Abstract
The world in which we live is surrounded by a number of forces that may each act independently or jointly to keep nature in a state of equilibrium. A force is defined as either a push or a pull whose resultant effect may be either translational, or distortional (Andy, 2002). In this practical experimental undertaking, we investigate the distortional effect of force on objects.
The main aim of this experiment is to prove the celebrated scientific law; Hooke’s Law. Aside from ascertaining the validity of the aforementioned principle, we proceed further to determine the spring constant of the spring used in this experiment under the prevailing conditions. The results will be tabulated and the relationship graphically analysed and presented.
Hooke’s Law of elasticity states that provided the elastic limit is not exceeded, a constant force exerted on a material is directly proportional to the extension of the material. In a simple language, strain and stress are directly proportional.
Therefore, the matter of concern here is that can the validity of this law proven in the laboratories using the simple available apparatus.
A force is a push or a pull whose resultant effect is a displacement in the direction of the application of force. Both Hooke’s Law explains the relationship of the applied force and the extension of the material that results due to the applied force (Andy, 2002; Serway, 2000). The law is given mathematically as in the equation 1 above.
In the experiment, the masses given are in grams so it is necessary to first covert, their values to equivalent kilograms then use the above expression to find the value of respective forces. When the force is applied the spring increases in length and return to its original position. As the magnitude of the force increase the extension increases up to elastic limit above which the spring undergo permanent deformation.
According to equation 1 the experiment yield a straight line graph through the origin whose slope gives the spring constant. The spring constant is also called the modulus of elasticity of the spring and it depends on the material with which the spring is made (Andy, 2002). The experiment seeks to prove Hooke’s law in the elastic region of the spring.
The masses are put onto a mass holder. Firstly, the extension due to the mass holder is determined and this is marked as the reference point. As the masses are added onto the mass holder observations are made in changes in length and the results are tabulated as is shown in the section describing the experiment design.
Experiment Design
In this experiment, focus is on undertaking an activity that relates the force applied to a spring and the spring’s extension from its rest position. This relationship is known as Hooke’s law and states that force is directly proportional to the extension of the spring provided the elastic limit of the spring is not exceeded (Andy, 2002). After the applied force is removed, the spring returns to its original rest position. The modules that we employed are three pieces of mass (20grams, 50grams and 100grams), a meter-rule, a spring with a pointer attached at one end and a stand.
Variables of the Experiment
Force will be the independent variable while the spring’s extension will be the dependent variable. Further, we are going to use one spring in the whole experiment, therefore the material with which the spring is made, the number of coils, mass of spring, pieces of the masses to be added on the mass holder and the coil diameter are the same. These constitute some of the controlled variables.
From above it is evident that the modules required for this experiment are readily available and cheap. Again, the experiment tests our knowledge of graphical techniques, data collection, and determining laws from graphs as well as carrying out independent work in groups. This is why this experiment is chosen.
Hypothesis
A graphical plot of force against extension yields a straight-line curve passing through the origin with a constant slope. This hypothetical relation is derived from Hooke’s Law that states that force is directly proportional to extension in the elastic region of the material used (Serway, 2000). From the mathematical standpoint, if a variable is proportional to another variable then their graphical plot yields a straight-line graph passing through the origin.
Methods of Data Collection
The methods of data collection that we are going to use are both experimental and participant observer. These methods are the most appropriate in that we are going to participate in setting up the experiment and at the same time observing its outcome under the prevailing conditions. The use of the experimental control method is used since force, which is an independent variable, is manipulated by the participant, its effect that is extension of the spring is observed, and the results recorded. Using tables and graphs helps us to observe the trends of the experimental development and allow interim values to be inferred. Finally, for conformity with the hypothetical statement we had to use a graph.
Why This Methods?
We chose these methods since through these methods we could monitor or watch as well as participate in the process or situation that we were evaluating as it occurred.
Seeing the place or environment where something takes place can help increase your understanding of the event, activity, or situation you are evaluating.
Finally, these methods do not depend on the respondents like questionnaire although it might depend to a greater extent on the observers’ bias.
The results of the experiment are as recorded in the table below. We measured the length of the spring as well as the length and mass of the weight holder. We then set up the table clamp, spring and mass holder as illustrated in the figure above. To reduce errors in measurements, we worked in a group where one of the members concentrated on adding the masses while the others take the readings, confirm the results and organizing the efforts of the group members. We added the masses onto the mass holder according to the procedures above and recorded our findings in the table below.
To reduce errors due to parallax, the observation was taken horizontally and before taking any observation, we ensured that the reading was taken when all the oscillations on the spring have died out. Having attached the spring and the mass holder it was assumed that the pointer’s position due to their masses was the zero mark. This helped us in taking these two masses into account. Finally the graph was a line of best fit so as to account for the other errors that might have arisen from sources that were beyond our control.
Figure: graph of force against position of pointer
The gradient of the curve that was found to be approximately 24.19N/m gives the spring constant. The initial pointer position is due to the weight of the mass holder. It is also very important to note that the experimental observations made assume that the mass of the spring is negligible. The validity of the results discussed herein may not conform to the actual results due to the following factors that could have been considered as threats:
When a spring is loaded it is set into oscillation that may take time before settling
Finally, the above three factors made the graph to an approximated plot whose may not give us exactly the spring constant.
Conclusion
Indeed, as can be deduced from the results of the experiment, the displacement on the spring is directly proportional to the force applied and this is exhibited in the linearity of the curve. This concurs well with the hypothetical statement that was given above. We determined the slope of the graph to be 24.19N/m which according to the laws of mathematics gives us the constant of proportionality. From Hooke’s law of elasticity, the constant of proportionality is the spring’s constant.
Replication, Reliability and Validity
The reliability and the validity of a research result are evaluated by the researcher through replication. In this experimental work, the ability of another experimenter to replicate the experimental results shown above is evaluated conveniently, given the assumption that this replication will be relative rather than exact, through a comparison of the effect sizes associated with each set of research results. The effect sizes in this case is the magnitude of the relation between force as an independent variable to extension in any given set of observational points in this experiment. Research results are considered to be replicated when the effect size of the results from the replication study is similar to the effect size of the results of the original study (i.e., they are homogeneous). The research results are not considered replicated when the results of the original and replication studies differ markedly (i.e., they are heterogeneous). If the homogeneity of the results is ascertained then we can conclude that the experiment is internally valid.
Experimental Design is so important in that it is a blueprint of the procedure that enables the researcher to test his hypothesis by reaching valid conclusions about relationships between independent and dependent variables. It refers to the conceptual framework within which the experiment is conducted. If by following the design, the results obtained do not conform to the expected results then, the controlled variables must be put in close checking. When making a good experimental design the following factors must be considered:
The problem at hand need to be identified and defined; the variables i.e. the dependent, independent and the controlled variables should also be identified.
The hypotheses of the experiment must be formulated and their consequences need to be stated effectively.
Finally, the experimental procedures must be well explained to be thoroughly understood by the experimenters.
References
Andy Darvill. (2002). Physics for You. Nelson Thomes Publishers.
Serway, Heichner. (2000). Physics for Scientists and Engineers Volume 1, 5th ed. Saunder College publisher.
