Laboratory work measuring the spring stiffness coefficient. Physics laboratory work "measuring spring stiffness"

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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 taped scale, set of weights 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 experiment, the rigidity is determined at different meanings elasticity and elongation forces, i.e. the experimental conditions change. Therefore, to find the average stiffness value, 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, which corresponds to the formula F yпp =k\x\. This is due to measurement errors. In this case, the schedule should be carried out so that approximately same number points, it turned out, according to 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. 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 division of the ruler against 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.

In physics for grade 9 (I.K.Kikoin, A.K.Kikoin, 1999),
task №2
to the chapter " LABORATORY WORK».

Purpose 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 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 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 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

Measuring means: 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.

Work order

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 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 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 load, add the second, third, etc. weights, each time writing down the elongation |x| springs. Based on the measurement results, fill out the table:

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 av was found (from 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 means: a set of weights, the mass of each is equal to m 0 = (0.1 ± 0.002) kg.

Ruler with millimeter divisions (Δx = ±0.5 mm). The procedure for performing the work is described in the textbook and does not require comments.

	weight, kg		extension |x|,

The purpose of the work is to check the validity of Hooke's law for
dynamometer springs and measure the coefficient
the stiffness of this spring.
Equipment:
tripod with coupling and clamp, dynamometer with
sealed with a scale, a set of weights of known mass
(100 g each), ruler with millimeter divisions.

PROGRESS:

10.

Laboratory work “Measuring spring stiffness” Purpose of the work: find the spring stiffness from measurements of the spring at different values ​​of the gravity force Ft, balancing the elastic force Fspr, based on Hooke’s law k = Fspr/x. In each experiment, rigidity is determined at different values ​​of elastic force and elongation, i.e. the experimental conditions change. Therefore, to find the average value, it is impossible to calculate the arithmetic mean of the measurement results. Based on the results of several experiments, we will construct a graph of the dependence of Fel on the elongation x. When constructing a graph based on the results of an experiment, the experimental points may not be on the same straight line, which is determined according to the formula Fpr=kx. 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 value of the spring stiffness kavg. The measurement result is written in the form of the expression k=kр±Δk, where Δk is the absolute k measurement error. Relative error εk= , from where Δk=εkk. There is a k 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 the calculation formula, then the relative errors are added up. In this work k= Fcontrol/x. Therefore εk=εF+εx. Equipment and materials: 1) A set of weights, a tripod with a coupling and a foot, a dynamometer, a ruler with millimeter divisions. The order of work. 1. Mount the dynamometer on a tripod. 2. Secure or install a ruler with millimeter divisions nearby. 3. Hang a load on the spring, measure the elastic force generated and the elongation of the spring. 4. Add a second, third, etc. weights and repeat the measurements. Based on the measurement results, fill out the table. Experiment number 1 2 3 4 F, N x, m 5. Based on the measurement results, plot the dependence of the elastic force on the elongation of the spring and, using it, determine the average value of the spring stiffness kavg. 6. Calculate the relative error with which kср was found (from the experiment with one F x load). In experiment εF= , εx= . Error when measuring elongation Δx=1 mm, F x error when measuring force ΔF=0.1N. 7. Find Δk=εkkср and in the output write the answer in the form k=kср±Δk. Laboratory work “Measuring the coefficient of friction” Purpose of the work: Determine the coefficient of friction of a wooden block sliding on a surface using the formula Ftr = μP. Using a dynamometer, measure the force with which you need to pull a block with loads evenly across horizontal surface. This force is equal in magnitude to the friction force Ftr. Using the same dynamometer, you can find the weight of a loaded block. Having thus determined the values ​​of the friction force at various values ​​of body weight, it is necessary to plot the dependence of Ftr on P and find the average value of the friction coefficient, as in the previous work. Equipment and materials: a wooden block, a surface (for example, a desk), a set of weights, a dynamometer. The order of work. 1. Place the block on a horizontal surface. 2. Attach a dynamometer to the block, pull it evenly across the surface, noticing the dynamometer readings. 3. Weigh the block and weight. 4. Add the second and third weights to the first weight, each time weighing the block and weights and measuring the friction force. Enter the measurement results in the table. Experiment number 1 2 3 4 P, N ΔP, N Ftr, N ΔFtr, N 5. Based on the measurement results, plot the dependence of Ftr on P and find the average value of the friction coefficient μav. 6. Calculate the relative error in measuring the friction coefficient. Because μ= Ftr/P, then ε μ=εFtr+εP. The friction coefficient was measured with the greatest error in an experiment with one load. Find the absolute error Δ μ= ε μ μav and write the answer in the output as μ= μav±Δ μ.