Physics crater investigation

CRATER EXPERIMENT

Strategy

Aim: The aim of this experiment is to discover the relationship between the height of the marble being dropped and the diameter of the crater produced.

The input variable (what I will measure) is the height that the marble is being dropped from. The output variable (what I will measure) will be the size of the crater produced.

The science behind this experiment is quite simple. The higher you drop the marble the bigger the diameter of the crater will be. Gravity and drag forces are involved in the dropping of the marble, and then as it hits the sand, a small amount of kinetic energy is created. The higher I drop the marble the more gravitational force and the more kinetic energy, therefore increasing the diameter of the crater. There is also drag in this experiment which could limit the speed of the marble being dropped, therefore decreasing the diameter of the crater.

Change in Gravitational Potential Energy = Mass x Gravity x Change in Height

Kinetic energy = ½ x Mass x Velocity2

Equipment

Marble – I decided to use a small marble for my experiment as it is very convenient. I have chosen to use a marble because it is perfectly rounded without any jagged edges, which will make the almost perfect semi-sphere for a crater. This will make my results all the more reliable and accurate.

Meter Ruler - To measure the height we drop the marble from we will use a meter ruler with increments of 1 cm. This is the perfect scale and size for me because I need it to go up to at least 60 cm and am planning to use increments of 5 cm.

Standard 30 cm Ruler – To measure the size of the crater I will be using a 30 cm standard ruler. The ruler has increments of millimetres; this is useful because I expect craters to be small enough to measure in millimetres. However, if I could I would like to use a ruler with an even smaller scale, maybe with tenths of millimetres on as this would allow me to be more precise and accurate when I measure the diameter of my crater.

Compass – This is very useful to help measure the diameter of the crater. I will use a compass to measure from one side of the crater to the other; this would allow me to get an accurate reading when I put the compass against the standard ruler. Using a compass would not cause disturbance in the sand but a ruler might, this is why it is a more accurate way of measuring the diameter.

Small Tin – I am going to use a small rectangular tin to hold the sand in, this will be where I drop the marble. The measurements of the tin are roughly 7x4 centre metres large.

Support Stand – I needed something to hold the meter ruler in place when I drop the marble. This meter stand is metal and tall enough to hold a meter ruler; it also has a claw extended from its body to hold the ruler. I can also change the height of the claw and the tightness of the claw. This will be very accurate and reasonable for this experiment. A lot more reasonable than holding the ruler upright with my hand.

Collecting Data

In order to make my test an accurate and reliable one, I will need to keep everything the same throughout the experiment, however one variable will be changed. I have chosen to vary the height of the marble being dropper from. This will vary my results, therefore making it easier and more reliable to make a clear conclusion on my results. Any sort of precautions has to be kept the same otherwise it could disturb any pattern on my results and therefore giving me a false interpretation on the experiment. For instance if the sand ...

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Collecting Data

I am going to do all of my experiment at room temperature.
I am going to use the same marble throughout the experiment.
I am going to use the same sand during the experiment.
I am going to flatten the sand after it is disturbed when the marble has been dropped.
The diameter of the crater after the marble has been dropped is going to be the dependent variable as this means that it is going to be measured throughout the experiment.

Method:

I took one small marble, which was cleaned and analysed before the experiment to check for any faults.
I took a small tin of sand roughly 4x7 centimetres and checked for any faults or inaccuracies.
I then took the support stand, which then held the meter ruler vertically, with 0cm just touching the sand, but make sure you do not disturb the sand and that the ruler will not get in the way of the experiment.
I then dropped the marble 5cm, which was the first stratum that was recorded.
After that, I got my compass and measured the diameter of the crater, measuring from the highest point of the crater to the other side.
I then placed my compass next to a ruler and recorded the width.
I did this in increments of 5cm up until 60cm.
I was then ready to draw up my results into a table format
I could then choose to repeat the experiment, which could make it more accurate and reliable.

All the diameter measurements were done to precision. Each measurement was done in millimetres, which made it very accurate, and for some I have chosen to include at least 1 d.p. I was then able to make clear and reliable justifiable judgements.

I chose to repeat each measurement 6 times, but in increments of 2, with averages after every two measurements and then a final average of all the averages. By using averages, it is much easier to make a clear judgment of how the results are. Also with more averages, it would make it far more accurate, thus giving me a more reliable conclusion and graphs.

During the experiment I had to be aware of some sources of errors. For instance if the temperature of the room had changed during the experiment, which could make the air moist, therefore making the sand more moist which will increase the density. This minor problem could be a major problem for my results. This is why I chose to repeat each reading 6 times to make sure of any changes. I also had to be careful with the dropping of the marble. I had to balance it on a ruler, which was horizontal to its axis, on the point of which I was measuring it from. I could then be sure that the marble was dropped from the right distance. If I were to drop it with my hand using the naked eye, this would make my results unreliable.

