Laboratory work measuring the coefficient of spring stiffness. Laboratory work "Measuring the stiffness of a spring" methodological development in physics on the topic
MOU "Gymnasium No. 6" Physical workshop Grade 10
Lab #3
Spring stiffness measurement
Objective: find the stiffness of the spring from measurements of the elongation of the spring at various values of the force of gravity balancing the elastic force
based on Hooke's law:
. In each of the experiments, the stiffness is determined at different meanings elastic and elongation forces, i.e. experimental conditions change. Therefore, to find the average stiffness value, it is not possible to calculate the arithmetic mean of the measurement results. Let's use graphically finding an average value that can be applied in such cases. Based on the results of several experiments, we construct a graph of the dependence of the modulus of the elastic force
from extension module X. When constructing a graph based on the results of the experiment, the experimental points may not be on a 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 is on opposite sides of the straight line. After plotting 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 .
The measurement result is usually written as an expression
, where
- the largest absolute measurement error. It is known that the relative error ( ) is equal to the absolute error ratio
to the value of the quantity k
:
, where
.
In that work
. That's why
, where
;
;
.
To use the preview of presentations, create a Google account (account) and sign in: https://accounts.google.com
Slides captions:
Laboratory work "Measuring the stiffness of a spring" Teacher of physics, GBOU secondary school No. 145 of the Kalininsky district of St. Petersburg Karabashyan M.V.
check the validity of Hooke's law for the dynamometer spring and measure the stiffness of this spring. Purpose of work Equipment: set "Mechanics" from the set L-micro - tripod with clutch and clamp, dynamometer with a sealed scale, a set of weights of known weight (50 g each), a ruler with millimeter divisions.
Preparatory questions What is elastic force? How to calculate the elastic force that arises in a spring when a load of mass m kg is suspended from it? What is body lengthening? 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 an extended 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 factor k by the formula
In each of the experiments, the stiffness is determined at different values of the elastic force and elongation, i.e., the conditions of the experiment change. Therefore, to find the average stiffness value, it is not possible to calculate the arithmetic mean of the measurement results. We will use a graphical method for finding the average value, which can be applied in such cases. Based on the results of several experiments, we construct a graph of the dependence of the modulus of the elastic force F control on the modulus of elongation \ x \ . When constructing a graph based on the results of the experiment, the experimental points may not be on a straight line, which corresponds to the formula F yпp =k\x\ . This is due to measurement errors. In this case, the graph should be drawn so that approximately the same number of points turns out to be on opposite sides of the straight line. After plotting 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 cf.
1. Attach the end of the coil spring to the tripod (the other end of the spring is provided with an arrow pointer and a hook). 2. Next to or behind the spring, install and secure a ruler with millimeter divisions. 3. Mark and write down the division of the ruler against which the spring pointer falls. 4. Hang a weight of known mass from the spring and measure the extension of the spring caused by it. 5. To the first weight, add the second, third, etc. weights, recording each time the extension \ x \ of the spring. According to the results of measurements, fill in the table PROGRESS OF WORK:
Experiment number 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 obtained experimental points. 7. Assess (qualitatively) the validity of Hooke's law for a given spring: are the experimental points located near one straight line passing through the origin. 8. Based on the measurement results, build a graph of the dependence of the elastic force on the elongation and, using it, determine the average value of the spring stiffness k cf. 9. Calculate the maximum relative error with which the value of k cp 10 is found. Write down your conclusion.
Control questions: What is the name of the relationship between the force of elasticity and the elongation of the spring? The spring of the dynamometer under the action of a force of 4N lengthened by 5 mm. Determine the weight of the load, under the action of which this spring is extended by 16 mm.
Laboratory work in physics Grade 9 Gendenshtein Orlov Progress
1 - Attach the end of the spring to the tripod. Measure the height at which the lower end of the spring is above the table.
2 - Hang a weight of 100 grams from the spring. Measure the height at which the lower end of the spring is now above the table. Calculate the elongation of the spring.
3 - Repeat the measurements, hanging two, three and four weights of 100 grams each from the spring.
4 - Record the results in a table.
5 - Draw a coordinate system for plotting the dependence of the elastic force on the elongation of the spring.
7 - Determine how the elastic force depends on the elongation of the spring.
The greater the elongation of the spring, the greater the elastic force, that is, the longer the spring is stretched, the greater the elastic force.8 - According to the constructed straight line, find the stiffness of the spring.
k = Fcontrol /|x|k = 4/0.1 = 40 H/m
9 - Determine if the stiffness of the spring depends on its length, and if it does, how does it change when the length of the spring decreases.
The stiffness of the spring does not depend on the elongation of the length of the spring. Each spring has k (spring stiffness) and it is constant, does not depend on Fsp and on ΔxIn physics for grade 9 (I.K. Kikoin, A.K. Kikoin, 1999),
a task №2
to chapter " LABORATORY WORKS».
The purpose of the work: to find the stiffness of the spring from measurements of the elongation of the spring at different values of gravity
balancing force of elasticity based on Hooke's law:
In each of the experiments, the stiffness is determined at different values of the elastic force and elongation, i.e., the conditions of the experiment change. Therefore, to find the average stiffness value, it is not possible to calculate the arithmetic mean of the measurement results. We will use a graphical method for finding the average value, which can be applied in such cases. Based on the results of several experiments, we plot the dependence of the modulus of elasticity F control on the modulus of elongation |x|. When constructing a graph based on the results of the experiment, the experimental points may not be on a 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 is 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. It will be the desired average value of the spring stiffness k cf.
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 in the experiment is the result of multiplying and dividing the approximate values included in the calculation formula, then the relative errors add up. In that work
Means of measurement: 1) a set of weights, the mass of each is equal to m 0 = 0.100 kg, and the error Δm 0 = 0.002 kg; 2) a ruler with millimeter divisions.
Materials: 1) tripod with clutches and foot; 2) coil spring.
Work order
1. Attach the end of the coil spring to the tripod (the other end of the spring is equipped with an arrow pointer and a hook - fig. 176).
2. Next to or behind the spring, install and secure a ruler with millimeter divisions.
3. Mark and write down the division of the ruler against which the spring pointer falls.
4. Hang a weight of known mass from the spring and measure the extension of the spring caused by it.
5. To the first load, add the second, third, etc. weights, each time recording the lengthening |x| springs. According to the measurement results, fill in the table:
6. Based on the measurement results, build a graph of the dependence of the elastic force on the elongation and, using it, determine the average value of the spring constant k cp.
7. Calculate the largest relative error with which the value of kav was found (from the experiment with one load). In formula (1)
since the error in measuring the elongation Δx=1 mm, then
8. Find
and write your answer as:
1 Take g≈10 m/s 2 .
Hooke's law: "The elastic force that occurs when a body is deformed is proportional to its elongation and is directed opposite to the direction of movement of body particles during deformation."
Hooke's law
Rigidity is the coefficient of proportionality between the elastic force and the change in the length of the spring under the action of the force applied to it. According to Newton's third law, the modulus of the force applied to the spring is equal to the elastic force that has arisen in it. Thus, the stiffness of the spring 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.
weight, kg |
elongation |x|, | |||