Laboratory work No. 8 "Measuring the acceleration of free fall using a pendulum."

The purpose of the work: to calculate the acceleration of free fall from the formula for the period of oscillation of a mathematical pendulum:

To do this, it is necessary to measure the period of oscillation and the length of the suspension of the pendulum. Then from formula (1) we can calculate the free fall acceleration:

Measuring:

1) a watch with a second hand;

2) measuring tape (Δ l = 0.5 cm).

Materials: 1) a ball with a hole; 2) thread; 3) tripod with clutch and ring.

Work order

1. Place a tripod on the edge of the table. At its upper end, strengthen the ring with a coupling and hang a ball on a thread from it. The ball should hang at a distance of 3-5 cm from the floor.

2. Deviate the pendulum from the equilibrium position by 5-8 cm and release it.

3. Measure the length of the hanger with a measuring tape.

4. Measure the time Δt 40 complete oscillations (N).

5. Repeat the measurements of Δt (without changing the conditions of the experiment) and find the average value of Δt cf.

6. Calculate the average value of the oscillation period T avg from the average value of Δt avg.

7. Calculate the value of g cp using the formula:

8. Enter the results in the table:

Number	l, m	N	Δt, s	Δtav, s

9. Compare the obtained average value for g cp with the value g = 9.8 m/s 2 and calculate the relative measurement error using the formula:

While studying physics, you often had to use the value of the acceleration of free fall on the surface of the earth in solving problems and other calculations. You took the value g \u003d 9.81 m / s 2, that is, with the accuracy that is quite sufficient for your calculations.

The purpose of this lab is to experimentally determine the free fall acceleration using a pendulum. Knowing the formula for the oscillation period of a mathematical pendulum T =

one can express the value of g in terms of quantities that can be easily established by experiment and calculate g with some accuracy. Express

where l is the length of the suspension, and T is the period of oscillation of the pendulum. The period of oscillation of the pendulum T is easy to determine by measuring the time t required for a certain number N of complete oscillations of the pendulum

A mathematical pendulum is a weight suspended from a thin inextensible thread, the dimensions of which are much less than the length of the thread, and the mass is much greater than the mass of the thread. The deviation of this load from the vertical occurs at an infinitely small angle, and there is no friction. In real conditions, the formula

is approximate.

Consider such a body (in our case, a lever). Two forces act on it: the weight of the loads P and the force F (the elasticity of the spring of the dynamometer), so that the lever is in balance and the moments of these forces must be equal in absolute value to each other. The absolute values ​​of the moments of forces F and P will be determined respectively:

In laboratory conditions, to measure with some degree of accuracy, you can use a small but massive metal ball suspended on a thread 1-1.5 m long (or longer, if such a suspension can be placed) and deflect it at a small angle. The course of work is entirely clear from its description in the textbook.

Means of measurement: stopwatch (Δt = ±0.5 s); ruler or measuring tape (Δl = ±0.5 cm)

Laboratory work №8.

"Measurement of the diameter and shape deviations of the hole surface with an indicator inside gauge".

The purpose of the work: To master the methods of measurement with an indicator caliper

hole diameters and hole shape deviations.

Task: Measure the diameter and shape deviations of the surface

holes in bushing-type parts with an indicator caliper.

Equipment: Indicator caliper with a head.

End measures of length (KMD).

Accessories for KMD.

Details of the bushing type and its drawing.

1. Theoretical part

Hole measurements are acceptable if ≤ i.e. the limiting error of measuring the head is less than the permissible error of measuring the hole.

2. Indicator caliper.

Tube 4 (Fig. 1) with a heat-insulating handle 6 serves as the basis of the indicator caliper. The upper opening of the tube with clamp 8 is used to install the sleeve of the measuring head or the dial indicator.

