Laboratory work measuring spring stiffness and solving crumbs. Study of the dependence of elastic force on spring elongation. Measuring spring stiffness. Draw a coordinate system to plot the elastic force versus spring elongation
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, which 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 grade) 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, recording each time 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 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|, | ||
Laboratory work
"Determination of spring stiffness"
Purpose of the work : Determination of the spring constant. Checking the validity of Hooke's law. Estimation of measurement error.
Work order .
Basic level
Equipment : tripod with coupling and foot, set of weights of 100 g, spring dynamometer, ruler.
L0 F
L1 in this case.
l= L0 - L1
kWed.by formulakWed=( k1 + k2 + k3 )/3
F,N
l,m
k,N/m
kWed, N/m
6. Draw a graph of the relationshipl ( F).
Advanced level
Equipment : tripod with coupling and foot, set of weights of 100 g, spring, ruler.
Mount the spring in a tripod and measure the length of the springL0 in the absence of external influence (F=0H). Record the measurement results in the table.
Hang a 1 N load on the spring and determine its lengthL1 in this case.
Find the deformation (elongation) of the spring using the formulal= L0 - L1 .Enter the measurement results in the table.
Similarly, find the elongation of the spring when hanging loads weighing 2 N and 3 N. Enter the measurement results in the table.
Calculate the arithmetic meankWed.by formulakWed=( k1 + k2 + k3 )/3
Estimate the error ∆kby the average error method. To do this, calculate the modulus of the difference│ kWed- ki│=∆ kifor each dimension
k = k Wed ±∆ k
F,N
l,m
k,N/m
kWed, N/m
∆k,N/m
∆kWed, N/m
Advanced level
Equipment: tripod with coupling and foot, set of weights of 100 g, spring, ruler.
Mount the spring in a tripod and measure the length of the springL0 in the absence of external influence (F=0H). Record the measurement results in the table.
Hang a 1 N load on the spring and determine its lengthL1 in this case.
Find the deformation (elongation) of the spring using the formulal= L0 - L1 .Enter the measurement results in the table.
Similarly, find the elongation of the spring when hanging loads weighing 2 N and 3 N. Enter the measurement results in the table.
Calculate the arithmetic meankWed.by formulakWed=( k1 + k2 + k3 )/3
Calculate relative errors and absolute measurement error∆ kaccording to formulas
ε F=(∆ F0 + FAnd) / Fmax
ε l=(∆ l0 + lAnd) / lmax
ε k=ε F+ε l
∆k= εk* kWed
Write the result obtained in the formk = k av±∆ k
Draw a graph of the relationshipl ( F).Formulate the geometric meaning of rigidity.
F,N
l,m
k,N/m
kWed, N/m
ε F
ε l
ε k
∆ k
Laboratory work.
Determination of spring stiffness coefficient.
Purpose of the work: Using the experimental dependence of the elastic force on the absolute elongation, calculate the spring stiffness coefficient.
Equipment: tripod, ruler, spring, weights weighing 100 g.
Theory. Deformation is understood as a change in the volume or shape of a body under the influence of external forces. When the distance between particles of a substance (atoms, molecules, ions) changes, the forces of interaction between them change. As the distance increases, the attractive forces increase, and as the distance decreases, the repulsive forces tend to return the body to its original state. Therefore, elastic forces are of an electromagnetic nature. The elastic force is always directed towards the equilibrium position and tends to return the body to its original state. The elastic force is directly proportional to the absolute elongation of the body.
Hooke's Law: The elastic force that arises during deformation of a body is directly proportional to its elongation (compression) and is directed opposite to the movement of body particles during deformation , F control = kΔx , Wherek– coefficient
stiffness [k] = N/m,Δ X = Δ L – body elongation module.
The stiffness coefficient depends on the shape and size of the body,
and also on the material. It is numerically equal to the elastic force
when lengthening (compressing) the body by 1 m.
The order of work.
1. Mount the dynamometer on a tripod.
2. Measure the original length of the spring with a rulerL 0 .
3 . Suspend a mass of 100 g.
4. Measure the length of the deformed spring with a rulerL. Determine the error in measuring length:ΔƖ= 0.5 div*C 1 , WhereWITH 1 – ruler division price.
5. Calculate the elongation of the springΔх = Δ L = L – L 0 .
6. A load at rest relative to a spring is acted upon by two mutually compensatingforces: gravity and elasticityF t = F control (see top picture)
7. Calculate the elastic force using the formula, F control = m g . Determine the error in force measurement: Δ F = 0.5 div*S 2 , WhereWITH 2 – dynamometer division price.
8. Hang a load weighing 200 g and repeat the experiment according to steps 4-6.
9. Hang a load weighing 300 g and repeat the experiment according to steps 4-6.
10. Enter the results into the table.
11. Calculate the spring constant for each measurementK= F control /Δx and record these values in the table. Determine the averageTO Wed
12. Determine the absolute measurement error Δ k = ( Δ F / F control + ΔƖ /L) * To measured , Where Δ F – force measurement error,ΔƖ – length measurement error.
13. Select a coordinate system and plot the dependence of the elastic forceF control from spring extension Δ L .
Measurement table
p/p
Initial length,L 0, m
Final lengthL, m
Absolute elongation Δx 1 =Δ L = L – L 0, m
Elastic force,F ex. N
Stiffness coefficient, K, N/m
14. Draw a conclusion. The spring stiffness coefficient obtained as a result of the experiments can be written:k = k Wed measured (each student has his own coefficient) ±Δ To (the error is different for everyone).
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Slide captions:
Laboratory work “Measuring spring stiffness” Physics teacher GBOU secondary school No. 145 Kalininsky district of 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 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.
Laboratory work in physics, grade 9 Gendenshtein Orlov Work progress
1 - Secure 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 100 gram weight on 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 weighing 100 grams from the spring.
4 - Record the results in a table.
5 - Draw a coordinate system to plot the elastic force versus 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 stretches, the greater the elastic force.8 - Using the constructed straight line, find the spring stiffness.
k = Fcontrol /|x|k = 4/0.1 = 40 H/m
