material point suspended on a weightless inextensible thread. The period of oscillation of a mathematical pendulum is determined by the formula:
,
Where l– thread length.
A physical pendulum is called solid, capable of oscillating around a fixed axis that does not coincide with its center of inertia. Oscillations of mathematical and physical pendulums occur under the influence of quasi-elastic force, which is one of the components of gravity.
The reduced length of a physical pendulum is the length of a mathematical pendulum whose period of oscillation coincides with the period of oscillation of the physical pendulum.
The moment of inertia of a body is a measure of inertia during rotational motion. Its magnitude depends on the distribution of body mass relative to the axis of rotation.
The moment of inertia of a mathematical pendulum is calculated by the formula:
,
Where m - mass of a mathematical pendulum, l - length of a mathematical pendulum.
The moment of inertia of a physical pendulum is calculated by the formula:
4 Experiment results
Determination of the moments of inertia of mathematical and physical pendulums
|
T m, With |
g, m/s 2 |
I m, kgm 2 |
|||||
|
m f, kg |
T f, With |
I f, kgm 2 |
I, kgm 2 |
|||||
Δ t = 0.001 s
Δ g = 0.05 m/s 2
Δ π = 0,005
Δ m = 0.0005 kg
Δ l = 0.005 m
I f = 0.324 ± 0.007 kg m 2 ε = 2.104%
Determination of the moment of inertia of a physical pendulum depending on the mass distribution
|
I f, kgm 2 |
I f, kgm 2 |
||||||
I f 1 = 0.422 ± 0.008 kg m 2
I f 2 = 0.279 ± 0.007 kg m 2
I f 3 = 0.187 ± 0.005 kg m 2
I f 4 = 0.110 ± 0.004 kg m 2
I f5 = 0.060 ± 0.003 kg m 2
Conclusion:
In the laboratory work done, I learned to calculate the moment of inertia of a mathematical pendulum and a physical pendulum, which is in some nonlinear dependence on the distance between the suspension point and the center of gravity.
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Laboratory work № 1.
Study of uniformly accelerated motion without initial speed
Goal of the work: establish a qualitative dependence of the speed of a body on time during its uniformly accelerated motion from a state of rest, determine the acceleration of the body’s movement.
Equipment: laboratory trough, carriage, tripod with coupling, stopwatch with sensors.
.
I have read the rules and agree to comply. _________________________________
Student signature
Note: During the experiment, the carriage is launched several times from the same position on the chute and its speed is determined at several points on different removals from the starting position.
If a body moves from a state of rest uniformly accelerated, then its displacement changes with time according to the law:S = at 2 /2 (1), and speed –V = at(2). If we express acceleration from formula 1 and substitute it into 2, we obtain a formula expressing the dependence of speed on displacement and time of movement:V = 2 S/ t.
1. Uniformly accelerated motion is ___
2. In what units in the C system is measured:
acceleration A =
speed =
time t =
moving s =
3. Write the acceleration formula in projections:
A x = _________________.
4. Using the velocity graph, find the acceleration of the body.
a =
5. Write the equation of displacement for uniformly accelerated motion.
S= + ______________
If 0 = 0, then S=
6. The movement is uniformly accelerated if the following regularity is satisfied:
S 1 :S 2 :S 3 : … : S n = 1: 4: 9: … : n 2 .
Find an attitudeS 1 : S 2 : S 3 =
Progress
1. Prepare a table to record the results of measurements and calculations:
2. Using a coupling, secure the chute to the tripod at an angle so that the carriage slides down the chute on its own. Fix one of the stopwatch sensors using a magnetic holder on the gutter at a distance of 7 cm from the beginning of the measuring scale (x 1 ). Fix the second sensor opposite the value of 34 cm on the ruler (x 2 ). Calculate the displacement (S), which the carriage will make when moving from the first sensor to the secondS = x 2 –x 1 = ____________________
3. Place the carriage at the beginning of the chute and release it. Take stopwatch readings (t).
4. Calculate the speed of the carriage using the formula (V), with which she moved past the second sensor and the acceleration of movement (a):
=
______________________________________________________
5. Move the lower sensor 3 cm down and repeat the experiment (experiment No. 2):
S = ________________________________________________________________
V = ______________________________________________________________
A = ______________________________________________________________
6. Repeat the experiment by removing the lower sensor another 3 cm (experiment No. 3):
S=
A = _______________________________________________________________
7. Draw a conclusion about how the speed of the cart changes with increasing time of its movement, and what the acceleration of the carriage turned out to be during these experiments.
___________
Laboratory work No. 2.
Measuring gravity acceleration
Goal of the work: determine the acceleration of gravity, demonstrate that in free fall the acceleration does not depend on the mass of the body.
Equipment: optoelectric sensors – 2 pcs., steel plate – 2 pcs., measuring unitL-micro, starting device platform, power supply.