As you can see I have averaged out every two measurements to make my results very accurate. From this table of results, it is quite simple to spot a trend. As you increase the height of the marble being dropped from, the diameter of the crater increases too. Any outliers are highlighted in red; this helps me distinguish accurate results to inaccurate results. By this I can decide not to use these outliers for my averages and my graphs, but as they are not that major and wouldn’t make much a difference to the trend that is being spotted.

As there are not many major outliers that I can spot from this graph, I have decided to include all my measurements in the averages.

The density of the sand was one of the only things I felt was unreliable. If the sand was compact then the marble would make a less deep crater than if the sand was less compact. However when dropping the marble I did not measure the volume manually. Instead I used the formula 2/3 x Pi x Radius3

This formula had its advantages and disadvantages. The advantages were that I did not have to worry about the density of the sand. And by using a formula results according to the accuracy of the diameters would be more reliable. The only disadvantage is that by using this formula, the crater has to be a perfect semi-sphere, however by eye the crater was obviously not a perfect semi-sphere. I have considered this and decided that I would use the formula anyway.

Interpreting Data

As you can see from my ‘Relationship between Height and Diameter’ graph there is a strong positive correlation, which is show by the line of best fit (grey). So from this information it would prove my hypothesis, as you increase the height of the marble being dropped from the diameter of the crater increases as well. I have also joined all the data with a dark blue, again indicating the strong correlation. There are just two obvious and clear outliers, which I have circled in blue as well. They are not major outliers and therefore I have chosen to plot them on my graph.

These anomalous results could be due to a few sources of errors. For instance when I any movement of the tin of sand could disturb the created crater and therefore changing the diameter of the crater. Also any slight mistake in using the compass could have changed my measurements, thus giving me these inaccuracies. However this is why I took many readings of every diameter, which would lower the amount of outliers and giving me more reliable results to work with.

As you can see from my ‘Relationship between Height and Volume’ Graph there is also a strong positive correlation, which is show by the line of best fit (grey). The gradient of the line of best fit is y = 360x – 300, where ‘x’ is positive and has a large gradient and so it is correct to say that the higher you drop the marble the bigger the volume and the lower you drop the marble the lower its volume. Once again I have decided to join up all the data with a dark blue colour, making it clear to me how positive and strong this correlation is. On this occasion there is no obvious and major outliers, which makes the graph very accurate and reliable.

The graphs produce an accurate and reliable view on the experiment, and correspond to my hypothesis. The higher you drop the marble the bigger the diameter and the bigger the volume, and vice versa. The science behind this experiment is quite simple. If you were to drop the marble from a low height, you will find that the marble doesn’t have enough distance to create high gravitational potential energy, and when the marble hits the sand, the amount of energy on the marble is low, therefore the diameter of the crater is small and has created little kinetic energy too. However if you were to drop the marble from a high distance, the gravitational potential energy is much higher, as it has more time to build up this energy, which gives you a bigger crater and more kinetic energy. For example, if I were to drop the marble from 5cm, the gravitational potential energy would be 10g(marble)*………………………….

Evaluation

Overall I believe my experiment was a success. I obtained accurate and reliable results, which enabled me to create revealing graphs. I believe I gained enough results in order to make an accurate conclusion on my hypothesis. The small increments of 5cm allowed me to work with a lot of results and a lot more accurate results. If I were to go from 5cm straight to 20cm, I would have missed a lot of important information, and therefore making my experiment all the more accurate.

I also believe by using a ruler to hold the marble in place on the meter ruler, contributed to the accurate results I obtained. If I didn’t use the ruler, I would be judging the height from eye, and this could change the results completely.

The hardest part in the experiment was the measurement of the diameter of the crater. I had to be extremely accurate with my compass, and had to make sure I measured from the very end of the crater to the other. The ‘end’ basically means where the sand is no longer being disturbed. If I were to repeat the experiment I could possibly use a different piece of equipment just so I can see if it would make a difference to my results. But on the whole I believe using the compass made my results far more accurate than they would be if I just used the ruler.

I also took my measurements in millimetres, which is an accurate scale to use in this type of experiment, however this could be improved by using tenths of millimetres or an even smaller scale.

The flattening of the disturbed sand was probably the most inaccurate part of the experiment, and could be improved. After I had dropped the marble and took my results, I had to shake the tin, until the sand was flat (in my eye). However I cannot be 100% sure that it was flat, and this is why it was the most inaccurate and unreliable part of the experiment. If I were to repeat the experiment I would use a machine or a flat surfaced object to smear the surface of the sand until it is flat.

I have thought about these precautions greatly and have decided that certain aspects of the experiment could have been improved. However, on the whole, I believe that I done everything to a precise degree of accuracy and to my best ability. This effort has given me a very accurate conclusion and reliable graphs and results, which corresponded greatly to my hypothesis and the science behind the experiment.

Jake Jeal