Ministry of Education and Science of Ukraine

Tauride National University named after V.I.Vernadsky

Faculty of Physics

Department of Experimental Physics

Laboratory works on the course of general physics

Mechanics

PartI

Guidelines for the study of the discipline "Mechanics"

for 1st year students, full-time education

6.070101, 7.070107 "Physics",

6.070203, 7.070203 Applied Physics

educational qualification levels

"bachelor", "specialist"

Simferopol, 2001

Published by decision of the Scientific and Methodological Council

Taurida National University named after V.I. Vernadsky

No. 2001

Introduction

In the process of forming a scientific worldview, an important role is played by laboratory research, the basis of which is the experiment. Experiment is a powerful means of obtaining new knowledge. Important steps in any experiment are:

knowledge of the relevant theory;

ability to work on an experimental installation;

clearly defined task;

correct measurements;

statistical processing of experimental data;

obtaining the desired physical quantity;

well-organized research.

To obtain primary knowledge and skills in conducting experiments, a cycle of introductory laboratory work is carried out in the section "Mechanics" of the general course. The cycle includes two laboratory works aimed at studying the theory of measurements and statistical processing of experimental data.

To measure a quantity means to compare it with a homogeneous quantity conventionally accepted as a unit of measurement. Some quantities, for example, the linear dimensions of bodies, mass, time, can be measured directly with the help of appropriate instruments. Such measurements are called direct. The majority of physical quantities can be determined only by working formulas expressing the initial value in terms of directly measured and tabular quantities. Such measurements are called indirect.

The imperfection of measuring instruments and the experimenter's sense organs lead to the fact that measurements are always accompanied by one or another error and, therefore, gives an inaccurate value of the measured quantity.

Knowledge of the numerical value of any physical, determined experimentally, is still not enough to draw a conclusion from the experiment. Therefore, the experimenter is faced with the task of not only measuring a physical quantity, but also assessing the accuracy of the measurement result.

Conducting classes in the laboratory is associated with work on experimental facilities, so you must first study the safety instructions.

FOREWORD

The publication contains guidelines for the implementation of laboratory work in physics. The description of each work consists of the following parts: title of the work; purpose of the work; instruments and accessories; studied patterns; instructions for performing observations; results processing task; test questions.

Job preparation task

In preparation for work, the student must:

1) study the job description and think over the answers to control questions;

2) prepare introductory part of the report: title page, title of the work, purpose of the work, description (diagram or sketch) of the laboratory setup and short description studied patterns;

3) prepare a protocol of observations.

The protocol of observations contains: the name of the work; tables that are filled during the work; student data (full name, group number). The form of tables is developed by the student independently.

Protocol of observations and lab report neatly drawn up on one side of A4 paper.

1) title page;

2) introductory part: the title of the work, the purpose of the work, instruments and accessories, an outline of the part of the methodological instructions “patterns under study”;

3) the settlement part in accordance with the "task for processing the results";

4) work conclusions.

Calculations must be detailed and provided with the necessary comments. The results of the calculations, if convenient, are summarized in a table. Drawings, graphs are made in pencil on graph paper.

WORK 1.1. STUDY OF THE MOTION OF BODIES IN A DISSIPATIVE ENVIRONMENT

Instruments and accessories: a vessel with the investigated liquid; balls of greater density than the density of the liquid; stopwatch; scale bar.

Purpose of the work: to study the motion of a body in a uniform force field in the presence of medium resistance and to determine the coefficient of internal friction (viscosity) of the medium.

Investigated patterns

Motion of a body in a viscous fluid. Three forces act on a sufficiently small solid ball falling in a viscous fluid (Fig. 1):

1) gravity mg = 4 3 r 3 πρ g , where r is the radius of the ball; ρ is its density;

2) buoyant force of Archimedes F a = 4 3 r 3 πρ c g , where ρ c is the liquid density;

3) medium resistance force (Stokes force)

where η is the coefficient of fluid viscosity; v is the falling speed of the ball.

Formula (1.1) is applicable to a solid ball moving in a homogeneous liquid at low speed, provided that the distance to the liquid boundaries is much greater than the diameter of the ball. Resultant force

F = 4 3 r 3 π(ρ−ρc ) g −6 πηrv .

