crater design lab

Anusha.S5/4/14

Design Lab:Investigating the Nature of Craters Formed on SandResearch Question: How does the height from which a mass is dropped affect the surface area of the crater that is formed?

Variables:Independent variable: The height from which the ball is dropped will be varied. The range of values for the height will be 50,100, 150, 200, 250 cm. This will be measured by first determining the required heights using a meter stick and marking it, and then the ball will be dropped from that point. Dependent variable: The surface area of the crater that is formed on the sand will be the dependent variable. To determine the surface area, first the diameter of the crater will be measured and then the area of the crate will be calculated using that. Five trials will be conducted for each height.

Controlled variables:

The type of sand on which the ball is dropped will be kept constantThe mass of the ball used will be the same for all trialsThe angle at which the ball is dropped will be perpendicular to the surface, so ideally there should be no wind interferenceThe sand should be clear from any rocks/debris and before the ball is dropped, the surface should be flattened by shaking the container till the sand is evenly settledApparatus:

-ball -container-sand-meter stick

Data Collection:Quantitative Data:Height (meters)Uncertainty: 0.1

Trial 1Diameter (cm)Uncertainty: 0.01





50.12.192.212.222.052.02

100.35.125.216.016.156.25

150.27.216.236.516.546.53

200.17.017.227.317.497.52

Only four trials were conducted due to time limitations. The measurement for the heights were taken using a meter stick which was precise to the ones place, thus the uncertainty was recorded as 0.1 m.To measure the diameter of the craters, a Vernier caliper was used, which allowed for readings that were accurate to the tenths place. So, the uncertainty was recorded as 0.01 cm.

Qualitative Data: The sand was hard to flatten out, so the surface of the sand was often curved. This made the ball roll down the curve created by the sand, when it was dropped, and affected the diameter of the crater. The shape of the craters was hard to distinguish in the sand, and since there were no clear outlines when measuring the diameters, the boundaries had to be estimated. At greater heights, the ball began to bounce off of the sand.Data Calculations:Height (cm)Uncertainty: 0.1

Average Diameter of crater (cm)

Area of crater (cm2)

50.12.14 0.103.60 0.34

100.35.75 0.5726.0 2.6

150.26.61 0.4934.3 2.5

200.17.31 0.2642.0 1.5

First, all the diameters were averaged for each height. To take the average I added all the values for the trials and then divided it by the total number of trials which was 5. To calculate the uncertainty I found the range of highest and lowest value and then divided it by two. So, Average diameter (cm) = = 2.19 cm + 2.21 cm + 2.22 cm + 2.05 cm + 2.02cm 5 = 2.138 cm = 2.14 cmUncertainty = 2.22 2.02 2 = 0.10 So, the average diameter is 2.14 0.10 cm

To find the area of the crater, I used the formula to find the area of a circle:

So first to find the radius I divided the diameter by two.

2.14 0.10 = 1.07 4.67289% cm 2Substituting the radius into the formula I get:

A = (1.07 4.67289%)2 = (1.1449 9.34578%) = 3.5968 9.34578% = 3.60 0.34 cm2These same steps were repeated for the rest of the calculations as well.

Data Presenting:

After calculating the surface area of the crater in relation to each height, I plotted the values on a graph with the independent variable as the height and the dependent variable as the area of the crater, and there is clearly a linear relationship because the best fit line passes through all the error bars. The uncertainty of the gradient is 0.2150 0.015 cm2/cm.

Conclusion:

In this experiment, I measured how the height affects the surface area of the crater that is created when a ball is dropped into the sand. There does seem to be a relationship between the height from which the ball is dropped and the surface area of the crater that is created as a result, because the values that were plotted on the graph demonstrate a clear linear, proportional relationship. There were no outliers. The slope of the graph which was 0.2150 cm2/cm, represents the constant, so for every 1 cm of increase in height, the area of the crater increases by 0.2150 cm2.

Evaluation:The results and the conclusion that an increase in height, will result in an increase the surface area of the crater, is reasonable, because there were multiple trials for each. Only four heights were tested though due to time limitations. The variables that were kept constant were the mass of the ball and the type of sand used. But it was hard to throw it directly perpendicular to the surface which mightve affected the diameter of the crater created. It was also hard to maintain a flat surface, and the ball often rolled down the container of sand or bounced out of it. So the trials had to often be repeated to get reasonable values. When lifting the ball out of the crater, the ball also slightly displaced the sand which couldve increased or decreased the actual diameter of the crater that was created. The graph doesnt intercept the origin which could suggest a systematic error. The range of values used were reasonable, because if the range was too small, there wouldnt be a significant variation in the dependent variable, but if the range was too big, with greater heights, it would be hard to make sure the ball always landed in the container and the ball would also bounce out of the container. The mass of the ball couldve been slightly heavier as well as the material, to avoid bouncing. More trials can be conducted to reduce the occurrence of random errors. To make sure the surface of the sand was flat, a larger container could be used which would allow for easier flattening.

crater design lab

Documents