Hooke’s Law indicates the relationship between the amount of extension, e, of a spring to the size of the force, F, acing on it. This relationship may be written as :-
F = ke
F = ke
where k is a constant for which particular spring you are using. It is the force constant of the spring.
* The force applying on the spring, F, is denoted by Newton in SI Units. (N) * The amount of extension of the spring, e, is denoted by meters in SI Units. (m) * The force constant of the spring, k, is denoted by Newton over meters in SI Units. (N/m or N m-1)
The variables for this experiment are as identified below:
* Independent Variable: Slotted Masses of 100 g each
* Dependent Variable: The Amount of Extension of the Spring, e * Controlled Variable: The Elasticity of the Spring-in-Use
* We have set up our equipment as shown in the diagram opposite. In doing so, we made sure that the spring and meter stick hang over the edge of the bench, where the experiment is being carried out. There should be no interaction between the mass & the spring and the meter stick or the edge of the bench. This will enable us to have larger extensions of the spring.
* Counter Balance
A clamp or a counter balance, such as a heavy book in this case, is preferable to use in order to provide for the balancing of the equipment since it prevents the whole set-up from falling over as masses gradually increase.
* Right after we formed our diagram following the instructions above, we have added an additional mass hanger of 100 g to the equipment. This will later be our 1st trial. Then at each trial we added additional 100g masses, one at a time, until we reached our 8th trial. It is recommended that we do not exceed the 700 g limit in order not to permanently stretch the spring. We recorded our values for extension of the spring as it is pointed out on the meter stick until we reached the 8th trial, which corresponds to the mass value of 700 g. Then we transferred these values into a raw data table and further processed them in a calculated data table. You can find them in the attachments.
* The uncertainty value for the slotted masses is specified as 1% in the raw data table, given the manufacturer’s claim. * The uncertainty value for the extensions of the spring is specified as 0.1 cm in the raw data table, since the smallest scale on the meter stick is equivalent to this value. * The uncertainty for the amount of extension of the spring, e, is specified as 0.2 cm in the calculated / processed data table since this value is the sum of two values for 0.1 cm uncertainty, featured in the raw data table. * Our calculations show that the uncertainty for weight is taken as 0.001 N in the plotting of data.
These featured uncertainties couldn’t be demonstrated in the Weight Versus Extension Graph in the attachments since the uncertainty value of 0.2 cm for the extension of the spring in the horizontal axis is too small to be shown. (This value corresponds to one tenth (1/10) of a square on the x-axis)
The experiment was carried out in order to find out the spring constant, k, using Hooke’s law and balancing forces. We had observed a considerable amount of extension of the spring arising from force applied by the masses to the diagram. Following the procedure described above, the mass on the spring was increased by 100 g at each trial and the tension this has caused on the spring was observed. Our experimental result for the spring’s constant, k, is indicated below:
* The R2 Linear Regression Analysis of 0.99993 suggests us that there is high precision but not necessarily a high accuracy. In addition to this, there is an experimental error of approximately 0.001 N throughout the experiment and as a result of this slight systematic error, our slope does not pass through the origin. This error can be due to some misreadings from the measurement equipments. Even slight variations from the actual value can cause the slope not to pass from the origin. More specialized and more precise equipments that could measure up to at least 2 decimal points could minimize the relative influences of this error and improve the results enabling the slope to pass through the origin.
* The mass of the hanger was given to us as 100 g. In the first trial, we have assumed that for an extension of “0” cm (the spring is at rest), there exists a force of 9.81 N. In order for this assumption to be a more trustworthy one, we would have had to measure the mass of the hanger by hand with at least 2 decimal points. This would give us a better understanding of the experimental procedure and reduce the errors caused by the method.
* Time was used efficiently throughout the experiment. Not a single error arising from a time management related issue was encountered.