The Obedience Of Different Materials To Hooke’s Law


Mert Chavushoglu

The aim of this experiment is to find how the relationship between the force and  deformation varies when different materials are used. Also the obedience of materials to Hooke’s Law is analysed. Simply Hooke’s Law points out that the extension of a spring is proportional to the load on the string until it reaches its elasticity limit which is the point of deformation. If the string exceeds its elasticity limit, it can never go back to its original length when the load is removed. The experiment was carried out by three different types of springs which have different spring constants(F=kx).

Figure 1:Deformation of a string.
Figure 2:The idea of spring constant
Table 1: Values used to plot graphs.

Values for x and y1 were given. The y2 was calculated by using the given formula of; y2= (a+0.5) x + c ; where c=0.2. Values for z was calculated by the formula z= x^3+b .

Figure 3: The trend line showing change in deformation with respect to force of material y1.

This graph is drawn with the given values of x and y1. It is know that the y1= ax + b. Values a and b are found to be 1.5583 and 1.375 respectively. The formula of the trend line is found by using the graph. The slope of the trend line and its straightness gives us an idea that it obeys Hooke’s Law. We can say that, the deformation in millimeters increases as the load on the string is increased. However, according to the trend line there are two points, which are not obeying the Hooke’s Law. These two points are 9 and 7 Newtons. There may be some errors during measurement which can cause this.

Figure 4: Values of y1 and y2 in the same graph.

y2 values were calculated by using the formula given which was; y2 = (a+0.5) x + 0.2. Values were plotted to the graph and the trend line was drawn. The formula of the trend line is also found. By looking at the graph value of the force applied estimated to have the same deformation for both y1 and y2 was 2.5 N. By equalizing the formula equations of y1 and y2 to each other with respect to y values the interception point is calculated to be 2.35 N. Just like y1, y2 has similar properties but it obeys Hooke’s Law more than y1. This is because measured values of y2 all lie on the trend line. It still did not reach its elasticity limit. We can say that from the line’s straightness.

Figure 6: The trend line showing change in deformation with respect to force of material z.
Figure 5: The polynomial line showing change in deformation with respect to force of material z.

Values of z are calculated, by using the formula z= x^3 + 1.375. After plotting the z values, the trend line connecting the points have been drawn. Then the equation have been found using the excel functions. Hooke’s Law says that deformation is directly proportional to the force applied. However, by looking at the values of the z in both figure 4 and 5,  we can say that z does not obey Hooke’s Law. The figure 5 has been drawn to show a line that passes through every point. Nonetheless, figure 4 is drawn to illustrate the relationship of the values with Hooke’s Law.

   In conclusion, I would like to expalin why we had three different graphs. As I said before, according to Hooke`s Law, the extension on the string is directly proportional to the force applied. By using the formula F=kx we can calculate the spring constant of our three graphs. Briefly, spring constant is a measure of elasticity of the spring. If we calculate the spring constant for each spring, we will get different results for each of them. I can say that because three graphs are different from each other. Value of a spring constant varies from others according to its original length, material it is made up of, so its density, and more. Even the temperature of the room that the experiment is held can affect the spring constant.

 References

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