Effect of Height and Mass of Ball on Crater Depth / Physics EEI

Discussion

This investigation involved observing the effect of changing the height a ball is dropped from and the mass of the ball on the depth of the crater formed in the sand both qualitatively and quantitatively. The experiment was designed to fairly and accurately test the formulated hypotheses.

Hypotheses investigated:

·         If the height in which the mass (ball) is dropped from is increased then the depth of the crater that is created in the sand will increase. Likewise, if the height is decreased then the depth of the crater will decrease.

·         If the mass of the ball is increased then the impact gravitational potential energy is increased, increasing the depth of the crater.  If the mass is decreased then the depth of the crater is also decreased.

Interpretation and Explanation of Results

The first hypothesis was tested by dropping a ball from varying heights. As there were seven balls, this experiment was repeated seven times allowing the results to be compared. In each test, the ball was a controlled variable, the depth of the crater was the dependent variable and was measured and the height the ball was dropped from was the independent variable (refer to research plan in log book on page 2).

The first test conducted involved the first ball (a small white ball). While most of the results obtained from the experiment were quantitative data in the depth of the crater created, some observations (qualitative data) were documented. It was seen that the ball was suspended in the air until released. When released, the ball fell in a reasonably vertical nature into the bucket of sand. On impact with the sand, the ball came to a stop. This impact created a crater in the sand (see image in appendix 1 for example).

The quantitative data that was collected, as seen in appendix 2, allowed a thorough analysis of the experiment. Ball #1 was dropped three times from each 1m, 2m, 3m, 4m and 5m. Each test, the depth of the crater was measured and recorded. An average of the three tests was then calculated so that it was easier to interpret and graph the results. Before an average was calculated it was noted that for each test, the average range of the three results was 0.1cm. As hypothesised, the results, when graphed (see log book page 50), show that the depth of the crater increased as ball #1 was dropped from a greater height up to 4 metres. Conversely, when dropped from 5 metres, the ball created a crater depth of 1.62cm, less than that created when dropped from 4 metres and only marginally more than when dropped from 3 metres. This result may have been due to a number of inaccuracies or errors that were involved in the experiment (as discussed in the next section – errors and improvements).

The graph of the results from ball #1 did support the hypothesis in that the depth of the crater tends to increased as the ball is dropped from greater heights when a line of best fit is plotted. This curve-fit for the graph has an equation of: y = 0.216x + 0.828 (depth of crater = 0.216 x drop height + 0.828) and an r-value of 0.8191 (a r-value of 1 would fit the plotted points perfectly). The r-value reveals that the line fits the points fairly well but does not accurately represent the relationship. However, considering that the test from 5 metres seems to be an anomaly, the removal of this point from the results and the graph revealed a clear relationship between the depth of the crater and the height ball #1 is dropped from. When the line of best fit is graphed on the line has a r-value of 0.9849, fitting the points fairly accurately (y = 0.3459x + 0.5871). Additionally, it is consistent with the observations that the y-intercept is positive on the graph. When placed on the sand (dropped from a height of 0m), a crater is created in the sand with a depth.

The test was repeated to ensure that the hypothesis was supported when the type of ball was changed. It was found that in addition to ball #1, balls #2, #3 and #6 had similar results in that the depth of the crater increased as the height increased from 1 – 4 metres. Again, with balls #2, #3 and #6, the test from 5 metres produced a crater of smaller depth than the test from 4 metres (see graphs on pages 50-53 of log book). The linear relationship between the two variables is especially clear in the results from ball #4 – the line of best fit with an r-value of 0.9715 and the equation of the line being y = 0.113x + 1.603. While it is clear that there is a relationship between the variables (they seem to increase proportionally), each ball has shown results that are independent and there is no correlation between the tests. While the hypothesis is supported as the graphs all have a positive gradient and tend upwards, the fact that there is no common gradient or y-intercept between the graphed results (see appendix 3) suggests that the depth of the crater has been affected by another variable relating to the difference in each ball.

