goal of the work: find the spring stiffness from measurements of the spring elongation at different meanings gravity
balancing the elastic force based on Hooke's law: 
in each experiment, the rigidity is determined at different meanings elasticity and elongation forces, i.e. the experimental conditions change. therefore, to find the average value of stiffness, it is impossible to calculate the average arithmetic results measurements. let's take advantage graphically finding an average value that can be applied in such cases. Based on the results of several experiments, we will construct a graph of the dependence of the elastic force modulus fel on the elongation modulus |x|. when constructing a graph based on the results of the experiment, the experimental points may not be on the straight line that corresponds to the formula 
this is due to measurement errors. in this case, the schedule must be carried out so that approximately same number the points turned out to be different sides from the straight line. After constructing the graph, take a point on the straight line (in the middle part of the graph), determine from it the values of the elastic force and elongation corresponding to this point, and calculate the stiffness k. it will be the desired average value of the spring stiffness k avg.
the measurement result is usually written as the expression k = = k cp ±δk, where δk is the largest absolute measurement error. from the algebra course ( VII class) it is known that the relative error (ε k) is equal to the ratio of the absolute error δk to the value of k: 
whence δk - ε k k. There is a rule for calculating the relative error: if the value determined experimentally is found as a result of multiplication and division of the approximate values included in calculation formula, then the relative errors add up. in this work 
That's why
measuring instruments: 1) a set of weights, the mass of each is m 0 = 0.100 kg, and the error δm 0 = 0.002 kg; 2) a ruler with millimeter divisions.
materials: 1) tripod with couplings and foot; 2) spiral spring.
order of work
1. Attach the end of the spiral spring to the tripod (the other end of the spring is equipped with an arrow and a hook - Fig. 176). 
2. Next to the spring or behind it, install and secure a ruler with millimeter divisions.
3. Mark and write down the division of the ruler against which the spring pointer arrow falls.
4. hang a weight from the spring known mass and measure the resulting elongation of the spring.
5. To the first load, add the second, third, etc. weights, recording each time the elongation |x| springs. Based on the measurement results, fill out the table:
number experience | m, kg | mg 1, n | |x|, m |
6. Based on the measurement results, plot the dependence of the elastic force on the elongation and, using it, determine the average value of the spring stiffness k cp.
7. calculate the largest relative error, with which the value of k avg was found (from an experiment with one load). in formula (1)
since the error in measuring elongation is δx=1 mm, then
8. find
and write the answer as:
1 take g≈10 m/s 2.
Hooke's law: “the elastic force arising during deformation of a body is proportional to its elongation and is directed opposite to the direction of movement of the particles of the body during deformation.”
Hooke's law
stiffness is the coefficient of proportionality between the elastic force and the change in the length of the spring under the influence of a force applied to it. According to Newton's third law, the force applied to the spring is equal in magnitude to the elastic force generated in it. Thus the spring stiffness can be expressed as:
where f is the force applied to the spring, and x is the change in the length of the spring under its action. measuring instruments: a set of weights, the mass of each is equal to m 0 = (0.1 ± 0.002) kg.
ruler with millimeter divisions (δх = ±0.5 mm). the procedure for performing the work is described in the textbook and does not require comments.
Experience no. | weight, kg |  | extension |x|, | k, n/m |
m |
Spring stiffness measurement
10th grade
Purpose of the work:
find the spring stiffness from measurements of the spring elongation at various values of gravity balancing the elastic force 
, based on Hooke's law: 
.
Devices and materials:
In each of the experiments, the rigidity is determined at different values of the elastic force and elongation, i.e. the experimental conditions change. Therefore, to find the average stiffness value, it is impossible to calculate the arithmetic mean of the measurement results. Let's use a graphical method for finding the average value, which can be applied in such cases. Based on the results of several experiments, we will construct a graph of the dependence of the elastic force modulus on the elongation modulus x. When constructing a graph based on the experimental results, the experimental points may not be on the straight line that corresponds to the formula 
.
This is due to measurement errors: In this case, the graph must be drawn so that approximately the same number of points are on opposite sides of the straight line. After constructing the graph, take a point on the straight line (in the middle part of the graph), determine from it the values of the elastic force and elongation corresponding to this point, and calculate the stiffness k. This will be the desired average spring stiffness 
.
The measurement result is usually written as an expression 
, Where 
-
the greatest absolute measurement error. It is known that the relative error ( 
) is different in relation to the absolute error
to the value of k :
, where 
.
In this work 
. That's why 
, Where 
,
,
Absolute errors:
= 0.002 kg ;
=1mm,
.
Work order
Attach the end of the coil spring to the tripod.
Next to the spring or behind it, install and secure a ruler with millimeter divisions.
Mark and write down the division of the ruler against which the spring pointer arrow falls.
Hang a load of known mass on a spring and measure the elongation of the spring caused by it.
Add the second, third, etc. to the first load. loads, recording each time the elongation x of the spring. Based on the measurement results, fill out the table:
|
Experience number |
||||
Municipal educational institution "Gymnasium No. 6" Physics workshop, grade 10
Laboratory work No. 3
Spring stiffness measurement
Purpose of the work: find the spring stiffness from measurements of the spring elongation at various values of gravity balancing the elastic force 
based on Hooke's law: 
. In each experiment, the rigidity is determined at different values of the elastic force and elongation, i.e. the experimental conditions change. Therefore, to find the average stiffness value, it is impossible to calculate the arithmetic mean of the measurement results. Let's use a graphical method for finding the average value, which can be applied in such cases. Based on the results of several experiments, we will plot the dependence of the elastic force modulus 
from extension module X. When constructing a graph based on the results of the experiment, the experimental points may not be on the straight line that corresponds to the formula 
. This is due to measurement errors. In this case, the graph must be drawn so that approximately the same number of points are on opposite sides of the straight line. After constructing the graph, take a point on the straight line (in the middle part of the graph), determine from it the values of the elastic force and elongation corresponding to this point and calculate the stiffness k. This will be the desired average spring stiffness 
.
