Using information from my preliminary work, I decided to take readings from nine different heights, as I thought this would be enough to allow an accurate graph to be drawn. So in total, I will take 27 readings as I will take three at each height (2 repeats) to ensure reliability. Also using preliminary readings (shown below) the range of x (the height) will be from 4cm to 28cm meaning that the range of y will be about 20cm to 70cm, giving a wide variety of results.
Preliminary results table
In this experiment, the factors investigated could have been things such as the gradient of the ramp, the material of the ramp (rough, smooth etc.), the height of the desk, the weight of the marble, the length of the horizontal section of ramp etc. and so these variables are to remain constant in my experiment. As mentioned previously, to ensure that the marble is launched from the same place on each repeat reading, the ramp will be marked and the ramp will be secured with a clamp so everything remains constant and the same marble will be used (weighing 6.0g). To ensure precision, the measurement in the sand box will be taken from the front of where the first indentation is made from the marble each time.
There is nothing potentially dangerous in this experiment so no particular precautions need be taken, except using general common sense, for example, ensuring the clamp stand is secure etc.
Results
My experiment was carried out safely and the following table contains my results.
Analysis
As I increased the perpendicular height of the marble on the ramp, the horizontal distance travelled by the marble also increased.
On drawing a graph of x against y, a curve was created, again telling me that as x is increased, y also increases. However, x and y are not proportional as a straight line could not be drawn connecting the points. Dissatisfied with this limited analysis, I then decided to investigate further the relationship between x and y and firstly made several calculations to discover the velocity of the marble at each height. Here is an example of the calculations used.
mgh = ½mv2
0.006 x 10 x 0.04 = ½ x 0.006 x v2
0.0024 = ½ x 0.006 x v2
0.0048 = 0.006 x v2
0.8 = v2
v = 0.894 cm/s
I then drew a graph of velocity against the horizontal distance travelled by the marble. This graph formed a straight line through the origin, showing that the distance travelled is directly proportional to the velocity of the marble. So the distance is directly proportional to the velocity and the potential energy, determined in this case by height (x), is equal to the kinetic energy (according to the law of the conservation of energy). This is, however, assuming that any other factors that could affect the velocity such as friction are negligible. Derived from the formula, the kinetic energy is determined by the velocity2, so, the height must be directly proportional to the distance2. To prove this I performed the following calculations and plotted a graph of height (x) against distance2 (y2). This graph again showed a straight line through the origin, meaning that distance2 and height are indeed directly proportional.
mgx = ½mv2 and v is directly proportional to y
gx = ½v2
2(10x) = v2
20x is directly proportional to y2 .
These results support my prediction that as the distance travelled by the marble increases when the launch height is increased. However, I was wrong in thinking x and y would be proportional and did not foresee the directly proportional relationship with the perpendicular height of the marble and the horizontal distance travelled2 . Although my original prediction was correct to a limited extent, I am happy that my calculations and graphs have helped me draw a more accurate and detailed conclusion than that I originally predicted.
Evaluation
I think that my experiment was a successful one and that my conclusion is valid and feasible. As most of the points are either on or very close to the lines on best fit, I think that the quality of the results is fairly good, and there are no outstanding anomalies. However, some of the repeat readings are fairly wide apart (up to 4cm), meaning that the procedure may not have been entirely suitable. There are several possible explanations for the variations in repeats, such as the ruler on the floor may have shifted slightly out of place, meaning a slightly inaccurate reading, the marble may have been held a few mm off the mark on the ramp before released, the indentation in the sand may have been misinterpreted and so the reading may again be a cm short or long.
Small errors such as those mentioned above are fairly inevitable in a manual experiment such as this. More accurate results could obviously be obtained through a mechanical or electronic procedure, so that all elements and factors were kept precisely constant, and that readings were entirely precise. However, without mechanical or electronic aid, minor adjustments could be made to the current procedure to help obtain more accurate readings. For example, the ruler on the floor could be secured with blu-tac or tape, more care could be taken to hold the marble at the same point on the mark (i.e. immediately behind it, in front of it or directly on it) or a more suitable material for the marble to land in could be found, so it could be more visible exactly where the marble first landed, for example some sort of sticky tack so that the marble could not move from its original landing position.
I am fairly sure that the conclusion I have reached through this experiment is correct, however, I can only be sure that this is true in the same environment and to the same extent that I am experimenting. For example, as the ramp I am using is fairly short, any acceleration is almost negligible within my experiment. However, were this experiment to be done on a larger scale, acceleration caused by gravity would have to be taken into account and the conclusion would very likely be different. To the same extent, if different materials were to be used for the ramp, the results would be likely to change as friction (which again is negligible in my experiment) may play a big part in the speed of the marble or ball. So, in terms of a school laboratory experiment with apparatus etc provided, I feel my conclusion is as detailed as possible. However, there is still much room for further investigation into the topic as a whole, and in a variety of situations, such as on a bigger scale, variations of ramp and ball material, or even in a place where gravity is different to that on earth.
Bibliography – Physics for AQA by Patrick Fullick