In the lower part of the tube there is an inside gauge head, consisting of a body 9, a centering bridge 11 and measuring rods-tips - movable 1 and rigid 10. The movement of the tip 1 through the lever 2, the stem 3 and the worm 5 is transmitted to the measuring head. Centering bridge 2 sets the measurement axis of the inside gauge (tip axis a1 and 10) to coincide with the diameter of the hole of the measured part (Fig. 2)

When measuring, it is necessary to shake the inside gauge in the axial plane in the longitudinal section and find the minimum position along the arrow of the measuring head, i.e. perpendicular to both generators of the hole.

Inside gauges with a centering bridge are produced with a measurement range: mm: 6…10; 10…18; 18…50; 50…100; 100…160; 160…250; 250…450; 450…700; 700…1000.

To measure holes of small diameters, inside gauges with ball inserts are accepted (Fig. 3) ball inserts have ranges: mm: 3 ... 6; 6…10; 10…18.

To set the indicator inside gauges to "0", adjusting rings or sets of end measures (KMD) and sidewalls are used. The KMD block is selected and installed in the holder along with the sidewalls. The operation when set to "0" is the same as when measuring a workpiece.

2.1 Measuring head.

The measuring head converts small movements of the measuring tip into large movements of the pointer of the reporting device.

Figure 4 shows a dial indicator. Measuring rod 1 of the indicator has a rail that engages with gear wheel 5 and transmits movement to tube 9 and arrows 8 through gear wheel 9. To set it to “0”, the round scale of the dial rotates together with rim 2. Arrow 6 shows the number of turns of arrow 8.

Dial gauges have a sleeve diameter of 8mm, a measuring rod stroke of 2; 5 or 10mm and a division price of 0.01mm.

In lever-toothed measuring heads, the movement of the measuring tip (turns) through the lever system is transmitted to the gear sector, which turns the gear wheel and the arrow sitting on the wheel axle. The heads have a division value of 0.001 mm and 0.002 mm, a measurement range of ± 0.05 mm ... 5 mm (multi-turn).

2.2 Preparation for measurement.

1. Fix the measuring head in the bore gauge tube. To do this, insert the sleeve of the measuring head into the hole of the tube so that the ball of the measuring tip touches the end of the rod and the dial scale is turned to the side with the centering bridge and secure the measuring head with a clamp, while the arrow should make a full turn. At the same time, it is necessary to maintain freedom of movement of the measuring rod of the head.

2. Dial the CMD block according to the nominal size of the hole and fix it between the sides in the CMD holder. Pre-wiping the tiles and sidewalls with gasoline. Wipe the weathered hole surface with a clean cloth.

3. check for compliance of the measurement limits of the inside gauge with the size of the measuring hole. If they do not match, replace the interchangeable measuring rod or select a set of extensions and washers for a rigid compound rod (depending on the type of inside gauge).

2.3 Setting the inside gauge to "0".

1. Take the inside gauge by the heat-insulating handle and insert the depth gauge between the sides.

2. Watching the arrow of the head and moving the inside gauge between the sides by swinging and rotating around the axis of the tube (see diagram), set the inside gauge to the position that matches the smallest distance between the measuring surfaces of the sides. In this case, the arrow will reach the farthest * (clockwise) division and turn back. For both types of movement (swinging and turning), this division must match.

3. Remember this division, remove the caliper from the sidewalls and turn the scale to the noted position with the rim of the dial (or the setting screw to “0”).

4.Check setting to "0". In the right position, the indicator needle should point to 0.

2.4 Hole diameter measurement.

1. Take the caliper with your right hand by the heat-insulating handle and, holding the part with your left hand, insert the caliper into the hole of the measured part with the measuring head up and the scale towards you. To do this, a movable rod with a bridge must be inserted to a shallow depth by tilting the inside gauge, and then straighten it so that the rigid rod rests against the opposite wall of the hole.

2. Move the caliper to the desired section and, shaking it in a vertical plane away from you - towards you, notice the farthest division of the scale, to which the arrow reaches.

