Materials:
- 1 Wooden meter ruler.
- 1 Rubber ball.
- 1 Metal stand holder (for the ruler).
- 1 Chronometer.
- Flat, even, solid surface.
- 1 Physics lab table.
Method:
- Put the ruler perpendicular to the flat surface.
- Place the ruler in the arm of the metal stand and secure it tight so that the ruler can stay still; it must be perpendicular to the surface and parallel to the stand.
- Grab the rubber ball and place it with one hand besides the 10cm mark in the ruler.
- With the other hand have the chronometer in 0 seconds and be ready because as you are going to release the ball you have to start the count in the chronometer.
- Drop the ball and start the count in the chronometer simultaneously.
- Wait until the ball to stop bouncing completely, this is, wait for the ball to start rolling so that you can see movement just in the horizontal way or x-axis and not in the vertical way or y-axis, and in that specific time, stop the count.
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In your physics lab table write the resultant time t for the height h of 10cm.
- Repeat steps 3-6 twice and write the multiple resultant times in your physics lab table in order to have three time samples. This is for avoiding random errors.
- Continue the pattern of releasing the ball from each multiple of 10 until reaching 100cm, measuring three times from each multiple of 10cm. Write the results in your physics lab table.
- Calculate the average of the three times you measure for each multiple of 10cm to 100cm by using this formula:
and write it in your physics lab table in an extra column.
Figure 1.0
For more accurate results:
-Do not move the experiment while taking your measurements. If you change the place of the experiment, the surface texture, evenness, or slope may change as well, making the results less accurate.
-Use the SAME ball throughout all the experiment; each ball has in general the same characteristics, except that they usually are not perfectly round and they have different sizes and masses. By using the same ball you are increasing accuracy in your measurements.
Uncerntanties
The uncertainty of the dependant variable, which is the time t, is ±0.35 s. This has been measured by subtracting the smallest value to the greatest value of time in every measurement of the height, and then the result of that was divided by 2. It can be better explained with this equation:
After that, the greatest difference of all the results is going to be the one that is chosen to be the uncertainty of time in every measure of height. In this experiment the greatest difference was found in the value of height 80cm, which was 0.35 because
Therefore, ±3.5 is going to be the uncertainty of time. All values of time have been rounded to 0.10cm.
The uncertainty of the independent variable, which is the height h, is ±0.1cm. This has been settled without any formal guidelines; the factor that just the human eye is used for this experiment and no other more accurate mechanism, gives an uncertainty because the human being is not perfect when measuring something. In this case, the hand can shake at the point of the ruler, or just the perspective of the experimenter can create some error coefficient when measuring the height using a ruler. All values of height have been rounded to 0.1cm.
Raw and processed data
Figure 1.2
Results
The following graph was made with Logger Pro Software. I included the uncertainty bars and the computer generated the best straight line and determined the gradient.
Figure 1.3
Now, the graph is repeated with maximum and minimum gradients based on the extremes of the first and last data point uncertainty bars.
Figure 1.4
Conclusion and Evaluation
In Figure 1.3, which is the first graph of our results, there seems to be a direct relationship between the increase of time and the increase of height in the experiment. The straight line that the computer generated shows an increase in both x and y axes which represent the height and the time, respectively.
I can conclude by saying that the experiment of releasing a ball at certain heights, that in this case they were from 10cm in multiples of 10 till reaching a meter, and measuring multiple times to get an average, that in this case was measuring 3 times per measure of height the time it took for the ball to stop bouncing completely and then making a average time, that the hypothesis of height being proportional to time was right and has been proved by analyzing the results and graphs. Time t and the height h were proportional to each other because in the result graph we find a straight line with a slope that proves that proportionality. This makes the experiment successful because the objective of proving the hypothesis was achieved.
After analyzing these factors, the answer to the question “How does altering the height when releasing a bouncing rubber ball affect the time until its complete rest in the vertical sense or y-axis?” is that as the height increases where the ball is released, it is going to take more time until its rest in the vertical sense, and in the other hand, as the height decreases, the ball is going to take less time to stop bouncing.
Problems and Improvement
Originally, the experiment was meant to measure the time until the ball reached complete rest (in both x and y axes) so that it could be easy to stop the chronometer and be more accurate. The problem was that the ball would roll on the floor, and as the floor is an even texture, the ball would stop completely taking a lot of time doing it, and sometimes the time it would take to stop in some cases would be very different to other cases because the ball rolls in different directions every time. Changing the experiment of measuring the time until the ball achieved complete rest to measuring time till the ball achieved complete rest in the vertical sense or the y-axis was the solution to overcome this problem. It created a minor problem though. The problem is that the eye can’t really see when the ball stops bouncing completely because there are some bounces in the y-axis that cannot be seen by the human eye because they are really minor, making the stopping of the chronometer count a little subjective and decreasing the accuracy of the experiment.
Some of the materials can be seen in figure 1.0.