Safety regulations. Read the rules carefully and sign that you agree to comply with them..
Carefully! There should be no foreign objects on the table. Careless handling of devices leads to their falling. In this case, you can get a mechanical injury or bruise, and put the devices out of working order.
I have read the rules and agree to comply. _________________________
Student signature
Note: To perform the experiment, a demonstration kit “Mechanics” from the equipment series is usedL-micro.
In this work, the acceleration of free fallg determined based on time measurementt time spent by a body falling from a heighth without initial speed. When conducting an experiment, it is convenient to record the movement parameters of metal squares of the same size, but of different thickness and, accordingly, different mass.
Training tasks and questions.
1. In the absence of air resistance, the speed of a freely falling body during the third second of fall increases by:
1) 10 m/s 2) 15 m/s 3) 30 m/s 4) 45 m/s
2. Oh . Which of the bodies at the moment of timet 1 acceleration is zero?
3. The ball is thrown at an angle to the horizontal (see picture). If air resistance is negligible, then the acceleration of the ball at the pointA codirectional to the vector
1) 1 2) 2 3) 3 4) 4
4. The figures show graphs of the velocity projection versus time for four bodies moving along the axisOh . Which body moves with the greatest acceleration in magnitude?
Using the graph of the projections of the displacement vectors of bodies versus the time of their movement (see figure), find the distance between the bodies 3 s after the start of movement.
1) 3 m 2) 1 m 3) 2 m 4) 4 m
Progress
1
.
Place the starter platform at the top of the chalkboard. Place two optoelectric sensors vertically below it, orienting them as shown in the figure. The sensors are located at a distance of approximately 0.5 m from each other in such a way that a body falling freely after being released from the launching device sequentially passes through their gates.
2. Connect the optoelectric sensors to the connectors on the trigger platform, and the power supply to the connectors of the connecting cable connected to connector 3 of the measuring unit.
3. Select the item “Determination of gravitational acceleration (option 1)” from the menu on the computer screen and enter the equipment setup mode. Notice the images of the sensors in the window on the screen. If only the sensor is presented, then the sensor is open. When the optical axis of the sensor is blocked, it is replaced by an image of the sensor with a cart in its alignment.
4. Hang one of the steel plates to the trigger magnet. In order to process the results use a simple formulah = GT 2 /2 , it is necessary to set exactly mutual arrangement steel plate (in the starting device) and the optoelectric sensor closest to it. The belt countdown begins when one of the optoelectric sensors is triggered.
5. Move the upper optoelectric sensor up towards the starting device with the body suspended from it until the image of the sensor with the cart in its alignment appears on the screen. Then very carefully lower the sensor down and stop it at the moment when the cart disappears from the sensor image .
Go to the measurement screen and perform a series of 3 runs. Write down the time that appears on your computer screen every time.
Measure the distanceh between optoelectric sensors. Calculate the average time the body fallst Wed and, substituting the obtained data into the formulag = 2 h / t 2 Wed , determine the acceleration of free fallg . Take measurements in the same way with another square.
Enter the obtained data into the table.
Experience no.
Sensor distance
h , m
Time
t , With
Time average
t Wed, s
Acceleration of gravity
g , m/s 2
Large plate
Smaller plate
Based on the experiments, draw conclusions:
__________________________
Laboratory work No. 3.
Study of the dependence of the oscillation period of a spring
pendulum on the mass of the load and spring stiffness
Goal of the work: experimentally establish the dependence of the oscillation period and oscillation frequency spring pendulum on the stiffness of the spring and the mass of the load.
Equipment: set of weights, dynamometer, set of springs, tripod, stopwatch, ruler.
Safety regulations. Read the rules carefully and sign that you agree to comply with them..
Carefully! There should be no foreign objects on the table. Careless handling of devices leads to their falling. In this case, you can get a mechanical injury or bruise and put the devices out of working order.
I have read the rules and undertake to comply.___________________________
Student signature
Practice tasks and questions
1. Sign oscillatory motion – ___________________
__________________________
2. In which pictures is the body in a position of equilibrium?
_______ ________ _________
3. The elastic force is greatest at the point _________ and __________ shown in the figures _______ ________ ________.
4. At each point on the trajectory of motion, except for the point ______, the ball is acted upon by an elastic force of the spring directed towards the equilibrium position.
5. Indicate the points where the speed is the greatest ____________ and the least _______ _______, the acceleration is the greatest ______ ______ and the least _______.
X 
od of work
1. Assemble the measuring setup according to the figure.
2. By spring stretch x and the mass of the load, determine the spring stiffness.
F control = k x – Hooke's law
F control = R = mg ;
1) ____________________________________________________
2) ____________________________________________________
3) ____________________________________________________
3. Fill out table No. 1 depending on the oscillation period on the mass of the load for the same spring.
4. Fill out table No. 2 depending on the oscillation frequency of a spring pendulum on the spring stiffness for a load weighing 200 g.
