An Experiment to Evaluate the Acceleration due to Gravity using a Spiral Spring
by
magisterartium (student)
An Experiment to Evaluate the Acceleration due to Gravity using a Spiral Spring
TEP062N
Introduction
Gravity affects all things that have mass and therefore must affect how much a mass placed on a spring will extend. Measuring the time period and extension of a mass on a spiral spring for oscillations allows for the calculation of g.
The experiment was carried out as described in the worksheet using masses of 0.2 – 1.2kg
Results and Plot
Figure 1
Figure 2
Figure 3
Figure 4
The mean value for g is calculated as 6.71 ms-2 with the standard deviation calculated as 2.17
Calculations
Calculating the extension of the spring or b
b=(l-l0)
b is the extension on the spring when a mass is loaded, l is the total length of the spring with the mass attached and l0 is the length of the spring without any mass attached, The original length of the spring used was 3.7cm (or 0.037m).
For a spring loaded with the 0.2kg the calculation is:
b=(l-l0)
b= 0.040-0.037
b=0.003m
The results for each load can ...
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The mean value for g is calculated as 6.71 ms-2 with the standard deviation calculated as 2.17
Calculations
Calculating the extension of the spring or b
b=(l-l0)
b is the extension on the spring when a mass is loaded, l is the total length of the spring with the mass attached and l0 is the length of the spring without any mass attached, The original length of the spring used was 3.7cm (or 0.037m).
For a spring loaded with the 0.2kg the calculation is:
b=(l-l0)
b= 0.040-0.037
b=0.003m
The results for each load can be found in Figure 1
From the plot in Figure 3, the gradient and therefore the value of k can be calculated using the following equations.
Gradient = 4 π2
k
This can be rearranged to give the value of k
k= 4 π2
Gradient
Gradient = dy = 0.253-0.036 = 0.217
dx 1.2-0.2
Therefore,
k = 4 π2
0.217
k= 181.93 Nm-1
This value of k was then used to work out the value of g for every mass used, by using the Hookes Law equation of
mg=kb
g=kb
m
Below is how g was calculated when the mass of 0.2kg was used, this is to show a working example of the equation:
g=kb = 181.93x0.003
m 0.2
g= 2.73ms-2
The calculation was used to calculate g for all loads and is shown in Figure 4
Discussion
The average value for g is calculated as 6.71ms-² compared to the accepted value of g as 9.81ms-²
There are a number of factors which could have caused such a large discrepancy in the results and the deviation from the standard value. Firstly, human error may have played a large part in the results especially when reading the oscillations of the spring with the lower masses loaded. The force exerted on the spring to begin the oscillations would not always be the same and so would cause faster/slower oscillations and smaller/wider oscillations. Slight variations in the angle of oscillation when the spring was released could also add significant errors into the investigation as it would add horizontal as well as vertical oscillations. The stopwatch used in the investigation read to 0.01sec and so this would give an error of +/- 0.005 sec. Errors with the timing and counting of the oscillations may have also occurred, especially when reading the oscillations of the spring when loaded with lower masses. The ruler used to measure the length of the spring gave readings to 0.001m and there would therefore be an error of 0.0005m
The closest value to the accepted value of g was that with a load of 1.2kg (g= 8.34ms-²). It can be seen that as the load increases, the g value calculated is closer to that of 9.81ms-². This is possibly due to the fact that as the load increased it became easier to read the oscillations and therefore gain more accurate results.
It can be clearly seen that there is a degree of uncertainty to the accuracy of the results. To calculate the value, g will be rounded to 2 significant figures. Therefore, g becomes equal to 6.71ms-² with a percentage error of compared to the accepted value of 9.81ms-²
This is an extremely high percentage of error and this can be attributed to the factors discussed previously.
If the investigation was to be repeated there are a number of improvements which would add to the accuracy of the results and give a value closer to that of 9.81ms-². Firstly, a stiffer spring with a known spring constant would be used to eliminate any errors in measurements or calculations of this. The point of release of the spring for each load would be the same each time and the spring would be held in a rigid tube to prevent any horizontal oscillation. A more accurate stopwatch and ruler would also be used to increase the accuracy of the measurements.
The standard deviation value for g was calculated at 2.17. This means the values of g show a large deviation from the mean value of 6.71ms-². which supports the inaccuracy of the data gathered.
Conclusion
The mean value of g is calculated at 6.71ms-2 +/-2.17ms-2