For ρ > ρ c , on initial stage movement, while the speed v is small, the ball will fall with acceleration. Upon reaching a certain speed v ∞ , at which the resulting

the force vanishes, the motion of the ball becomes uniform. The speed of uniform motion is determined from the condition F = 0, which gives for v ∞ :

The time dependence of the speed v (t) at all stages of movement is described by the expression

which is obtained after integrating the equation of motion of the ball and substituting initial conditions. Time τ , during which the body could reach the stationary speed v ∞ , moving uniformly accelerated with an acceleration equal to the initial

is called the relaxation time (see Fig. 2). Having determined experimentally the steady velocity v ∞ of a uniform fall of the ball, we can find the viscosity coefficient of the liquid

where D is the diameter of the ball, m = π 6 ρ D 3 is its mass.

The viscosity coefficient η is numerically equal to the force of friction between adjacent layers of a liquid or gas with a unit area of ​​contact between the layers and a unit velocity gradient in the direction perpendicular to the layers. The unit of viscosity is 1 Pa s = 1 N s / m2.

Energy losses in a dissipative system. In the steady state, the

In this case, the friction force and the force of gravity (taking into account the Archimedes force) are equal to each other and the work of the force of gravity passes completely into heat, energy dissipation occurs. Energy dissipation rate (power loss) in steady state

find as P ∞ = F 0 v ∞ , where F 0 = m a 0 = m v ∞ / τ ; thus

P ∞ = m v ∞ 2 / τ .

Observation Instructions

The body whose motion is being investigated is a steel ball (ρ = 7.9. 10–3 kg/cm3) of known diameter, and the medium is viscous liquids (various oils). The liquid is filled into a cylindrical vessel with a scale on which two transverse marks are noticed on different levels. By measuring the fall time of the ball on the way ∆ l from one mark to another, its average speed is found. The found value is the steady value of the velocity v ∞ if the distance from the upper mark to the liquid level exceeds the relaxation path l τ = v ∞ τ / 2, which is performed in this work.

1. Record the diameter of the ball, the density of the investigated liquid and the density of the material of the ball in the observation protocol. Calculate the mass of the ball and record the result in the observation protocol. Prepare 5 balls for measurements.

2. Lowering the balls one by one into the liquid through the inlet pipe with zero initial speed, measure the time with a stopwatch t passing by each ball

distance ∆ l between the marks in the vessel. Record the results in a table.

3. Measure the distance ∆ l between the marks. Record the result in the protocol of observations.

Results Processing Task

1. Determining the relaxation time. Based on the data obtained, calculate the movement speed v for each ball. Calculate the initial acceleration using the formula a 0 = g (1 - ρ c / ρ ).

For one of the balls (any) estimate the relaxation time τ = v ∞ / a 0 . Using formula (1.2) plot v (t), for the time interval 0< t < 4τ через интервал 0.1 τ . Проанализировать, является ли движение шарика установившимся к моменту прохождения им первой метки, для чего оценить путь релаксации по формуле l τ = v ∞ τ .

2. Estimation of energy dissipation. Calculate the power of friction losses in the steady state of motion for the ball, according to the results of observations of the motion of which the relaxation time was determined.

3. Determination of the coefficient of internal friction . Based on the speed of movement of each ball, determine the coefficient of internal friction (η ) liquids. Calculate Mean and Confidence Error∆η .

test questions

1. What media are called dissipative?

2. Write down the equation of motion of a body in a dissipative medium.

3. What is called the relaxation time, and on what parameters of the body and environment does it depend?

4. How will the relaxation time change with a change in the density of the medium?

WORK 2.1. DETERMINATION OF THE MOMENT OF INERTIA OF THE OBERBECK PENDULUM

Instruments and accessories: Oberbeck pendulum, set of weights, stopwatch, scale ruler.

Purpose of the work: study of the laws of rotational motion on the cruciform Oberbeck pendulum, determination of the moment of inertia of the pendulum and the moment of friction forces.

The Oberbeck pendulum is a table device (Fig. 1). On the vertical stand of the base 1, three

brackets: top 2, middle 3, bottom 4. The position of all brackets on the vertical rack is strictly fixed. A block 5 for changing the direction of movement of the thread 6 is attached to the upper bracket 2, pa of which the load 8 is suspended. The rotation of the block 5 is carried out in the bearing assembly 9, which makes it possible to reduce friction. An electromagnet 14 is mounted on the middle bracket 3, which, with the help of a friction clutch, when voltage is applied to it, keeps the system with loads in a stationary state. On the same bracket there is a bearing assembly 10, on the axis of which a two-degree pulley 13 is fixed on one side (it has a device for fixing the thread 6). At the other end of the axis there is a cross, which is four metal rods with risks applied to them every 10 mm and fixed in the boss 12 at right angles to each other. Weights II can move freely and be fixed on each rod, which makes it possible to stepwise change the moments of inertia of the pendulum cross.