5. Draw conclusions about the dependence of the period and frequency of oscillation of a spring pendulum on the mass and stiffness of the spring.
__________________________________________________________________________________________________
Laboratory work No. 4
Study of the dependence of the period and frequency of free oscillations of a thread pendulum on the length of the thread
Goal of the work: find out how the period and frequencies of free oscillations of a thread pendulum depend on its length.
Equipment: a tripod with a clutch and a foot, a ball with a thread attached to it about 130 cm long, a stopwatch.
Safety regulations. Read the rules carefully and sign that you agree to comply with them..
Carefully! There should be no foreign objects on the table. Use the devices only for their intended purpose. Careless handling of devices leads to their falling. In this case, you can get a mechanical injury or bruise and put the devices out of working order.
I have read the rules and agree to comply. _______________________
Student signature
Practice tasks and questions
1. What vibrations are called free? ___________________________
________________________________________________________________
2. What is a thread pendulum? ___________________________
________________________________________________________________
3. The period of oscillation is _________________________________________________
________________________________________________________________
4. Oscillation frequency is _________________________________________________
5. Period and frequency are _______________________ quantities, since their products are equal to ___________________.
6. In what units in the C system is measured:
period [ T] =
frequency [ν] =
7. The thread pendulum completed 36 complete oscillations in 1.2 minutes. Find the period and frequency of the pendulum's oscillations.
Given: C Solution:
t= 1.2 min = T =
N = 36
T - ?, ν - ?
Progress
1. Place a tripod on the edge of the table.
2. Secure the pendulum thread to the tripod leg using a piece of eraser or thick paper.
3. To conduct the first experiment, select a thread length of 5–8 cm and deflect the ball from its equilibrium position by a small amplitude (1–2 cm) and release.
4. Measure a period of time t, during which the pendulum will make 25 - 30 complete oscillations ( N ).
5. Record the measurement results in the table
6. Carry out 4 more experiments in the same way as the first, with the length of the pendulum L increase to the maximum.(For example: 2) 20 – 25 cm, 3) 45 – 50 cm, 4) 80 – 85 cm, 5) 125 – 130 cm). 
7. For each experiment, calculate the period of oscillation and write it in the table.
T 1 = T 4 =
T 2 = T 5 =
T
3 =
8
.
For each experiment, calculate the value of the oscillation frequency or
and write it down in the table.
9. Analyze the results recorded in the table and answer the questions.
a) Did you increase or decrease the length of the pendulum if the period of oscillation decreased from 0.3 s to 0.1 s?
________________________________________________________________________________________________________________________________
b) Increased or decreased the length of the pendulum if the oscillation frequency decreased from 5 Hz to 3 Hz
____________________________________________________________________________________________________________________________________
Laboratory work No. 5.
Study of the phenomenon of electromagnetic induction
Goal of the work: study the phenomenon of electromagnetic induction.
Equipment: milliammeter, coil-coil, arc-shaped or strip magnet, power source, coil with an iron core from a dismountable electromagnet, rheostat, key, connecting wires.
Safety regulations. Read the rules carefully and sign that you agree to comply with them..
Carefully! Protect devices from falling. Do not allow extreme loads on measuring instruments. When conducting experiments with magnetic fields, you should take off your watch and put away your mobile phone.
________________________
Student signature
Practice tasks and questions
1. Induction magnetic field- This ______________________________________
characteristic of the magnetic field.
2. Write down the formula module of the magnetic induction vector.
B = __________________.
Unit of measurement of magnetic induction in the C system: IN =
3. What is magnetic flux? _________________________________________
_________________________________________________________________
4. What does magnetic flux depend on? ____________________________________
_________________________________________________________________
5. What is the phenomenon of electromagnetic induction? _________________
_________________________________________________________________
6. Who discovered the phenomenon of electromagnetic induction and why is this discovery considered one of the greatest? ________________________________________
__________________________________________________________________
Progress
1. Connect the coil to the clamps of the milliammeter.
2. Insert one pole of the magnet into the coil, and then stop the magnet for a few seconds. Write down whether an induced current arose in the coil: a) during the movement of the magnet relative to the coil; b) during its stop.
__________________________________________________________________________________________________________________________________
3. Record whether the magnetic flux has changedF piercing the coil: a) during the movement of the magnet; b) during its stop.
4. Formulate under what condition an induced current arose in the coil.
5 . Insert one of the poles of the magnet into the coil, and then remove it at the same speed. (Select the speed so that the needle deflects to half the scale limit.)
________________________________________________________________
__________________________________________________________________
6. Repeat the experiment, but at a higher speed of the magnet.
a) Write down the direction of the induced current. ______________
_______________________________________________________________
b) Write down what the magnitude of the induction current will be. __________________
_________________________________________________________________
7. Write down how the speed of the magnet affects:
a) By the amount of change in magnetic flux.__________________________
__________________________________________________________________
b) To the induction current module. ____________________________________
__________________________________________________________________
8. Formulate how the modulus of the strength of the induction current depends on the rate of change of the magnetic flux.
