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Crater formation

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Introduction

Gracja Kowalska    2IB

CRATER FORMATION

Research question:

Does the height from which the ball is let affect the depth of the crater formed?

Variables:

  • Independent
  1. Height- four different heights (40,60,80,100 cm) were established. At each height both balls were let freely and the depth of the crater formed was measured.
  2. Ball- two balls of different diameters and weights were used in the experiment. Both were used to measure the depth of the crater.
  • Dependent
  1. Depth of crater formed- after each ball was let freely, the crater in the sand was formed. The surface of the sand in the tank was established using a sheet of paper. When the ball formed a crater the ruller was used to measure its depth.
  • Controlled
  1. Ball- each ball has its own characteristic. The bigger ball has a diameter of 4.2 cm and the mass of 97.14 g. The smaller one has a diameter of 2.8 cm and the mass of 79.04 g. only those two ball were used in the experiment.
  2. Volume of the sand in the tank- the same volume of sand was used in each measurement. No sand was taken nor added so as not to interrupt the crater formation.
  3. Initial velocity- as each ball was let freely, the inital velocity was equal to zero

Apparatus:

  • Tank with the sand
  • Two metal balls
  • Measuring tape (2 m) [±0.05 cm]
  • Slide calliper [±0.05 cm]
  • Balance [±0.01 g]

image00.png

Sketch2: The experiment.

Method:

  1. Prepare the equipment and make sure the sand surface is flat.
...read more.

Middle

Having done more measurements than needed, two of them could be omitted. I chose two extreme values (minimal and maximal) to be not included in further calculations. Later on I calculated the average values for the craters using the equation:

image01.png

The uncertainty of the average value of measurement was calculated using equation:

image09.png

Table 2: Average values of measurements of craters.

Height [±0.05 cm]

Big ball

Small ball

Avarage depth [cm]

∆ average depth

Avarage depth [cm]

∆ average depth

40.00

1.37

0.15

1.52

0.10

60.00

1.63

0.25

1.85

0.25

80.00

1.75

0.15

2.02

0.10

100.00

2.10

0.05

2.23

0.05

image10.png

Graph2: Best fit lines for big and small ball.

image11.png

Graph2: The relationship between height of the ball and the depth of crater. Ball first.

image12.png

Graph3: The relationship between height of the ball and the depth of crater. Ball second.

CE

I calculated the gradient for both balls.

First ball:

y=0.0115x + 1.1

x=60

y=1.79

gradient= image13.png=0.029

Later on I calculated the uncertainty. I used data on the graph (the steepest and least steep):

uncertainty=image02.png=image14.png=0.00335

I made the same calculations with second ball:

Second ball:

y=0.01155x + 0.904

x=60

y=1.597

gradient=image15.png=0.026

Later on I calculated the uncertainty. I used data on the graph (the steepest and least steep):

uncertainty=image02.png=image03.png=0.00264

...read more.

Conclusion

- in this experiment only four heights were established. The more heights the better the relationship between the height and the depth of the crater could be shown. Later on, the similarities between the big and small ball could be made.Uneven surface of the sand and the paralax effect- in measuring the depth of the crater only human eye and the side clipper were used. The sand around the crater was flattened (but as it was human eye to decide whether or not it is flat- the paralax effect should be mentioned) and the depth was measured using side clipper. I suggest to use transparent tank with sand and to check from each side whether the sand  has even surface.

All errors noted above could cause the differences between the values of measurements [Table1.]. To reduce the disparity I suggest to make all improvements also listed above and make more measurements at different heights.

Possible further experiments that could be done:

  • Check whether or not the humidity of the sand influences the results
  • Check whether or not the weight of the ball affect the depth of crater formed
  • Measure the dependence between the velocity reached by the ball and the depth of the crater

Bibliography:

  • Giancoli
  • http://www.usoe.k12.ut.us/curr/Science/sciber00/8th/forces/sciber/potkin.htm
  • http://www.classzone.com/books/earth_science/terc/content/investigations/es2506/es2506page07.cfm
  • http://www.lpi.usra.edu/publications/books/CB-954/chapter3.pdf.


[1] http://www.usoe.k12.ut.us/curr/Science/sciber00/8th/forces/sciber/potkin.htm

...read more.

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