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| Introduction | Materials/Procedure | Planning | Results | Conclusion | Bibliography | Related Links | Return to Research Page |

Introduction:

According to thermodynamics, when an object is heated it causes the velocity of the molecules to increase. As the velocity of the molecules increases the rate at which the molecules hit the walls of the object also increases. This results in an increase in the force of impact on the walls and causes the walls to be pushed out and therefore causes an increase in the volume of the object itself. Likewise, when metal is cooled down, the molecular velocity decreases and the force of impact on the walls is lessened, allowing for a compaction of volume. The research question now becomes, what effect does the increase in volume of the spring’s coils have on the spring constant itself? When assessing this question, two potential frames of reasoning come to mind. One may assume that because the spring volume is increasing and typically thicker springs typically hold more weight, or have a higher spring constant, the expansion in volume would allot for an increase in the spring constant. However, the opposing idea would be that because the matter of the spring is not increased, simply the volume, the spring would actually become weaker because the molecules are no longer as tightly packed. However, the focus of our research is simply to see whether an effect is present, not why it is or is not. Based upon research, it is our hypothesis that by increasing the temperature of a steel spring, the increase of volume of the spring will lead to a decrease in the spring constant. Support for this idea is as follows,

“Most objects expand when they are heated and contract when they are cooled. Most objects also get hotter when they are compressed and cooler when they are expanded. This effect can get complicated because the values of the elastic module also depend on temperature, usually getting smaller for higher temperatures” (2000 Oxford Dictionary of Physics). This

means that as the temperature increases, the spring constant decreases and a visible weakening of the spring should be noted.

As far as accounting for potential room for error there are three main areas that must be taken into consideration. The first of these is the ability of the spring to resist deformation. The atomic volume of steel is said to increase exponentially with its temperature.  While the increase is relatively small, particularly when considering an increase of almost 2000 Kelvins is required to increase the atomic volume by 1e-3 mm3, it is still enough to cause a significant change in the ability of the spring to resist deformation.  However, to avoid this, temperatures will be kept well under 2000 Kelvins.

The second of these is the possibility of the spring becoming plastically deformed. Hooke’s Law states that stress is linearly proportional to strain.  If the stress is doubled then the strain is doubled; if the stress is tripled than the strain increases threefold.  However, there are limitations to the validity of Hooke’s Law; it is usually only valid “for strains of far less than 1 percent.  In most pure metals, for example, the elastic limit is reached for strains as small as .001 percent.  For larger strains, the object never reverts exactly to its original shape on removal of the stress but remains changed to some extent; it is said to be plastically deformed” (1996 Macmillian Encyclopedia of Physics).

The third potential room for error is creep. “Creep is the term used to describe the time-dependent plastic flow under conditions of constant load or stress.  Whilst creep can occur over the whole temperature range…with engineering metals and alloys, creep is of practical importance only at high temperatures” (1972 Creep of Metals at High Temperatures).  However, high temperatures typically pertain to those close to the melting point of the given metal, and in this case the temperature to which the steel spring will be heated will not be within range of its melting point.

Materials: one steel spring, ammeter, power supply, leads A and B, stand, clamp, paperclip, mass holder (50 grams), and masses (grams).

Procedure:

1)      Locate a stand to suspend the spring from. The stand should be about ten times longer than the spring (at least).

2)      Attach a clamp to the stand to suspend the spring from. Make sure that the clamp is at least 5 inches away from the stand itself so that no contact between the spring and the stand is made.

3)      Locate a spring to be used. The spring should have a loop at the top of it perpendicular to the rest of the coils to allow it to be hung.

4)      Attach the spring so that it is dangling from the clamp. The spring should form a 90-degree angle with the clamp and be parallel to the stand. The spring should be hanging straight with no curve in it.

5)      Hook the ammeter up the power supply.

6)      Attach lead A to the top spring loop; secure lead B to the bottom spring coil.

7)      Take a paper clip and bend it into a crescent shape and suspend it from the bottom spring coil.

8)      Attach the mass holder to the paper clip (the mass holder should be equal to 50 grams).

9)      Run the experiment with approximately each of the following amounts of current: 0A, 1A, and 3A. For each current use masses of 50, 100, 150, and 200 grams to stretch the string. Remember that the mass holder itself has a mass of 50 grams and use only it for the 50 grams mass. Then add a 50 grams mass to the mass holder for a total of 100 grams and so on. Record results.

Planning:

The procedure above was the one used in actually when running our lab, however, it was not the original one planned. While actually running our lab we had to account for certain aspects, which in turn required an alteration to our original procedure. The first of these would be that it was anticipated we would be able to use actual temperature calculations to mark the decrease in the spring constant. However, it became increasing difficult to find a way to heat the spring in the first place. We originally had planned to heat the spring in water and use a thermometer to get the temperature of the water and then assume that temperature would equal the temperature of the spring because we would allow it to remain submerged for some time. However, we decided this would leave too much room for error because the container the water was heated in would have to be exposed to some source of heat, obviously, and we knew that the spring would sink to the bottom of the container and come in direct contact with the container. This would potentially cause the spring to be laid up against the part of the container being heated and the heat source would cause the container to be hotter in that spot then that actual over all temperature of the water. However, because we would be relying on the temperature reading of the water and not the temperature of the actual container directly above the heat source, we would have an inaccurate temperature reading. Also, it would take a lot of time to heat each spring and water to different temperatures and we could not be certain as to how long the spring would need to be submerged before taking on the temperature of the water in the first place. Instead we decided to run current through the spring, which would cause an increase in the spring temperature, and use qualitative data. We found that the increase in current caused a notable change in temperature simply by touching the spring and therefore could tell the current was having the desired effect on our spring. We also made sure that we attached connector cables A and B directly to the endpoints of the spring. This was done out of fear that attaching the connector cables anywhere other than directly to the spring would cause a discrepancy between the actual amount of current running through the spring and the reading of the ammeter because it would not be running only through the spring but through other apparatus.

