-wooden wedges (to make the table into a ramp)
Fig 1. Diagram of materials
Data Collection
Table 1. Mass of the weights and trolley travelling times
Data Processing
In Table 2, we processed the collected data from Table 1, using the following formulas :
Applied pulling force = mw x g
Measured acceleration
Measured pulling force =
Uncertainty of measured acceleration (sample for trial #1):
Estimated reaction time is 0,2 seconds
Ideal acceleration (per Newton’s 2nd law)
Table 2: Pull forces, measured acceleration with uncertainty, and ideal acceleration
Data Presentation
In Fig 2, using the data from Table 2, we plotted the measured acceleration on the x axis and the pulling force on the y axis. Here we calculated the pulling force by multiplying measured acceleration by total mass (Newton's 2nd law).
Fig 2: Measured acceleration vs. Applied Pulling Force
To better compare the measured acceleration and acceleration predicted by Newton's 2nd law, we also presented the data from Table 2 in Fig 3 graph. Here we plotted the applied pulling force (calculated from an independent variable mw) on the x axis, and both the measured acceleration and the ideal acceleration on y axis.
Fig 3: Applied pulling force vs. measured and ideal acceleration.
Conclusion
In Fig 2 graph (measured pull force vs. acceleration) the line is a curve because the mass was changing during the experiment. The slope of the line at any given point represents the total mass at that acceleration. The slope is steeper when acceleration is higher because the mass of the Weight was greater so the total mass was greater.
If Newton 2nd law is correct and if our measurement is precise, the acceleration that we measured by measuring the time should be similar to the acceleration predicted by the Newton's 2nd law (measured and «ideal» acceleration from Table 2). This data is plotted in Fig 3 graph. The data shows that for the lower pulling force, the measured acceleration is close to the ideal. For the higher pulling force, the uncertainty of time measurement was the reason for the high uncertainty of acceleration. It seems that we consistently came up with longer times, when the trolley was moving faster. We also suspect the changing friction coefficient at different trolley speeds. Also, as in the Fig 2, the best-fitting line is not a line, but a curve because the total mass was changing during the experiment.
Sources of error
- It was difficult to precisely measure time. Our reaction time was large compared to the travelling time of the trolley. This contributed the most to the acceleration uncertainty.
- We measured time only once for each trial.
- We ignored the friction, since we angled the table. But, we suspect that friction also contributed to the uncertainty of the results.
Improvements
- Lengthen the trolley travelling time to reduce the relative time measurement error. For example, we could raise table and lenghten the string.
- Measure the time in each trial multiple times (three at the minimum).
- Eliminate some of the smaller weights from the measurement, to minimize effect of the friction force at lower speeds.
- Use smoother surface.
- Keep total mass constant. This means that we start with maximum Weight and move the mass from the Weight to the trolley for each trial. Then the lines in both graphs would be more linear.