The measurement result is usually written as an expression 
, Where 
- the greatest absolute measurement error. It is known that the relative error ( 
) is equal to the ratio of the absolute error to the value of the quantity k
: 
, where 
.
In this work 
. That's why 
, Where 
; 
; 
.
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Slide captions:
Laboratory work “Measuring spring stiffness” Physics teacher, secondary school No. 145, Kalininsky district St. Petersburg Karabashyan M.V.
check the validity of Hooke's law for the dynamometer spring and measure the stiffness coefficient of this spring. Purpose of work Equipment: “Mechanics” set from the L-micro kit - tripod with coupling and clamp, dynamometer with a sealed scale, set of weights of known mass (50 g each), ruler with millimeter divisions.
Preparatory questions What is elastic force? How to calculate the elastic force arising in a spring when a load weighing m kg is suspended from it? What is body elongation? How to measure the elongation of a spring when a load is suspended from it? What is Hooke's law?
Safety Precautions Be careful when working with a stretched spring. Do not drop or throw loads.
Description of work: According to Hooke's law, the modulus F of the elastic force and the modulus x of the elongation of the spring are related by the relation F = kx. By measuring F and x, you can find the stiffness coefficient k using the formula
In each of the experiments, the rigidity is determined at different values of the elastic force and elongation, i.e., the experimental conditions change. Therefore, to find the average stiffness value, it is impossible to calculate the arithmetic mean of the measurement results. Let's use a graphical method for finding the average value, which can be applied in such cases. Based on the results of several experiments, we will construct a graph of the dependence of the elastic force modulus Fel on the elongation modulus \x\. When constructing a graph based on the results of the experiment, the experimental points may not be on the straight line, which corresponds to the formula F yпp =k\x\. This is due to measurement errors. In this case, the graph must be drawn so that approximately the same number of points appear on opposite sides of the straight line. After constructing the graph, take a point on the straight line (in the middle part of the graph), determine from it the values of the elastic force and elongation corresponding to this point, and calculate the stiffness k. This will be the desired average value of the spring stiffness k avg.
1. Attach the end of the coil spring to the tripod (the other end of the spring has an arrow and a hook). 2. Next to or behind the spring, install and secure a ruler with millimeter divisions. 3. Mark and write down the ruler division opposite which the spring pointer arrow falls. 4. Hang a load of known mass on the spring and measure the elongation of the spring caused by it. 5. To the first weight, add the second, third, etc. weights, recording each time the elongation x\ of the spring. Based on the measurement results, fill out the table PROGRESS OF WORK:
Experiment no. m, kg mg, H x, m 1 0.1 2 0.2 3 0.3 4 0.4
6. Draw the x and F coordinate axes, select a convenient scale and plot the resulting experimental points. 7. Evaluate (qualitatively) the validity of Hooke’s law for a given spring: are the experimental points located near one straight line passing through the origin of coordinates? 8. Based on the measurement results, plot the dependence of the elastic force on the elongation and, using it, determine the average value of the spring stiffness k avg. 9. Calculate the largest relative error with which the value of k cp 10 was found. Write down your conclusion.
Test questions: What is the relationship between elastic force and spring elongation called? The spring of the dynamometer under the influence of a force of 4 N lengthened by 5 mm. Determine the weight of the load under the action of which this spring is extended by 16 mm.
Lesson 13/33
Subject. Laboratory work No. 2 “Measuring spring stiffness”
Purpose of the lesson: check the validity of Hooke's law for a dynamometer spring and measure the stiffness coefficient of this spring
Lesson type: control and assessment of knowledge
Equipment: tripod with coupling and clamp, dynamometer with taped scale, set of weights of known mass (100 g each), ruler with millimeter graduations
PROGRESS OF WORK
1. Mount the dynamometer on a tripod at a sufficiently high height.
2. Hanging different quantities weights (from one to four), calculate for each case the corresponding value F = mg, and also measure the corresponding extension of the spring x.
3. Write the results of measurements and calculations in the table:
m, kg |
mg, N |
||
4. Draw the coordinate axes x and F, select a convenient scale and plot the points obtained during the experiment.
6. Calculate the stiffness coefficient using the formula k = F /x, using the results of experiment No. 4 (this provides the greatest accuracy).
7. To calculate the error, we should use the experience that we obtained during experiment No. 4, because it corresponds to the smallest relative measurement error. Calculate the limits Fmin and Fmax within which the true meaning F, assuming that Fmin = F - ΔF, F = F + ΔF. Take ΔF = 4Δm g, where Δm is the error during the manufacture of weights (for assessment, we can assume that Δm = 0.005 kg):
where Δх = 0.5 mm.
8. Using the error estimation method indirect measurements, calculate:
9. Calculate the average value of kcep and the absolute measurement error Δk using the formulas:
10. Calculate the relative measurement error:
11. Fill out the table:
Fmin, H |
Fmax, H |
xmin, m |
xmax, m |
kmin, N/m |
kmax, N/m |
k sir, N/m |
||
12. Write down the result in your notebook for laboratory work in the form k = kcep ± Δk, substituting it into this formula numeric values found values.
13. Write down the conclusion in your laboratory notebook: what you measured and what result you got.