_________________________________________________________________
9. Assemble the setup for the experiment according to the drawing.
1 – reel-skein
2 – coil
10. Check whether there is a problem in the spool1 induced current during: a) closing and opening of the circuit in which the coil is connected2 ; b) flowing through2 direct current; c) changing the current strength with a rheostat.
________________________________________________________________________________________________________________________________
11. Write down in which of the following cases: a) the magnetic flux passing through the coil changed1 ; b) an induced current appeared in the coil1 .
Conclusion:
________________________________________________________________________________________________________________________________________
Laboratory work No. 6
Observation of continuous and line spectra
emissions
Goal of the work: observation of a continuous spectrum using glass plates with beveled edges and a line emission spectrum using a two-tube spectroscope.
Equipment: projection apparatus, two-tube spectroscope, spectral tubes with hydrogen, neon or helium, high-voltage inductor, power source (these devices are common to the entire class), glass plate with beveled edges (issued to everyone).
Description of the device.
Carefully! Electricity! Make sure that the insulation of the conductors is not damaged. Do not allow extreme loads on measuring instruments.
I have read the rules and agree to comply. ______________________
Student signature
Practice tasks and questions
1. The spectroscope was designed in 1815 by a German physicist
________________________________________________________
2. Visible light is electromagnetic waves frequency:
from _________________ Hz to __________________Hz.
3. What bodies emit a continuous spectrum?
1. ______________________________________________________________
2. ______________________________________________________________
3. ______________________________________________________________
4. What is the spectrum of low-density luminous gases?
________________________________________________________________
5. Formulate G. Kirchhoff’s law: _________________________________
_______________________________________________________________
Progress
1. Place the plate horizontally in front of the eye. Through the edges forming an angle of 45º, observe a light vertical stripe on the screen - an image of the sliding slit of the projection apparatus.
2. Select the primary colors of the resulting continuous spectrum and write them down in the observed sequence.
________________________________________________________________
3. Repeat the experiment, examining the strip through the faces forming an angle of 60º. Record the differences in the form of spectra.
________________________________________________________________
4. Observe the line spectra of hydrogen, helium or neon by viewing luminous spectral tubes using a spectroscope.
Write down which lines you were able to see.
__________________________________________________________________
Conclusion: ____________________________________________________________
__________________________________________________________________
Laboratory work No. 7
Study of the fission of the nucleus of a uranium atom by
photos of tracks
Goal of the work: verify the validity of the law of conservation of momentum using the example of fission of a uranium nucleus.
Equipment: photograph of tracks of charged particles formed in a photographic emulsion during the fission of the nucleus of a uranium atom under the influence of a neutron, measuring ruler.
Note: The figure shows a photograph of the fission of the nucleus of a uranium atom under the influence of a neuron into two fragments (the nucleus was at the pointg ). The tracks show that the fragments of the uranium atom nucleus scattered in opposite directions (the break in the left track is explained by the collision of the fragment with the nucleus of one of the emulsion atoms). The greater the particle energy, the greater the track length. The greater the charge of the particle and the lower its speed, the greater the thickness of the track.
Practice tasks and questions
1. Formulate the law of conservation of momentum. ___________________________
__________________________________________________________________
2. Explain physical meaning equations:
__________________________________________________________________
3. Why does the fission reaction of uranium nuclei release energy in environment? _______________________________________________
_______________________________________________________________
4. Using any reaction as an example, explain what the laws of conservation of charge and mass number are. _________________________________
_________________________________________________________________
5. Find the unknown element of the periodic table formed as a result of the following β-decay reaction:
__________________________________________________________________
6. What is the principle of action of photo emulsion?
______________________________________________________________
Progress
1. Examine the photo and find the tracks of fragments.
2. Measure the fragment track lengths using a millimeter ruler and compare them.
3. Using the law of conservation of momentum, explain why the fragments formed during the fission of the nucleus of a uranium atom scattered in opposite directions. _____________________________________
_________________________________________________________________
4. Are the charges and energies of the fragments the same? _____________________________
__________________________________________________________________
5. By what signs can you judge this? _________________________________
__________________________________________________________________
6. One of the possible fission reactions of uranium can be written symbolically as follows:
Where z x – the nucleus of an atom of one of the chemical elements.
Using the law of conservation of charge and the table of D.I. Mendeleev, determine what this element is.
____________________________________________________________________________________________________________________________________
Conclusion: ______________________________________________________________
____________________________________________________________________________________________
Laboratory work No. 8
Studying tracks of charged particles using ready-made
photos
Goal of the work: explain the nature of the movement of charged particles.
