Introduction

The purpose of this experiment was to investigate the behaviours of three different materials, two in the elastic state and one in the plastic region. This experiment was used to highlight Hook’s law which states that; Within certain limits, the force required to stretch an elastic object such as a metal spring is directly proportional to the extension of the spring. This is known as Hooke’s law and commonly written:

F=−kx(1)

Where F = the Force

X = the Displacement of the material

K = spring constant

Method

1. Figure 1
2. Assemble the apparatus as shown in the diagram at right. Be sure to clamp the ring stand to the lab table, or weight it with several books.
3. Construct a data table. You will need to record the mass that you hang from the spring and the position of the end of the spring before and after the mass is added. From this, you will calculate the force applied to the spring and the resulting stretch of the spring. You should allow for at least 8-10 trials
4. For each trial, record the mass, the starting position of the spring (before hanging the mass) and the ending position of the spring (while it is being stretched).
5. Repeat the process for a rubber band. (2)

Results

Figure 2 a = 1.5515 b= 1.4182

Figure 3

The graph in figure 2 explains the relationship between the force applied to the material and the displacement of the material, it shows that as the force increases so does the displacement of the material which proves that there is a linear relationship between the two variables.

The graph in figure 3 shows the relationship between the two materials that are in the elastic region, this graph shows that in both material’s the relationship between the force and the material is linear which supports the theory of hooks law. From the graph you can see that the line generated from the deformation of y2 is more inclined compared to the line of y1 this indicate that the material of y2 was more difficult to stretch as it required more force. The graph also shows the intersection of both graphs which from the estimate was at the points (2.5,5.2). Calculating the points of intersection theoretically through the use of simultaneous equations gave me the points (2.4,5.2) which compared to the estimated value was 96.2% accurate as per the error percentage calculations.

Solving simultaneously

Y₂= 2.0515x+0.2

Y₁= 1.5515x+1.4182

2.0515x+0.2=1.5515x+1.4182

0.5x=1.2182

X=2.4

2.0515(2.4) +0.2=y

Y = 5.2

Figure 4

The graph in figure 4 shows the relationship between the force and the Material, in this graph the relationship between the two variables is not a linear one, the relationship is an exponential/polynomial one. The relationship is like this because the material z has now gone past the elastic region and is in the plastic region which means that it can not return to its normal shape due to the amount of force that was applied to it. For this reason, we do not see a linear graph instead we see an exponential/polynomial graph as the material has reached permanent deformation and will continue like that until the material breaks.

Conclusion

The aim of this experiment was to investigate the behaviours of three materials and how it relates to hooks law. Hook’s law states that the force required to stretch an elastic object such as a metal spring is directly proportional to the extension of the spring. The graph in figures 2 and 3 help to support this theory as the relationship in both graphs were linear. The graph in figure 4 however does not support this however this is because the material had reached the plastic region due to excess force being applied causing the material to become permanently deformed.

In figure 2 you can see that at two points the results show anomalies as it does nt follow the linear relationship as the other points do, this could be due to equipment errors, for example; the material could have been deformed this could leave errors in the results. In order to make the results more accurate, the experiment should have been completed at least 3 times with the same material.

References;

https://www.khanacademy.org/science/physics/work-and-energy/hookes-law/a/what-is-hookes-law (1)

http://www.batesville.k12.in.us/physics/phynet/mechanics/newton3/Labs/SpringScale.html (2)

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