A photoelectric sensor 15 is mounted on the lower bracket 4, which outputs an electrical signal to the stopwatch 16 to complete the counting of time intervals. A rubber shock absorber 17 is attached to the same bracket, against which the load hits when it stops.

The pendulum is equipped with an 18 mm ruler, which determines the initial and final positions of the weights.

The installation allows to carry out an experimental verification of the basic law of the dynamics of rotational motion M = I ε . The pendulum used in this work is a swing

vetch, which is given a cruciform shape (Fig. 2). On four mutually perpendicular rods, loads of mass m f can move. There is a pulley on the common axis, a thread is wound around it, thrown over an additional block, with a set of loads m i tied to its end. Under the action of a falling load m i

the thread unwinds and sets the flywheel in uniformly accelerated motion. The motion of the system is described by the following equations:

where a is the acceleration with which the load is lowered; I 1 – moment of inertia of the additional block with radius r 1 ; M tr 0 is the moment of friction forces in the axis of the additional block; I 2 - the total moment of inertia of the cross with the load, the two-stage pulley and the boss of the cross; M tr - the moment of friction forces in the axis of the pulley; r 2 - the radius of the pulley on which the thread is wound (r 1 \u003d 21 mm, r 2 \u003d 42 mm); ε 1 , ε 2 are the angular accelerations of the block and

Various values ​​of ε 2 are provided by a set of weights m i suspended from the thread.

Thus, having obtained experimental points linear dependence M from ε 2 , it is possible, using (2.3), to find both the value of I 2 and M tr . I 2 and M tr are determined by the formulas of linear regression (method least squares).

Instructions for Making Observations

1. Place weights on four mutually perpendicular rods of the cross at the same distance from the ends of the rods.

Adjust the position of the base with the help of the adjusting supports, using the thread with the main weight as a plumb line (the weights should move parallel to the millimeter ruler, falling into the middle of the working window of the photocell).

3. Rotating the crosspiece counterclockwise, move the main weight to the upper position, winding the thread around a disk of a larger radius.

4. Press the “NETWORK” button located on the front panel of the stopwatch (in this case, the photosensor lamps and digital indicators of the stopwatch should light up, and the electromagnetic friction clutch should work) and fix the crosspiece

in given position.

5. Press the “RESET” button and make sure that zeros are set on the indicators.

6. Press the “START” button (the main weight starts to move) and, holding it pressed, make sure that the electromagnet is de-energized, the crosspiece starts to unwind, the stopwatch counts the time, and at the moment the main weight crosses the optical axis of the photocell, the count time stops. After the termination of the counting of time, the “START” button should be returned

in initial position. In this case, the electromagnetic friction clutch should work and slow down the crosspiece.

7. When pressing the “START” button, raise the load to the upper position, winding the thread on a disk of a larger radius. Return the “START” button to its original position and record the scale value of the ruler h 1, against which is the lower edge of the main

cargo. The position of the optical axis of the photosensor corresponds to the value h 0 = 495 mm on the ruler scale. Reset the stopwatch indicators by pressing the “RESET” button.

8. Following the instructions of item 6, count down the time of lowering the load. Record the results in a table.

9. Measurements according to paragraphs. 7 and 8 to spend 3 times.

10. Adding additional weights to the main weight, measure 3 times for each value of the mass of suspended weights S and t: S \u003d h 0 - h 1.

11. Measurements according to paragraphs. 8..10 to carry out, winding the thread on a disk of smaller radius.

12. Design the table view yourself.

Results processing tasks

From equation (2.3), using the least squares method (LSM), determine

I 2 and M tr.

a) To do this, using formulas (2.4) and (2.5), for all values ​​of m i and I 2, calculate the values ​​of M k and ε 2 k (total 18 pairs of values);

b) comparing the linear dependence Y = aX + b and equation (2.3), we obtain

X \u003d ε 2, Y \u003d M, a \u003d I 2, b \u003d M tr.

By the formulas of normal linear regression, we find , ∆a and , ∆ b for a given confidence level.