Despite the variation in results, the tendency of the ball to create a deeper crater as it is dropped from a greater height can be explained using relevant theory. Each ball, as it is raised to a height, gains gravitational potential energy (Hyperphysics, 2014). Gravitational potential energy is stored as a result of the gravitational attraction of the Earth for the object and is stored in an object because of its vertical position or height (The Physics Classroom, 2014). This gravitational potential energy is stored in the balls as the product of the work done in lifting it away from the Earth. If an object is lifted straight up at a constant speed, then the force needed to lift it is equal to its weight, mg (Inkling, 2014). The work done on the mass is then [work = force x distance = mass x gravity x height]. So the potential energy of the objects (balls) is associated with the state of separation between two objects that attract each other by the gravitational force (see pages 6-9 of log book) and is dependent on the mass of the ball and the height to which it is raised. Since G.P.E. (gravitational potential energy)=mgh (mass x gravity x height), increasing the height (as was done in the first experiment) will increase the gravitational potential energy – when mass is kept constant.

When the balls are released and start to fall, the gravitational potential energy that they possess is converted to kinetic energy (TJHSST, 2012). They are pulled toward the ground by the gravitational force of the Earth and begin to accelerate. This acceleration has an approximate value of 9.81 m/s², which means that, ignoring the effects of air resistance, the speed of an object falling freely near the Earth’s surface will increase by about 9.81 metres per second every second (Labman, 2013). According to the Law of Conservation of Energy (see page 17 and 18 of log book), the loss of gravitational potential energy is in fact the transformation of this energy into kinetic energy. The further the object (ball) fell, the less gravitational potential energy it had and the more kinetic energy it had. When the object (ball) hits the sand, all of the gravitational potential energy has been transferred into kinetic energy (Finnen, 2012). So, increasing the height from which the ball was dropped increased the gravitational potential energy that it possessed. Increasing the gravitational potential energy increases the kinetic energy as the ball hits the sand. As kinetic energy is proportional to the product of the mass and speed of the object and mass is kept constant, the velocity of the ball as it hits the sand is greater when there is a greater amount of kinetic energy. This is consistent with the knowledge that the further the ball has to fall the greater the eventual speed because of the constant acceleration (9.81 m/s²).

Any object in motion interacting with any other object will transfer energy to that other object. Sand (a mass or some quantity of sand instead of just one grain) is a collection of many individual objects. So, when you drop a ball into the sand, the ball will hit the sand and transfer its energy into the sand. Each sand grain will absorb some sand and move to hit another piece of sand till it eventually disseminates the movement enough that nothing else has the energy to move another piece of sand. The kinetic energy of the ball is a function of its mass and velocity squared and this energy must be absorbed in the collision between the ball and the sand. This means that the more kinetic energy that must be absorbed in a collision, the greater the potential for the movement of sand.

It was also observed that some of the balls bounced on the sand before coming to a stop. This is because, according to Newton’s law (see page 34 of log book), all actions have an equal and opposite reaction. If not all of the kinetic energy can be dissipated by the contact with the sand, it will push back against the ball sending it up.

In the second experiment – testing the second hypothesis – the height from which the balls were dropped was kept constant so that a comparison between the results obtained from changing the mass of the ball. While the hypothesis predicted that the depth of the crater would increase as the mass of the ball was increased it is clear that the results collected from the experiment do not reflect or support this hypothesis (see page 48 and 54-56 of log book).

When dropped from 1 metre, 2 metres and 5 metres the ball of mass 160g achieved the greatest depth of crater. This ball had a greater mass than only 3 other balls and was smaller than 3 balls. If the results supported the hypothesis the heaviest ball, ball #7 should have achieved the greatest depth of crater and the smallest ball, ball #1 should have made the smallest crater in the sand when dropped. Unfortunately, even through manipulating the data, it is seen in the graphs on page 34-56 that no relationship can be found between the mass of the ball and the depth of the crater. It may be possible to conclude that the mass of the ball has no particular influence on the depth of the crater. However, it must also be noted that there was a major flaw in the design of this experiment in that the surface area of the balls was not controlled. So, while air resistance, the frictional force that acts upon objects as they travel through air, may be considered neglected due to its negligible magnitude, it is impossible to draw accurate conclusions as a number of influential variables have not been controlled (Nave, 2014). Theoretically, as in the hypothesis, a greater mass should create a larger crater depth because it results in the object having a greater gravitational potential energy and therefore a greater amount of kinetic energy on impact (Hyperphysics, 2013).