Results:

1

Data Table: Mass vs. Current Data for Stretch Length

We have calculated an exponential growth for the amount that each spring stretches with the amount of mass on it for each current. Of greater significance, however, is that the exponential growth is shown to increase with the increase of temperature.  Please also note these graphs.

Data Table: Exponential Growth Equations

Conclusion:

We have concluded that the spring constant decreases and the exponential growth of the amount of length stretch increases with the increase in temperature. This is important to the field of science for multiple reasons. The first of these is that in the field of mechanical engineering, springs are often used in machines. However, when work is done by machines, it is usually accompanied by the transformation of energy into heat energy. This would cause an increase in temperature to the machine and therefore an effect of the machine’s performance. The decrease in the spring constant of the machine could lead to dangerous malfunctions and a decrease of productivity. This information is helpful to mechanical engineers so they can account for this problem and devise some form of cooling device for the machines to insure proper functioning.  Furthermore, it could be possible that experiments run in different environments could lead to a discrepancy in results. For example, an experiment run outdoors in Alaska involving a spring could have different results than experiment run outdoors in California. This should be taken into account when scientists run their future experiments.

Within our data there are two possible areas where potential error occurred. The first of these is that during testing, we did not check to see whether the spring, upon removal of the mass, had reverted back to its previous form. In other words, we did not check between the masses to make sure the spring had not become plastically deformed and stretched to a longer length. This could generate room for error because the amount of length stretched with each mass applied would have been calculated incorrectly because we subtracted the original length of the spring, 6.5 cm, from the length with mass applied and if the spring did not revert back to the 6.5 cm then the stretch distance would actually be less than calculated. To avoid this in the future, it is recommended that the spring length be measured between each application of mass and then that length be used to subtract from the corresponding length measurement to calculate the stretch distance.

The second potential room for error occurred during testing because when we ran the current of 3.15 Amps through the spring and applied 200 grams mass to it, upon removal the spring was plastically deformed. For all practical purposes, the spring remained at the same length it had stretched to while the mass was applied. Due to this we had to stop testing because our materials could no longer be used. In retrospect, it would have been better if we had been able to continue research and get more data to support our hypothesis. Although we feel we have sufficient data to accept our hypothesis, more would have been preferred. The lack of data that the deformation resulted in could lead to room for error because not enough testing was done. Also, the fact that after the 3.15 Amps the spring was plastically deformed, supports the previous concern that the spring length should have been measured between each stretch with mass to ensure we were subtracting the correct length. For the future, we would recommend that a stronger spring be used and the current be increased in smaller increments. The stronger spring would allow a higher current to be reached before becoming plastically deformed and the smaller increments of increase would allow for the collection of more data.

Although potential room for errors should be taken into consideration when choosing to either accept or reject our hypothesis, we still feel that we are able to accept our hypothesis for the following reasons. In reference to the possibility of the spring becoming plastically deformed during testing and not reverting back to its original length, we feel that if any permanent stretch had occurred that was significant enough to really alter our results, it would have been visibly noticeable and caused us to stop our experiment. Therefore, if any plastic deformity occurred during testing it was not significant enough to cause a large miscalculation in data and we feel that because of this our data is reliable enough to accept our hypothesis. Furthermore, regarding our having to stop testing prematurely, we still feel that even though only three current readings were used, because we can notice a marked increase in exponential growth based upon those three, it is enough to be able to generalize that had we proceeded to use an increase in current and gain more data, we would have seen the same marked increase that was visible from the three exponential equations we were able to originally generate. Therefore, although we would have preferred more data, it has not handicapped our ability to accept our hypothesis.

Bibliography

Cook, J Gordon.  Creep of Metals at High Temperatures.  London: Mills & Boon Limited, 1972.

Isaacs, Alan.  “Elastic Modulus.”  Oxford Dictionary of Physics, 2000 ed.

Meiners, Harry F.  Physics Demonstration Experiments, 1970 ed.

Ridgen, John S.  “Elasticity,” “Elastic Moduli and Constants.” Macmillan Encyclopedia of Physics, 1996 ed.

Trigg, George L.  “Steel.”  Encyclopedia of Applied Physics, 1997 ed.

Determining a Spring Constant - This page is an outline of a physics lab designed to demonstrate the basic concepts behind measuring a spring constant.  These concepts are essential to determining a spring constant as well as understanding the foundation on which our research rests.

Plastic Deformation - This webpage contains detailed data about plastic deformation under different levels of strain.  This explains why the spring reacts as it does when it is heated and weighted down.

Electric Current & Heat - This site has an idea for a brief experiment that can be performed to show that when an electrical current is run through metal, it generates heat.  This concept is at the center of our research.

Advanced Creep - This is a link to a British site containing research on advanced creep of metals in industrial settings.  This gives an idea of how creep can be problematic in the real world.

Understanding Coil Springs - This is a car enthusiast site.  In this particular section, a very detailed and technical guide explains the effects of creep on coil springs within a vehicle, and how this affects its performance.  This is another real world example of how creep affects us.