Sample Calculations
Conversion of cm to m Conversion of g to kg Finding Average (s) Finding Average Uncertainty (s)
Data Processing:
Table 3-Finding Period of 1 Oscillation
Sample Calculations
Finding Time for 1 Oscillation Finding Uncertainty
=0.008
Table 4-Transforming Data to plot onto graph
Squaring Time
0
Finding Uncertainty
Graph 1-Transforming Graph in order to get a linear relationship
- Uncertainty too small to be seen
Finding Uncertainty of Slope
Y-Value Uncertainty-1st Point=
-2nd Point=
Finding Constant
Finding Constant Uncertainty
Calculating E Value
= ()
Percent Error
=28%
Conclusion:
In conclusion it was found that the stiffness of the specific sample of steel used was. Stiffness is the physical property of being hard to bend. It was assumed that the blade was made up of steel. According to the psi value for the different types of steel at 21 ranges from 27-30. Assuming that the room temperature was approximately 21, and the type of steel was nickel steel, it can be said that the 28% difference between the actual and calculated values in this experiment is acceptable, since it was not known what specific compound of steel the hacksaw blade was made up of, or what the exact temperature of the room was.
As seen on the graph, the stiffness was found when T^2 was graphed against X^3, and the slope was taken and then substituted into the equation. The second point on the graph was labeled as a random error, and the slope of the line did not take into consideration that point. The random error occurred most likely because of human error, more specifically, not being able to count exactly 5 oscillations. It is likely that 4 oscillations were counted and therefore there was a decrease in time when compared with other values.
There were quite a few limitations in the procedure. First of all, it is nearly impossible to count exactly five oscillations. There is always a human error, because it is impossible to tell where exactly the oscillation starts, and where exactly it ends. Along with that, the human factor also affects the data, because it is impossible to start a timer at exactly where the oscillation starts, and at exactly where it ends. But it could be said that the delayed reaction time in the beginning and in the end cancel each other out. Another limitation was the fact that only the mass of the magnet was taken into account. Ideally, both the mass of the magnet, and the mass of the hacksaw blade sticking out from the clamp would be taken into account. The biggest limitation of all was not knowing what exact material the hacksaw blade was made up of. This in turn made it difficult to compare the experimental value to an actual value. Another limitation was not knowing the temperature of the room, because as temperature increases the stiffness of the steel decreases.
There a number of ways these weaknesses can be addressed. First of all in order to be able to count an exact number of oscillations, a high quality video camera can be utilized. By slowing down the video it can be found with reference to the recording time, when one oscillation started and where it ended. In order to take into account the mass of part of the hacksaw blade; the whole blade would have to be weighed first and its length measured. A ratio can then be used according to how long the distance is from the clamp to the end of the blade, and then a mass can be of the specific part of the hacksaw blade. This is of course assuming that the mass of the hacksaw blade is spread out evenly. Next time, a specific compound of steel should be used; this in turn would allow the calculated values to be compared to the actual values. The temperature should also be recorded during the beginning and the end of the experiment, because that has to be taken into account when comparing to actual values.
Works Cited
Young Modulus of Elasticity for Metals and Alloys." Engineering ToolBox. 08 Mar. 2009
<http://www.engineeringtoolbox.com/young-modulus-d_773.html>.