A clockwise deviation of the arrow from “0” indicates a decrease in the hole diameter and a “-” sign, and a counterclockwise deviation indicates a decrease in diameter and a “+” sign.

4. Take the reading of the caliper, taking into account the scale division of the head and the sign, and write it down in the reference table. Measurements should be taken for each section in two mutually perpendicular directions.

Rice. 1Indicator caliper

Rice. 4 Dial indicator

3. Measurement results.

1. Taking into account the nominal size of the KMD block, calculate the actual dimensions of the part.

2. Compare the dimensions of the part with the allowable limiting dimensions and give a conclusion on the suitability of the part.

Having considered the dimensions of the part by sections, determine the deviations of the shape of the part from cylindricity.

3.Fill out a report on the work.

After checking the measurement results by the teacher, wipe the caliper, head, KMD and accessories to them with a dry cloth and put them in cases. Tidy up the workplace.

Target– to determine the moment of inertia of the body by the method of torsional vibrations.

Devices and materials: measuring installation, set of bodies, stopwatch.

Description of installation and measurement method

The measuring setup is a round disk suspended on an elastic steel wire and designed to accommodate bodies, the moment of inertia of which should be determined (Fig. 8.1).

Rice. 8.1

The device is centered using two movable weights fixed on the disk. Turning the disk of the device at a certain angle around the vertical axis, the steel suspension is twisted.

When the body rotates through an angle , the wire twists and a moment of forces arises M seeking to return the body to a position of equilibrium. The experiment shows that in a fairly wide range the moment of forces M proportional to the angle of twist  , i.e.
(compare: elastic force
). The disk is released, allowing it to perform torsional vibrations. The period of torsional vibrations is determined by the expression
, where f– torsion modulus; J is the moment of inertia of the oscillating system.

For instrument
. (8.1)

Equality (8.1) contains two unknown quantities f and J etc. Therefore, it is necessary to repeat the experiment, after placing a reference body with a known moment of inertia on the setup disk. A solid cylinder is taken as a standard, the moment of inertia of which is J this .

Having determined the new oscillation period of the device with the standard, we compose an equation similar to equation (8.1):

. (8.2)

Solving the system of equations (8.1) and (8.2), we determine the torsion modulus f and the moment of inertia of the device J etc with this load position. (Derivation of calculation formulas for f and J etc do it yourself in preparation for the laboratory work and include it in the report). Having removed the standard, a body is placed on the disk of the device, the moment of inertia of which relative to the axis of the device must be determined. The installation is centered and the period of torsional vibrations is determined again T 2 , which in this case can be written as

. (8.3)

Knowing and f, calculate the moment of inertia of the body relative to the axis of the device based on formula (8.3).

The data of all measurements and calculations are entered in table. 8.1.

Table 8.1

Measured and calculated quantities for determining the moment of inertia using the torsional vibration method

	t etc	T etc	t 1	T 1	t 2	T 2
		< T etc >=	< T 1 >= < ¦ >= < J etc >=	< T 2 >= < J t >

Task 1. Determination of the periods of torsional vibrations of a device, a device with a standard, a device with a body

1. Measure the time with a stopwatch t etc 20-30 complete vibrations of the device and determine
.

2. Repeat the experiment 5 times and determine < T etc > .

3. Place a standard on the disk of the device and similarly determine < T 1 >.

4. Place the body on the disk of the device, center the installation, determine < T 2 > .

Record the measurement results in table. 8.1

MINISTRY OF EDUCATION OF THE RUSSIAN FEDERATION

SIBERIAN STATE AEROSPACE UNIVERSITY

named after academician M.F. Reshetnev

Department of Technical Physics

Lab #8

FOUR-PROBE METHOD FOR MEASURING THE RESISTANCE OF SEMICONDUCTORS

Guidelines for performing laboratory work on the course "Solid State Electronics"

Compiled by: Parshin A.S.