Equipment: photographs of tracks of charged particles obtained in a cloud chamber, bubble chamber and photographic emulsion.
Practice tasks and questions
1. What methods of studying charged particles do you know? _____________
________________________________________________________________________________________________________________________________________________________________________________________________
2. What is the operating principle of a cloud chamber? ___________________
________________________________________________________________________________________________________________________________
3. What is the advantage of a bubble chamber over a cloud chamber? How are these devices different? _________________________________________
________________________________________________________________________________________________________________________________________________________________________________________________
4. What are the similarities between the emulsion method and photography?
________________________________________________________________________________________________________________________________________________________________________________________________
5. Formulate the left-hand rule to determine the direction of the force acting on a charge in a magnetic field. ____________________________
________________________________________________________________________________________________________________________________________________________________________________________________
6
.
The figure shows the track of a particle in a cloud chamber placed in a magnetic field. The vector is directed away from the plane. Determine the sign of the particle's charge.
______________________________________________________________________________________________________________________________________________________________________________________________________________________________________
Progress
1
.
Which photographs presented to you (Fig. 1, 2, 3) show tracks of particles moving in a magnetic field? Justify your answer.
______________________________________________________________________________________________________
Rice. 1
__________________________________
2. Consider a photograph of the tracks of α-particles moving in a cloud chamber (Fig. 1).
a) In what direction did the α particles move?
__________________________________________________________________________________________________________________________________________________________________________
b) Why are the lengths of α-particle tracks approximately the same?
______________________________________________________________________________________________________
Rice. 3
__________________________________
__________________________________
c) Why does the thickness of α-particle tracks increase slightly towards the end of the movement? ______________________________________________________________
________________________________________________________________________________________________________________________________
3. Figure 2 shows a photograph of α-particle tracks in a cloud chamber located in a magnetic field. Answer the following questions.
a) In which direction did the particles move? _____________________________
________________________________________________________________________________________________________________________________
b) How was the magnetic induction vector directed? ___________________
________________________________________________________________________________________________________________________________
c) Why did the radius of curvature and thickness of the tracks change as the α particles moved? _______________________________________________________
________________________________________________________________________________________________________________________________
4. Figure 3 shows a photograph of an electron track in a bubble chamber located in a magnetic field. Answer the following questions.
a) Why does the electron track have the shape of a spiral? _____________________
________________________________________________________________________________________________________________________________
b) In what direction did the electron move? __________________________
________________________________________________________________________________________________________________________________
c) How was the magnetic induction vector directed? ___________________
________________________________________________________________________________________________________________________________
d) What could be the reason that the electron track in Figure 3 is much longer than the α-particle tracks in Figure 2? _______________________
________________________________________________________________________________________________________________________________
Conclusion: _________________________________________________________
______________________________________________________________________________________________________________________________________________________________________________________________________
Laboratory work No. 9
Measuring natural background radiation
dosimeter
Goal of the work: obtaining practical skills in using a household dosimeter to measure background radiation.
Equipment: household dosimeter, instructions for its use.
Safety regulations. Carefully read the rules for using the dosimeter and sign that you undertake to comply with them. Carefully! Protect the device from falling.
I have read the rules and agree to comply. _______________________(_student signature)
Note: household dosimeters are designed for operational individual monitoring of the radiation situation by the population and allow an approximate estimate of the equivalent radiation dose rate. Most modern dosimeters measure radiation dose rate in microsieverts per hour (µSv/h), but another unit, microroentgen per hour (µR/h), is still widely used. The relationship between them is: 1 μSv/h = 100 μR/h. The average equivalent dose of absorbed radiation due to natural background radiation is about 2 mSv per year.
Practice tasks and questions
1. The absorbed dose of radiation is ___________________________________
________________________________________________________________________________________________________________________________________________________________________________________________
2. Absorbed dose formula:
G 
de: ________________________________
___________________________________
___________________________________
3. Absorbed dose units: =
4. The equivalent dose of H is determined by the formula:
Where: ________________________________
___________________________________
5. The unit of measurement for equivalent dose is ____________________
6. How many times will the initial number of radioactive nuclei decrease during a time equal to the half-life? ________________________________________
Progress
1. Carefully read the instructions for using the dosimeter and determine:
what is the procedure for preparing him for work;
what types of ionizing radiation does it measure;
in what units does the device record radiation dose rate;
what is the duration of the measurement cycle;
what are the limits of absolute measurement error;
what is the procedure for monitoring and replacing the internal power supply;
what is the location and purpose of the device controls.
2. Perform an external inspection of the device and test switch it on.
3. Make sure the dosimeter is in working order.
4. Prepare a device to measure the radiation dose rate.
5. Measure the background radiation level 8–10 times, recording the dosimeter reading each time.
6. Calculate the average background radiation value.
________________________________________________________________________________________________________________________________
7. Calculate what dose of ionizing radiation a person will receive during the year if the average value of background radiation does not change throughout the year. Compare it with a value that is safe for human health.
