• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

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 image00.png where m is mass, and image01.png 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,image09.png 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 image16.png.  Plugging in this equation, the potential energy present in the crater is represented byimage20.png.

...read more.

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 image04.png. 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 image03.png 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 image03.png

...read more.

Conclusion

image18.png.1 cm. The experiment was also weaker because in order to measure crater depth the object had to be carefully removed first. This inherently weakened the crater, sometimes causing the depth to be slightly changed from what it had initially been.  The experiment was limited by the fact that only two trials were conducted for each height for a respective mass. Three trials would have been better, as a more accurate average could be defined than if only two trials were conducted. This would also help to eliminate outliers better, because there would be two other data points to average with, versus only one.

 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.  

...read more.

This student written piece of work is one of many that can be found in our International Baccalaureate Physics section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related International Baccalaureate Physics essays

  1. Marked by a teacher

    Investigating the factors related to the crater formed by a falling object.

    3 star(s)

    In this case, increase the height by 10 centimeters. * Use five different drop heights to make the relationship more clear: 10 cm, 20 cm, 30 cm, 40 cm and 50 cm. * The type of surface will be controlled by using the same sand for all the different drop heights and by keeping the surface of the sand parallel to the ground.

  2. How does the mass of the paper helicopter affect the drop time of the ...

    had the highest average drop time of(63 � .02s) while the paper helicopter with a mass of 3.8g (�.1g) had the lowest average drop time of (.40 � .06s). This is due to Newton's first and second law. Newton's laws states that an object will accelerate if the forces acting

  1. In this extended essay, I will be investigating projectile motion via studying the movement ...

    Mark a point onto a paper vertically below the muzzle of the spring gun. This will be the starting point of the projectile. 7. Adjust distance height y between the bottom of metal ball and the table to 10cm using the meter rule as reference.

  2. Energy density experiment - Aim: To determine the energy density of ethanol

    Evaluation: The results conducted from this experiment is judged to be unreliable as heat was able to easily escape mainly because not 100% of the energy was transferred to the water from burning the ethanol as it is most likely that other objects absorbed the energy or it was lost to the atmosphere.

  1. The Affect of Mass on the Time It Takes an Object To Fall

    experiment we set up our materials as illustrated in the previous diagram, with a measured piece of PVC pipe of 184cm in length taped to a table. We then measured the mass of the paper helicopter with no added mass, which was 1.1g, and also the mass of each of the nine paperclips, all of which were 0.4g each.

  2. Physics-investigate the relationship of temperature and the height of the bounce of a squash ...

    which a squash ball bounces and the temperature of the squash ball is directly proportional. As the temperature increases so does the height at which the ball bounces, this proves that my hypothesis is correct. The ball never bounced back up to the same height it was dropped, because it

  1. Physics Lab: Images formed by a plane mirror

    is located at infinity, one can project its image on a screen held infinity units away.

  2. How does the sinkage depth of a tyre affect its rolling resistance ?

    In soft surfaces such as sand and loose surface the tire has to do more work as compared to hard surfaces such as asphalt because the tire sinks deeper in the surface and in order to get over the interlocking force between tire and sand more work is done as compared.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work