Krasnoyarsk 2003

Laboratory work №8. Four-probe method for measuring the resistance of semiconductors1

Method theory . 1

Experimental setup . 3

Work order .. 5

Report formatting requirements . 7

test questions .. 7

Literature . 7

Laboratory work №8. Four-probesemiconductor resistance measurement method

Objective: study of the temperature dependence of the specific electrical resistance semiconductor by the four-probe method, determination of the band gap of a semiconductor.

Method theory

Four-probe the method of measuring the resistivity of semiconductors is the most common. The advantage of this method is that its application does not require the creation of ohmic contacts to the sample; it is possible to measure the resistivity of samples of the most diverse shapes and sizes. The condition for its use in terms of the shape of the sample is the presence of a flat surface, the linear dimensions of which exceed the linear dimensions of the probe system.

The circuit for measuring resistance by the four-probe method is shown in fig. 1. Four metal probes with a small contact area are placed along a straight line on the flat surface of the sample. Distances between probes s 1 , s2 and s3 . Through external probes 1 and 4 pass electric current I 14 , on internal probes 2 and 3 measure the potential difference U 23 . By measured values I 14 and U 23 the resistivity of a semiconductor can be determined.

To find the calculation formula for resistivity, let us first consider the problem of potential distribution around a separate point probe (Fig. 2). To solve this problem, it is necessary to write the Laplace equation in a spherical coordinate system, because the potential distribution has spherical symmetry:

.(1)

The solution of equation (1) provided that the potential at r=0 positive, tends to zero, at very large r has the following form

Integration constant With can be calculated from the condition for the electric field strength E some distance from the probe r=r0 :

.

Since the density of the current flowing through a hemisphere with a radius r0 , j =I/(2πr0 2), and in accordance with Ohm's law j =E/ρ , then E(r0)=I ρ / (2π r0 2).

Thus

If the contact radius r1 , then the potential of its tip

It is obvious that the potential on the sample at the point of its contact with the probe has the same value. According to formula (3), it follows that the main voltage drop occurs in the near-contact region and, therefore, the value of the current flowing through the sample is determined by the resistance of the near-contact region. The length of this region is the smaller, the smaller the radius of the probe.

The electric potential at any point of the sample can be found as the algebraic sum of the potentials created at that point by the current of each probe. For the current flowing into the sample, the potential is positive, and for the current flowing out of the sample, it is negative. For the probe system shown in fig. 1, the potentials of the measuring probes 2 and 3

;

.

Potential difference between measuring contacts 2 and 3

Hence the resistivity of the sample

.(5)

If the distances between the probes are the same, i.e. s 1 =s 2 =s 3 =s , then

Thus, to measure the specific electrical resistance sample using the four-probe method, it is enough to measure the distance between the probes s , voltage drop U 23 on the measuring probes and the current flowing through the sample I 14 .

Experimental setup

The measuring setup is implemented on the basis of a universal laboratory stand. The following devices and equipment are used in this laboratory work:

1. Heat chamber with sample and measuring head;

2. DC source TES-41;

3. DC voltage source B5-47;

4. Universal digital voltmeters V7-21A;

5. Connecting wires.

The block diagram of the experimental setup is shown in fig. 3.

The sample is placed on the measuring stage of the heat chamber. The measuring head is pressed by the spring mechanism of the manipulator to the flat polished surface of the sample. Inside the measuring table there is a heater, which is powered by a stabilized direct current source TES-41, operating in the current stabilization mode. The sample temperature is controlled by a thermocouple or thermal resistance. To speed up the measurement process, you can use the graduated curves presented in the appendix, which allow you to determine the temperature of the sample from the heater current. The heater current value is measured by an ammeter built into the current source.