________________________________________________________________________________________________________________________________
8. Compare the resulting average background value with the natural background radiation taken as the norm - 0.15 µSv/h.
Draw a conclusion_________________________________________________
_______________________________________________________________
________________________________________________________________
Laboratory work No. 1
The movement of a body in a circle under the influence of gravity and elasticity.
Goal of the work: check the validity of Newton's second law for the motion of a body in a circle under the influence of several.
1) weight, 2) thread, 3) tripod with coupling and ring, 4) sheet of paper, 5) measuring tape, 6) clock with second hand.
Theoretical background
The experimental setup consists of a weight tied on a thread to a tripod ring (Fig. 1). On the table under the pendulum there is a sheet of paper on which a circle with a radius of 10 cm is drawn. Center ABOUT circle is located vertically under the suspension point TO pendulum. When the load moves along the circle depicted on the sheet, the thread describes a conical surface. That's why such a pendulum is called conical
Let's project (1) onto coordinate axes X and Y.
(X), (2)
(U), (3)
where is the angle formed by the thread with the vertical.
Let us express from the last equation
and substitute it into equation (2). Then
If the circulation period T pendulum in a circle of radius K is known from experimental data, then
The circulation period can be determined by measuring time t , during which the pendulum makes N rpm:
As can be seen from Figure 1,
, (7)
Fig.1
Fig.2
Where h =OK – distance from the suspension point TO to the center of the circle ABOUT .
Taking into account formulas (5) – (7), equality (4) can be represented as
. (8)
Formula (8) is a direct consequence of Newton’s second law. Thus, the first way to verify the validity of Newton’s second law comes down to experimental verification of the identity of the left and right sides of equality (8).
The force imparts centripetal acceleration to the pendulum
Taking into account formulas (5) and (6), Newton’s second law has the form
. (9)
Force F measured using a dynamometer. The pendulum is pulled away from its equilibrium position by a distance equal to the radius of the circle R , and take dynamometer readings (Fig. 2) Load mass m assumed to be known.
Consequently, another way to verify the validity of Newton’s second law comes down to experimental verification of the identity of the left and right sides of equality (9).
order of work
Assemble the experimental setup (see Fig. 1), choosing a pendulum length of about 50 cm.
On a piece of paper, draw a circle with a radius R = 10 c m.
Place the sheet of paper so that the center of the circle is under the vertical suspension point of the pendulum.
Measure the distance h between the suspension point TO and the center of the circle ABOUT measuring tape.
h =
5. Set the conical pendulum in motion along the drawn circle at a constant speed. Measure time t , during which the pendulum makes N = 10 revolutions.
t =
6. Calculate the centripetal acceleration of the load
Calculate
Conclusion.
Laboratory work No. 2
Checking the Boyle-Mariotte law
Goal of the work: experimentally test the Boyle–Mariotte law by comparing gas parameters in two thermodynamic states.
Equipment, measuring instruments: 1) a device for studying gas laws, 2) a barometer (one per class), 3) a laboratory tripod, 4) a strip of graph paper measuring 300*10 mm, 5) a measuring tape.
Theoretical background
The Boyle–Mariotte law determines the relationship between the pressure and volume of a gas of a given mass at constant temperature gas To make sure this law or equality is fair
(1)
just measure the pressurep 1 , p 2 gas and its volumeV 1 , V 2 in the initial and final states, respectively. An increase in the accuracy of checking the law is achieved by subtracting the product from both sides of equality (1). Then formula (1) will look like
(2)
or
(3)
The device for studying gas laws consists of two glass tubes 1 and 2 50 cm long, connected to each other by a rubber hose 3 1 m long, a plate with clamps 4 measuring 300 * 50 * 8 mm and a plug 5 (Fig. 1, a). A strip of graph paper is attached to plate 4 between the glass tubes. Tube 2 is removed from the base of the device, lowered down and secured in the tripod leg 6. The rubber hose is filled with water. Atmospheric pressure is measured by a barometer in mm Hg. Art.
When the movable tube is fixed in the initial position (Fig. 1, b), the cylindrical volume of gas in the fixed tube 1 can be found using the formula
, (4)
Where S – cross-sectional area of the 1st tube
The initial gas pressure in it, expressed in mm Hg. Art., consists of atmospheric pressure and the pressure of a water column with a height in tube 2:
mmHg. (5).
where is the difference in water levels in the tubes (in mm). Formula (5) takes into account that the density of water is 13.6 times less than the density of mercury.
When tube 2 is lifted up and fixed in its final position (Fig. 1, c), the volume of gas in tube 1 decreases:
(6)
where is the length of the air column in fixed tube 1.
The final gas pressure is found by the formula
mm. rt. Art. (7)
Substituting the initial and final gas parameters into formula (3) allows us to represent the Boyle–Mariotte law in the form
(8)
Thus, checking the validity of the Boyle–Mariotte law comes down to experimental verification of the identity of the left L 8 and right P 8 parts of equality (8).
