HOOKE S LAW FORCE AND STRETCH OF A SPRING

Transcription

1 HOOKE S LAW FORCE AND STRETCH OF A SPRING NAME DATE PERIOD

2 Hooke's Law Lab Report 1 of 5 PURPOSE: The purpose of this experiment was to determine the relationship between the stretch of a spring and the subsequent tension in the spring. This relationship is known as Hooke s Law. It is expected that for a basic cylindrical spring, it will be found that the tension in the spring will be directly proportional to the spring s stretch. EQUIPMENT SET-UP: The following equipment is needed: Joly Balance (as shown in Figure 1) Several 50.0 (+/- 0.1) g masses Graphical Analysis Software Program Pointer Mirrored centimeter scale Spring Mass Mass holder Stand Figure 1: Joly Balance with mass on mass holder. Place the Joly Balance on a level surface. With no mass on the mass holder, adjust the scale up or down so the pointer attached to the spring reads zero on the centimeter scale. PROCEDURE: 1. Set-up the Joly balance as shown in the set-up instructions 2. Increase the load on the spring by placing a 50 g mass on the mass holder. 3. Look at the pointer on the centimeter scale and record its location. Ensure that the reflection of the needle in the mirror and the needle is line-up with your eye to avoid parallax errors. Record this as the stretch of the spring. 4. Repeat steps 3 and 4 increasing the load in 50 g increments for at least 6 trials. 5. Divide the each load by 100 to calculate the force on the spring. (Newtons). Record. 6. Convert the values of stretch from centimeters into meters. Record. 7. Plot a graph of Force vs. Stretch. Determine the slope and equation of the line. 8. Compare the experimental value of the spring constant to the accepted value provided by the manufacturer.

3 Hooke's Law Lab Report 2 of 5 DATA: Force and Stretch Measurements of a Cylindrical Spring on a Joly Balance Load placed on tray (g) Stretch of spring (cm) Stretch of spring (m) Force on spring (N) Accepted Spring Constant (k)... Experimental Spring Constant (k E ) N/m 32.2 N/m Absolute Error of Spring Constant N/m Percent Error of Spring Constant % Figure 2: Hooke s Law Graph: Force vs. Stretch of a Cylindrical Spring

4 Hooke's Law Lab Report 3 of 5 ANALYSIS: Conversion of Stretch Measurements from cm to m (using data from the 50.0 g trial) 100 cm = 1 m 1.50 cm 1m.0150 m 100cm Calculation of Force on Spring (using data from the 50.0 g trial) Force (N) = Load (g) 50.0 g =.500 N Determination of the Experimental Relationship (Hooke's Law) F = kx Where F is the load on the spring, x is the amount the spring is stretched and k is the spring constant whose experimental value (k E ) is 32.2 N/m. This value is represented by the slope of the line of the Force vs. Stretch Graph. The equation and the experimental value of the spring constant were determined by Graphical Analysis 3.4. Absolute Error (AE) of Spring Constant (k): AE = Experimental Value (k E) - Accepted Value (k) 32.2 N/m N/m = 0.3 N/m Percent Error (%E) of Spring Constant (k): %E = AE x 100% 0.3N/m x 100% = 0.9% Accepted Value 32.5N/m

5 Hooke's Law Lab Report 4 of 5 CONCLUSION Springs are used in a variety of applications, and they come in many different forms and shapes. Basic cylindrically-coiled tension springs are often used to help open a garage door and compression springs can be found in pens. Coiled springs with other shapes are often found in mattresses and flat, bar-like springs can be found in the suspensions to automobiles. And there are many other types of springs, but one thing that all springs have in common is that there is some kind of relationship that exists between the amount that the spring is deflected and the force contained within that spring. This experiment was performed to verify the relationship first noted by Robert Hooke, that in a basic cylindrically-coiled tension spring, the tension within the spring is directly proportional to the amount that the spring stretches. The experiment was performed using the Joly balance, shown in Figure 1, which allows mass to be added to a mass holder causing a vertically aligned spring to stretch. The load was added in equal increments, the stretch was measured after each addition and both values converted were to standard units. The converted values of stretch and force were graphed and the result of the graph was expected to show a linear relationship between the two variables. The data obtained strongly supports this hypothesis and verifies Hooke s Law in that the tension in the tested spring was directly proportional to the amount the spring was stretched. This relationship is visually evident from the linear plot in Figure 2: Hooke s Law Graph: Force vs. Stretch of a Cylindrical Spring as well as from the equation obtained from this plot, F = kx; where F was the force in the spring in N, x the spring s stretch in meters and the spring constant, k, is represented by the slope of the line. The experimental value of the spring constant, 32.2 N/m, is only 0.9 % different from the accepted value of 32.5 N/m. The direct proportional relationship found between the force within a spring and the amount of stretch of the spring and the resulting law, can be used when analyzing any situation containing a cylindrically-coiled tension spring. Therefore, for certain garage door springs as described above, the equation F = kx should apply. This relationship is also the basis for spring scales which indicate force by measuring the stretch of a cylindrically-coiled spring. But whether or not this relationship can globally be applied to all kinds of springs is not yet known at this point. DISCUSSION There is a high degree confidence in the experiment and its results. The experiment provided a linear relationship between force and stretch as suggested by Hooke s Law where the measured data points all lie on or within close proximity of the line. Also, there was a very low 0.9% error between the experimental and actual values of the spring constant that is well within the uncertainty of the equipment used. All these provide evidence for the validity of the experiment and its results. Two measures were used to determine the spring constant - the force and the stretch of the spring. Errors in these measures would lead to errors in the determination of the spring constant. Although the error obtained was within the equipment s capabilities, a few experimental aspects could have contributed to that error. The most prominent is the uncertainty in the stretch measures. A mirrored scale and pointer was used as the spring's length indicator to avoid parallax errors. Accuracy of the stretch was compromised because as it was being measured, the mass tray would bob (vibrate) slightly causing the pointer to bob as well. This vibration was the cause of the uncertainty. Waiting a sufficient time to allow for all bobbing to stop, will help to avoid this error. A second source of this error in the stretch may be present because the needle was somewhat tilted during the experiment. It was then up to the judgment of the experimenter to ensure the same area of the pointer (such as its very tip) was used to record each potion. If this was not done carefully, as it was somewhat difficult to see the very tip, the stretch measurements may not be consistent with one another. Brightly coloring the tip of the pointer might make it easier to see it and help avoid this error.

6 Hooke's Law Lab Report 5 of 5 It is difficult to imagine any error with the force measures, as known masses with tight tolerances were used. Additional mass due to a foreign substance on the mass tray could compromise this data or lost mass due to chips in their surfaces, but this was neither observed nor would it be expected to alter the data much. The small variation in the data due to any of these errors is evident in the plotted data points that stray from the experimental regression line. These variations are small compared to the size of the data collected; and hence, it is not believed that they greatly affected the results. Full confidence in these results can be attained. To verify that this relationship is global, as opposed to being present on just the one spring-type tested, all types of springs can be tested. Also, additional tests can be done to see how a spring that has been stretched beyond its elastic limit reacts. Would this spring provide the same linear relationship, have the same or a different spring constant, or would the relationship be of a non-linear type? Similar test could be performed on compression springs, again to determine the nature of this relationship. All these tests could be accomplished to gain a thorough understanding of the behavior of springs.