Current through contacts 1 and 4 is created using an adjustable stabilized DC source B7-47 and controlled by a universal digital device V7-21A, switched on in the ammeter mode. The voltage that occurs between the measuring probes 2 and 3 is recorded by a high-resistance digital voltmeter V7-21A. Measurements must be carried out at the lowest current through the sample, determined by the possibility of measuring low voltages. At high currents, heating of the sample is possible, which distorts the measurement results. Reducing the operating current simultaneously reduces the modulation of the sample conductivity caused by the injection of charge carriers during the current flow.

The main problem in measuring electrical resistance probe methods is the problem of contacts. For high-vacuum samples, it is sometimes necessary to carry out electrical forming of contacts to obtain low contact resistances. The forming of the contacts of the measuring probe is carried out by briefly applying a constant voltage of several tens or even hundreds of volts to the measuring probe.

Work order

1. Familiarize yourself with the description of the devices necessary to perform the work. Assemble the scheme of the measuring setup according to fig. 3. When connecting universal voltmeters V7-21A, pay attention that one must work in the voltage measurement mode, the other - in the current measurement. In the diagram, they are indicated by icons. " U" and " I" respectively. Check the correct setting of the mode switches on these devices.

2. After checking the correctness of the assembly of the measuring installation by the teacher or engineer, turn on the voltmeters and the B7-47 voltage source.

3. Set the voltage of the B7-47 source to 5V. If the voltage and current on the sample changes with time, then with the help of teachers or an engineer, electrical molding of the contacts of the measuring probe.

4. Carry out voltage drop measurements U+ 23 and U– 23 for different current directions I 14 . The obtained voltage values ​​are averaged for th, in order to exclude in this way the longitudinal thermo-EMF arising on the sample due to the temperature gradient. Enter the data of the experiment and calculations of stress values ​​in Table 1.

Table form 1

	I load, A	T,K	I 14, mA	U + 23 , AT	U – 23 , AT

5. Repeat measurements at a different sample temperature. To do this, you need to set the current of the heater of the thermal chamber I load,= 0.5 A, wait 5–10 minutes for the sample temperature to stabilize, and record the instrument readings in Table 1. Determine the sample temperature using the calibration curve presented in the Appendix.

6. Similarly, make measurements sequentially for heater current values ​​of 0.9, 1.1, 1.2, 1.5, 1.8 A. Record the results of all measurements in Table 1.

7. Process the obtained experimental results. To do this, using the results presented in Table 1, calculate 10 3 /T , specific electrical resistance sample at each temperature ρ according to formula (6), electrical conductivity

natural logarithm of electrical conductivity ln σ . Record all calculation results in Table 2.

Table form 2

	T,K	, K-1	ρ, Ohm m	σ, (Ohmm) -1	log σ

8. Build a dependency graph. Analyze the course of the curves, mark the areas of impurity and intrinsic conductivities. a brief description of the task set in the work;

· measurement setup diagram;

· results of measurements and calculations;

· dependency graph;

· analysis of the obtained results;

· work conclusions.

test questions

1. Intrinsic and extrinsic semiconductors. Band structure of intrinsic and impurity semiconductors. bandgap width. Impurity activation energy.

2. Mechanism of electrical conductivity of intrinsic and extrinsic semiconductors.

3. Temperature dependence of the electrical conductivity of intrinsic semiconductors.

4. Temperature dependence of the electrical conductivity of impurity semiconductors.

5. Determination of the band gap and the activation energy of an impurity from the temperature dependence of the electrical conductivity.

6. Four-probe Method of measurement electrical resistance semiconductors: scope, its advantages and disadvantages.

7. The problem of the distribution of the potential of the electric field near the probe.

8. Derivation of the calculation formula (6).

9. Scheme and principle of operation of the experimental setup.

10. Explain the experimentally obtained dependence graph, how was the band gap determined from this graph?

Literature

1. Pavlov L.P. Methods for measuring the parameters of semiconductor materials: A textbook for universities. - M .: Higher. school., 1987.- 239 p.

