- Level: International Baccalaureate
- Subject: Physics
- Word count: 1608
How does the mass of a spherical object and the height from which it is dropped into sand affect the width and depth of the crater formed?
Extracts from this document...
Introduction
000345-056
An Investigation of the Formation of Craters
Question:
How does the mass of a spherical object and the height from which it is dropped into sand affect the width and depth of the crater formed?
Introduction:
Background Information:
The formation of a crater is caused by the transfer of kinetic energy from the dropping object to potential energy present in the possible crater. In order to determine the relationship between the mass of the object, the height from which it is dropped from, and the size of the crater the relationship between these two energies must be determined.
The potential energy is equivalent to lifting the crater volume out of the substance and depositing it nearby. This energy can be represented by the equation where m is mass, and
is the depth of the crater. The mass of the crater is equal to Vd, where d is the density of the crater and V is volume. The crater volume can be defined by the equation for the volume of a spherical cap (a spherical cap is a portion of a sphere which is cut off horizontally). Thus,
where a is the radius of the cap and h is the depth. Put into terms of the diameter s, volume can be represented as
. Plugging in this equation, the potential energy present in the crater is represented by
.
Middle
.165
.0075
.0430
5.67
4.25
2
.0193
.065
.0075
.0380
4.47
3.36
.065
.0075
.0390
4.70
3.53
.115
.0080
.0440
6.35
5.08
.115
.0085
.0430
6.49
5.53
.165
.0085
.0480
8.01
6.81
.165
.0090
.0470
8.19
7.37
3
.0284
.065
.0100
.0390
6.50
6.50
.065
.0100
.0390
6.50
6.50
.115
.0105
.0450
8.96
9.40
.115
.0110
.0430
8.68
9.55
.165
.0110
.0465
10.0
11.0
.165
.0110
.0450
9.44
10.39
4
.0053
.065
.0070
.0286
0.243
1.70
.065
.0065
.0240
1.61
1.049138
.115
.0075
.0310
3.05
2.288454
.115
.0080
.0280
2.73
2.184873
.165
.0100
.0340
5.06
5.0632
.165
.0090
.0300
3.56
3.206309
*The height of drop is not 10, 15 or 20 cm as described in the procedure because the depth of the sand in the container was taken into consideration.
**The volume was generated from the formula . The units are cm for purposes of readability.
Columns 6 and 7 are processed data, generated from the raw measurements of crater depth and width.
Graphs:
The graphs which compared volume crater depth to the height of the drop were generated using data from each individual object, in order to ensure that mass was kept constant. The graphs which compared volume
Conclusion

If the experiment was repeated, then each of these weaknesses or limitations could be addressed. The inconsistency associated with using my hand could be eliminated by using a clamping system to drop each ball. This would eliminate much of the induced error, as the clamp could be set at a given height without any unsteadiness or inaccuracy. The problems associated with measuring crater depth could be resolved if a set of steel balls of differing mass were used. A magnet could then be used to extract each ball, rather than lifting each one out with my fingers. This would allow for easier and gentler extraction, again helping to eliminate inconsistency. Also, more trials could be conducted, helping the experiment to achieve a more accurate representation of the data. If these changes were implemented then the experiment would become more accurate.
This student written piece of work is one of many that can be found in our International Baccalaureate Physics section.
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