Work order
7.Measure the difference in water levels in the tubes.
Raise the movable tube 2 even higher and fix it (see Fig. 1, c).
Repeat the measurements of the length of the air column in tube 1 and the difference in water levels in the tubes. Record your measurements.
10.Measure Atmosphere pressure barometer.
11.Calculate the left side of equality (8).
Calculate the right side of equality (8).
13. Check equality (8)
CONCLUSION:
Laboratory work No. 4
Investigation of mixed connection of conductors
Goal of the work : experimentally study the characteristics of a mixed connection of conductors.
Equipment, measuring instruments: 1) power supply, 2) key, 3) rheostat, 4) ammeter, 5) voltmeter, 6) connecting wires, 7) three wirewound resistors with resistances of 1 Ohm, 2 Ohm and 4 Ohm.
Theoretical background
Many electrical circuits use a mixed connection of conductors, which is a combination of series and parallel connections. The simplest mixed connection of resistances = 1 Ohm, = 2 Ohm, = 4 Ohm.
a) Resistors R 2 and R 3 are connected in parallel, so the resistance between points 2 and 3
b) In addition, with a parallel connection, the total current flowing into node 2 is equal to the sum of the currents flowing out of it.
c) Considering that the resistanceR 1 and equivalent resistance are connected in series.
, (3)
and the total resistance of the circuit between points 1 and 3.
.(4)
The electrical circuit for studying the characteristics of a mixed connection of conductors consists of a power source 1, to which a rheostat 3, an ammeter 4 and a mixed connection of three wire resistors R 1, R 2 and R 3 are connected through a switch 2. Voltmeter 5 measures the voltage between different pairs of points in the circuit. Scheme electrical circuit is shown in Figure 3. Subsequent measurements of current and voltage in the electrical circuit will allow you to check relationships (1) – (4).
Current measurementsIflowing through the resistorR1, and the equality of potentials on it allows you to determine the resistance and compare it with a given value.
. (5)
Resistance can be found from Ohm's law by measuring the potential difference with a voltmeter:
.(6)
This result can be compared with the value obtained from formula (1). The validity of formula (3) is checked by an additional measurement using a voltage voltmeter (between points 1 and 3).
This measurement will also allow you to estimate the resistance (between points 1 and 3).
.(7)
The experimental values of resistance obtained from formulas (5) – (7) must satisfy relation 9;) for a given mixed connection of conductors.
Work order
Assemble an electrical circuit
3. Record the current measurement result.
4. Connect a voltmeter to points 1 and 2 and measure the voltage between these points.
5.Record the voltage measurement result
6. Calculate resistance.
7. Write down the result of the resistance measurement = and compare it with the resistance of the resistor = 1 Ohm
8. Connect a voltmeter to points 2 and 3 and measure the voltage between these points
check the validity of formulas (3) and (4).
Ohm
Conclusion:
We experimentally studied the characteristics of mixed conductor connections.
Let's check:
Additional task. Make sure that when connecting conductors in parallel, the equality is true:
Ohm
Ohm
2nd course.
Laboratory work No. 1
Study of the phenomenon of electromagnetic induction
Goal of the work: prove experimentally Lenz's rule, which determines the direction of current during electromagnetic induction.
Equipment, measuring instruments: 1) arc-shaped magnet, 2) coil-coil, 3) milliammeter, 4) strip magnet.
Theoretical background
According to the law of electromagnetic induction (or Faraday-Maxwell's law), the emf of electromagnetic induction E i in a closed loop is numerically equal and opposite in sign to the rate of change of magnetic flux F through the surface bounded by this contour.
E i = - Ф ’
To determine the sign of the induced emf (and, accordingly, the direction of the induced current) in the circuit, this direction is compared with the selected direction of bypassing the circuit.
The direction of the induced current (as well as the magnitude of the induced emf) is considered positive if it coincides with the selected direction of bypassing the circuit, and is considered negative if it is opposite to the selected direction of bypassing the circuit. Let us use the Faraday–Maxwell law to determine the direction of the induced current in a circular wire coil with an area S 0 . Let us assume that at the initial moment of time t 1 =0 the magnetic field induction in the coil region is zero. At the next moment in time t 2 = the coil moves into the region of the magnetic field, the induction of which is directed perpendicular to the plane of the coil towards us (Fig. 1 b)
For the direction of traversing the contour, we choose the clockwise direction. According to the gimlet rule, the contour area vector will be directed away from us perpendicular to the contour area.
Magnetic flux penetrating the circuit in the initial position of the turn, equal to zero (=0):
Magnetic flux at the final position of the coil
Change in magnetic flux per unit time
This means that the induced emf, according to formula (1), will be positive:
E i =
This means that the induced current in the circuit will be directed clockwise. Accordingly, according to the gimlet rule for loop currents, the intrinsic induction on the axis of such a coil will be directed against the induction of the external magnetic field.