2. Lysov V.F. Workshop on semiconductor physics. –M .: Enlightenment, 1976.- 207 p.

3. Epifanov G.I., Moma Yu.A. Solid State Electronics: Tutorial. for university students. - M .: Higher. school., 1986.- 304 p.

4. Ch. Kittel, Introduction to Solid State Physics. - M.: Nauka, 1978. - 792 p.

5. Shalimova K.V. Semiconductor Physics: Textbook for High Schools. - M .: Energy, 1971. - 312 p.

6. Fridrikhov S.A., Movnin S.M. Physical foundations of electronic technology: A textbook for universities. - M .: Higher. school ., 1982.- 608 p.

In this lesson, we will consider the practical application of the acquired knowledge on the example of laboratory work in physics in order to measure the specific heat of a solid. We will get acquainted with the main equipment that will be needed to conduct this experiment, and consider the technology for carrying out practical work on measuring physical quantities.

1. Place a metal cylinder in a glass of hot water and measure its temperature with a thermometer. It will be equal to the temperature of the cylinder, since after a certain time the temperatures of the water and the cylinder will equalize.

2. Then we pour cold water into the calorimeter and measure its temperature.

3. After that, we place the cylinder tied on a thread into a calorimeter with cold water and, stirring the water in it with a thermometer, measure the temperature established as a result of heat transfer (Fig. 6).

Rice. 6. Lab progress

The measured steady-state final temperature in the calorimeter and other data will allow us to calculate the specific heat capacity of the metal from which the cylinder is made. We will calculate the desired value based on the fact that, when cooling, the cylinder gives off exactly the same amount of heat as the water receives when heated, the so-called heat exchange occurs (Fig. 7).

Rice. 7. Heat transfer

Accordingly, we obtain the following equations. To heat water, the amount of heat required is:

, where:

Specific heat capacity of water (table value), ;

The mass of water, which can be determined using scales, kg;

The final temperature of the water and the cylinder, measured with a thermometer, o ;

The initial temperature of cold water, measured with a thermometer, o.

When a metal cylinder cools, the amount of heat released is:

, where:

Specific heat capacity of the metal from which the cylinder is made (desired value), ;

The mass of the cylinder, which can be determined using scales, kg;

The temperature of hot water and, accordingly, the initial temperature of the cylinder, measured with a thermometer, o ;

The final temperature of the water and the cylinder, measured with a thermometer, o.

Comment. In both formulas, we subtract the smaller temperature from the larger temperature to determine the positive value of the amount of heat.

As mentioned earlier, in the process of heat transfer, the amount of heat received by water is equal to the amount of heat given off by the metal cylinder:

Therefore, the specific heat capacity of the cylinder material is:

It is convenient to record the results obtained in any laboratory work in a table, and to carry out several measurements and calculations to obtain an averaged, as accurately as possible, approximate result. In our case, the table might look something like this:

Mass of water in the calorimeter	Initial water temperature	Cylinder weight	Initial cylinder temperature	Final temperature

Conclusion: the calculated value of the specific heat capacity of the material of the cylinder .

Today we reviewed the methodology for conducting laboratory work on measuring the specific heat of a solid. In the next lesson, we will talk about the release of energy during the combustion of fuel.

Bibliography

1. Gendenstein L.E., Kaidalov A.B., Kozhevnikov V.B. / Ed. Orlova V.A., Roizena I.I. Physics 8. - M.: Mnemosyne.
2. Peryshkin A.V. Physics 8. - M.: Bustard, 2010.
3. Fadeeva A.A., Zasov A.V., Kiselev D.F. Physics 8. - M.: Enlightenment.

1. Internet portal "5terka.com" ()
2. Internet portal "k2x2.info" ()
3. Internet portal "youtube.com" ()

Homework

1. At what stage of the laboratory work is it likely to get the largest measurement error?
2. What should be the materials and design of the calorimeter to obtain the most accurate measurement results?
3. *Suggest your method for measuring the specific heat capacity of a liquid.