This investigation sought to determine the relationship between the height from which the ball is dropped, the mass of the ball and the depth of the crater in the sand it created. In summary, as the balls are falling from a certain height, their gravitational potential energy is transformed into kinetic energy. This kinetic energy causes the movement of sand as it transfers itself to the sand in the collision. It was found that if the ball possessed a greater amount of gravitational potential energy as a result of its height above the ground then a greater amount of kinetic energy was transferred into the sand and the crater had a greater depth. Although it wasn’t supported by the results, it is also still believed that increasing the mass of the ball will have the same effect as increasing the height. The errors made in the experiment seem to explain the confusing results.

Errors and Improvements

A number of errors were made during the experiment that may have affected the accuracy and validity of the results. As mentioned above, the inaccuracy of the measuring technique may have affected the results and observations made during the experiment. As a 30cm metre ruler was used with increments of 0.1cm and the resulting depth of crater was fairly small a more accurate ruler would have eliminated a greater amount of uncertainty. Another error that may have contributed to the inaccuracy of the results was the levelling of the sand in the bucket. After each test the sand was meant to be evened out and a level surface so the depth of the next crater could be accurately measured using this level sand. Unfortunately, it may have occurred that the sand was not smoothed out evenly and the next measurement to be made based on this level was inconsistent and inaccurate. Another mistake that was made during the experiment was that in the second experiment the variables were not controlled. The balls all had varying surface areas and characteristics. The unexpected nature of the results suggests that these variables did influence the experiment and without controlling them a fair test cannot be conducted. It can also be seen that the bucket braking seemed to have an effect on the results. It is believed that the broken bucket may have caused the anomalies seen when the balls were dropped from 5 metres in the first experiment. The depths of the craters from these experiments were smaller than anticipated and this may be because the broken bucket allowed a wider dispersion of the kinetic energy. It also changed the conditions of the experiment, rendering that part of the experiment inaccurate and not a fair test. As well as this, during the experiment it was difficult to obtain results as the method that was employed to drop the balls into the bucket was imprecise. It allowed for the possibility of accidentally throwing a ball, giving it a greater amount of kinetic energy, and also made it difficult to aim into the bucket, often the ball completely missed the bucket. Lastly, as is seen (page 48 of log book), there were also no results collected for ball #7 from 4 and 5 metre drops. This was because the bucket had completely broken and could no longer be used.

Improvements should be made to this investigation in order to obtain fairer, more accurate, results and to relate the experiment to a real-life situation. As in the example experiments on page 12 of the log book, it would have been beneficial to measure the diameter of the craters as well as the depth of the craters. This additional measurement would have allowed the volume of sand displaced to be calculated and a clear representation of the amount of sand moved to be seen. It also would have been advantageous to use a wider variation of both heights that the balls were dropped from and masses of balls (with the same surface area) so that there was a greater amount of data to be analysed. It may also be beneficial to add an additional experiment to this investigation to observe the effect of differing surface areas on the displacement of sand (controlling both mass and height). This additional experiment may show the effect of air resistance and the influence it had over this experiment. To further improve this investigation a larger area of sand should be used as to keep the level of sand consistent, remove the possibility of ‘breaking’ the container and make it easier to drop the ball on to the right spot. The use of more accurate measuring tools would certainly increase the accuracy and reliability of the results of this investigation. Finally, the calculation of the impact force to determine the effect of falling objects may prove to increase the usefulness of this experiment as the results may be used to demonstrate the effect of falling pieces of infrastructure/coconuts/rain.