DESCRIPTIVE ASTRONOMY 101

Lab #6 - Impact Craters

The purpose of this experiment is to determine the impact velocity of different free falling objects and to observe the resulting impact crater features.

a) large, flat basin

b) one small ball bearing, 0.00353 kg

c) one large ball bearing, 0.01634 kg

d) a meter stick

e) white sand

***All materials listed above are available in the Quad Cities Campus
ILC or the East Campus LRC.

f) Energy Released Graph - click on this link to download ERG. This
file is a Microsoft Word document and can be downloaded as either a PowerPoint
97 version document, PowerPoint 4.0
version document or Word 97 verision
document.

In this experiment the ball bearings will be the free
falling objects which will simulate a meteorite or asteroid impact. Any
object which is allowed to free fall in the Earth's gravitational field
will experience an acceleration (*g*) equal to 9.8 m/s^{2}.
In order to determine the velocity of the ball bearing at the moment of
impact, two equations are needed. The equation,

(1) v_{f} = v_{i}- gt

states that the final velocity, *v _{f}*, is equal to the
initial velocity,

(2) *d = v*_{i}t - 0.5gt^{2}

Equation (2) allows you to calculate the distance, *d*, an object
will fall within the Earth's gravitational field, if the amount of fall
time is known. It should be noted that *d* is negative (-) for objects
moving towards the Earth. In other words a falling object has a negative
displacement. For objects moving away from the Earth, *d* will be
positive (+). Notice that time, *t*, is still a part of equation (2).
By substitution, we can eliminate *t *and can then calculate *v _{f}*
based solely on the distance the object falls.

The initial velocity in these experiments is equal to zero, since the ball bearing is not moving prior to being released. This then simplifies the equations (1) and (2) to:

(3) *v*_{f} = -gt

(4) *d = -0.5gt*^{2}

By manipulation of equation (3) we get

(5) *t = -v*_{f} /g

Substituting equation (5) into equation (4) results in the following:

(6) *d = -0.5g(-v*_{f} /g)^{2}

Simplification of equation (6) results in:

(7) *v*_{f }^{2} = -(2dg)

(8) *v*_{f } = (-2dg)^{0.5}

By using equation (8), if you know the distance the free falling object has moved, you can calculate its impact velocity. Velocity is measured in meters per second.

To calculate the amount of energy released during the impact, the following equation is used:

(9) *E = mv*^{2}

*E* is the energy release in joules (J), *m* is the mass of
the falling object in kilograms and *v* is the impact velocity in
meters per second. For example, if a 10 kg meteorite hit the Earth with
an impact velocity of 10 m/s, the energy released would be:

(10) *E = 10kg(10m/s)*^{2} = 1000J

An impact basin and enough white sand to fill it are available in the ILC. Gently even out the sand in the basin. Be sure not to spill any of the sand. Place the basin on the floor. The ball bearings are available from the ILC desk. This material is may not be available at East Campus. If you set up your own material at home you will need to measure the mass of each ball bearing or marble. The measurements need to be accurate. To do this you will need to use a scientific balance or scale. If one is not available to you, the instructor will be able to measure the mass for you. Contact the instructor for further directions.

Hold the small ball bearing at a height of one meter
above the sand surface in the impact basin. Use the meter stick to insure
that you have the ball bearing at the proper height. Aim the ball bearing
at the center of the basin. Release the ball bearing. Record your observations
on Table 1. The mass of the ball bearing is given in the materials list.
Measure the crater width in **meters**. The crater width is measured
from crater rim to crater rim. Measure this as accurately as possible.

Repeat Impact I using the large ball bearing. Record your data in Table 1.

Repeat Impact I. This time use the small ball bearing, but increase the height to two meters. Record your data in Table 1.

Repeat Impact III using the large ball bearing. Record your data in Table 1.

Table 1 |
|||||
---|---|---|---|---|---|

Impact | Ball Bearing Mass (kg) | Height, d (meters) |
Initial Velocity, v (m/s)_{i} |
Impact Velocity, v (m/s)_{f} |
Crater Width (meters) |

I | |||||

II | |||||

III | |||||

IV |

Carefully remove the ball bearings from the basin. Be careful not to spill any of the sand. Return the bearings to the ILC desk.

Table 2 | |
---|---|

Impact | Energy Released |

I | |

II | |

III | |

IV |

1. Calculate the energy released at the time of impact for each of the impacts. Record your results in Table 2.

2. Compare the results from Impacts I and II. Which crater was larger? Explain why.

3. Compare the results from Impacts I and III. Which crater was larger? Explain why.

4. Compare the results from Impacts II and IV. Do these results differ from questions 2 and 3?

5. Plot the energy released vs. the crater width on the graph below. Be sure to label the scales with the appropriate values. Is there a relationship between the size of the crater and the energy released? If yes, describe this relationship.

6. Examine the image of the Moon shown below. Describe the appearance of the following craters; Van de Graaff, Birkeland, Thomson and the craters labeled A, B and C. Do all of the craters have the same appearance? Explain any differences seen.

7. What is the main erosive process on the surface of the Moon? Remember there is no atmosphere on the Moon.

8. Looking at Craters A, B and C, which crater is the oldest and which is the youngest? How can you tell?

The lunar farside crater Van de Graaff is the large, flat-floored double crater in this south-looking, high-oblique view. Its long dimension is approximately 270 kilometers. Adjoining Van de Graaff on the southeast is the crater Birkeland, which has terraced walls and a central peak. The circular, mare-filled crater on the right horizon is Thomson. (Image courtesy of NASA)

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