According to Lenz's rule, the induced current in the circuit has such a direction that the magnetic flux it creates through the surface limited by the circuit prevents the change in the magnetic flux that caused this current.
An induced current is also observed when the external magnetic field is strengthened in the plane of the coil without moving it. For example, when a strip magnet moves in a coil, the external magnetic field and the magnetic flux penetrating it increase.
Path traversal direction
F 1
F 2
ξi
(sign)
(eg)
I A
B 1 S 0
B 2 S 0
-(B 2 –B 1)S 0<0
15 mA
Work order
1. Connect coil 2 (see Fig. 3) to the clamps of the milliammeter.
2. Insert the north pole of the arc-shaped magnet into the coil along its axis. In subsequent experiments, move the magnet poles to the same side of the coil, the position of which does not change.
Check the consistency of the experimental results with Table 1.
3. Remove the north pole of the arc magnet from the coil. Present the results of the experiment in the table.
Path traversal direction measure the refractive index of glass using a plane-parallel plate.
Equipment, measuring instruments: 1) plane-parallel plate with beveled edges, 2) measuring ruler, 3) student’s square.
Theoretical background
The method of measuring the refractive index using a plane-parallel plate is based on the fact that a ray passing through a plane-parallel plate exits it parallel to the direction of incidence.
According to the law of refraction, the refractive index of the medium
To calculate and on a sheet of paper, draw two parallel straight lines AB and CD at a distance of 5-10 mm from each other and place a glass plate on them so that its parallel edges are perpendicular to these lines. With this arrangement of the plate, parallel straight lines do not shift (Fig. 1, a).
Place the eye at table level and, following straight lines AB and CD through the glass, rotate the plate around the vertical axis counterclockwise (Fig. 1, b). The rotation is carried out until the beam QC appears to be a continuation of BM and MQ.
To process the measurement results, trace the contours of the plate with a pencil and remove it from the paper. Through point M draw a perpendicular O 1 O 2 to the parallel faces of the plate and a straight line MF.
Then equal segments ME 1 = ML 1 are laid on straight lines BM and MF and perpendiculars L 1 L 2 and E 1 E 2 are lowered using a square from points E 1 and L 1 to straight line O 1 O 2 . From right triangles L a) first orient the parallel faces of the plate perpendicular to AB and CD. Make sure that the parallel lines do not move. b) place your eye at table level and, following the lines AB and CD through the glass, rotate the plate around the vertical axis counterclockwise until the QC ray appears to be a continuation of BM and MQ. 2. Trace the outlines of the plate with a pencil, then remove it from the paper. 3. Through point M (see Fig. 1,b), using a square, draw a perpendicular O 1 O 2 to the parallel faces of the plate and a straight line MF (continuation of MQ). 4. With the center at point M, draw a circle of arbitrary radius, mark points L 1 and E 1 on straight lines BM and MF (ME 1 = ML 1) 5. Using a square, lower perpendiculars from points L 1 and E 1 to straight line O 1 O 2. 6. Measure the length of the segments L 1 L 2 and E 1 E 2 with a ruler. 7. Calculate the refractive index of glass using formula 2. Physics is the science of nature. As a school subject, it occupies a special place, because along with cognitive information about the world around us, it develops logical thinking, forms a materialistic worldview, creates a holistic picture of the universe, and has an educational function. The role of 7th grade physics in the development of personality, regardless of a person’s chosen profession, is enormous and continues to grow. In many countries, physics as a discipline began to be introduced into the programs of humanitarian universities. Deep knowledge of physics is a guarantee of success in any profession. Mastering physics most effectively through activities. The acquisition (consolidation) of knowledge in physics in the 7th grade is facilitated by: Real Physics worksheet for grade 7 for the textbook by authors L.A. Isachenkova, Yu.D. Leshchinsky 2011 year of publication provides ample opportunities in such activities as problem solving, presenting computational, experimental problems, problems with a choice of answers and problems with unfinished conditions. Each type of task has a certain methodological load. So, tasks with unfinished conditions invite the student to become a co-author of the problem, supplement the condition and solve the problem in accordance with the level of his preparation. This type of task actively develops students' creativity. Tasks-questions develop thinking, teach the student to see physical phenomena in everyday life. The applications contain important information both for solving the problems given in the Manual and for solving everyday problems of a household nature. In addition, the analysis of reference data develops thinking, helps to establish relationships between the properties of substances, and allows one to compare scales of physical quantities, characteristics of instruments and machines. But the main goal of this manual is to teach the reader to independently acquire knowledge, through solving problems of various types, to deepen the understanding of physical phenomena and processes, to master the laws and patterns connecting physical quantities. We wish you success on the difficult path of learning physics.
