Investigating the Hookes law by Determining the Spring Constant - Lab Report Example

Investigating the Hooke’s law by determining the spring constant By of the of the School (University) City Date Abstract: The main aim of this experiment was to investigate the Hooke’s law by determining the spring constant for a spring. This was done plotting a graph of extension and force proportional to each other. The spring constant of a mass was determined both statically, by measuring its stretch when subjected to loading, and dynamically, by measuring the period of a mass hung from one end and set into vertical oscillation. The resulting value was 53.55  7.46 N/m, indicating that the springs behavior follows the Hookes law to within the limits of accuracy of the experiment. Introduction: The Hook’s law states that the displacement of spring is directly proportional to the force experienced by this spring. If by any chance the force surpasses the limit of flexibility, the spring shape is changed permanently. In symbols, we can express this as follows; In this case, is the spring constant which measure the firmness of the spring with unit newton per second (N/m). The above expression implies that an increase in the value of k results to the spring becoming stiffer. on the other hand represents the extension of string after force applied. The above figure shows a good application of the of the Hooke’s law to the spring. The spring at m is in its normal extension no load is attached and thus the force is zero, when we attach a box (load), the spring experiences some tension resulting to its extension by . When the load is removed, the spring contracts back past its normal position. We realize that though the spring extends, it does not surpass its elastic limit (elastic limit is the maximum point at which the spring extend). Beyond the elastic limit, the Hooke’s law is disobeyed. We represent this assumption by the graph given below; There exists a relation between stress and strain and this relationship is called young modules and it represents the elasticity of the object. Thus young modulus is given as; Hypothesis The change in length of spring (extension) is directly proportional to the force applied, that is, greater force applied will result to a greater extension (change in length) of the spring. This hypothesis is supported by the formula of force, , where is the applied force, is the spring constant of the spring, and is the change in length or extension of the spring. Since the spring used is the same, the spring constant will always be the same for any value of force applied and extension of the spring. Theory The relationship between a load force and a light spring was the first determined by an English scientist, Robert Hooke (1635-1703) in the 17th century. Hooke’s law states that when an elastic material is subjected to a force, its extension is proportional to the applied force. The value of is constant for a particular spring. When an elastic material is subjected to a force, its extension is proportional to the applied force, the value of is constant for a particular spring. Method: We set up the apparatus as shown below, but with no load. We set the pointer to be exactly on zero, this made it easy for the extension to be measured as each 100 g mass was added. Next we carefully added 100 g masses and recorded the extension each time. This was repeated until 900 g was reached. Results Mass/g Force/N Extension/cm Extension/m 0 0 0 0 100 0.98 30 0.3 200 1.96 59 0.59 300 2.94 91 0.91 400 3.92 122 1.22 500 4.9 149 1.49 600 5.88 180 1.8 700 6.86 219 2.19 800 7.84 249 2.49 900 8.82 280 2.8 Calculations Discussion In overall, the experiment was conducted with minimum errors and the given procedures were followed to the latter. There were 9 data points. The experiment was aimed at investigating the relationship the force (F/N) and the extension (e/m). We plotted a graph of force (F/N) against the extension (e/m), so as to determine the gradient (which is the spring constant). The x-axis represents the extension (in metres) while the represents the force (in newton). According to the Hooke’s law, the graph remains linear until it exceeds the elastic limit. We consider the graph to be accurate but not precise. Hooke’s law states that the spring extension and the applied force are directly proportional to each other so the graph should pass through the origin, which is shown in the graph. The spring constant was found to be 53.55 N/m which is less than the expected accurate result. The more accurate result should approximately be 55  5 N/m. This clearly shows that there were some flaws/errors in this experiment. Most error is a result of measuring judgments, parallax (eye sight) and non-zero reading. Some error has been found because a ruler where not on surface. Many other experimental errors may be found either systematic or random errors. The length measured by the ruler is said to be more than the measured number, this number was considered because it is the minimum measurement we were using. In the gradient we used  7.46 as the highest error possibly to occur and it’s higher than expected value which must be ±5. Using well developed equipment and fixing the ruler with the clamp stand may help reduce the errors. Conclusion From the workings, it is clear that there is a positive linear relationship between force (F/N) and the extension (e/m). The gradient of the graph represented the spring constant and this result was found to be . Though the graph is accurate we cannot certainly be 100% precise since it is subject to human errors. References Breithaupt, j. (2011). Physics. 3rd edn. London: Palgrave Macmillan. Bueche, F. J., (1980). Introduction to Physics for Scientists and Engineers, Third Edition, McGraw-Hill, N.Y. Wilchinsky, Z., (1939). "Theoretical Treatment of Hookes Law," Am. J. Phys. 7, 134. Walker, J. (2011) Principle of Physics. 9th edn. California: John Wiley & sons inc. Read More