Impact Craters are the craters formed when meteorites strike the surface of a rocky planet or moon. In the late stages of planet formation, cratering played a major role in determining the final appearance of planetary surfaces. On earth, weathering and tectonic processes continually recycle the crust and have obliterated most impact craters. This is not true most places in the solar system, where cratering is probably the single most important process in determining the appearance of a surface.
Impact craters vary in size from microscopic to hundreds of kilometers across, and valuable insights into crater formation dynamics have come from laboratory experiments- firing small projectiles into various surfaces at very high velocities. We cannot approach the energies of these collisions with our simple equipment, but many fundamental principles of cratering can still be seen.
The system consists of a box of fine sand and a slingshot which can be used to fire steel spheres ("ball bearings") into the sand. You also have rulers for "raking" the sand smooth when required and for measuring the "stretch" of the slingshot, and protractors for measuring the angle of impact in cases when you are not shooting straight down. There are also "scoops" to help you recover the projectiles from the sand. Note that the slingshot is potentially hazardous! Do not point it horizontally at any time! Point it only into the sandbox! Be sure that no breakable objects, lab partners, or other students are anywhere near the line of fire! Use caution and good sense.
Basic Crater Morphology
Smooth the sand surface well with a straight edge. Use the slingshot to fire a ball bearing vertically into the sand. Observe the crater that you made. Draw two pictures of your crater, roughly to scale, one looking down from above (map view) and one as seen from ground level (cross-sectional view). Label the drawings with the words crater, rim, and ejecta. Measure the sizes of these things and add the dimensions to your drawings- note that measuring the depth can be difficult.
Energy and Crater Formation
In general, impact craters are much larger than the projectiles which made them. One way to interpret this is that the projectile dumps a lot of energy into the surface and then the crater is formed by an explosive process, rather than thinking that the projectile simply pushes the surface material away. A basic study here is to relate projectile energy to crater size.
When you pull the slingshot back, you store (potential) energy in the rubber bands. When the slingshot is released, this stored energy is converted into the kinetic energy of the projectile as it blasts toward the surface:
Kinetic Energy of Projectile = Stored Energy in Slingshot = (1/2)*k*x2
where k is called the spring constant for the slingshot (measured by stretching the slingshot with a fish scale) and x is the distance the slingshot has been stretched from its "limp" state. The spring constants have been measured for you and are on the blackboard. As the projectile is fired down into the sand, it is also accelerated by gravity. It loses gravitational potential energy and exchanges it for additional kinetic energy. The additional energy is m*g*h, where m is the mass of the projectile and h is the height the projectile falls between when the slingshot is released and when the projectile hits the sand. This additional energy is negligible.
Launch your projectile four times using a different extension each time. Create a table that has a line for each trial and columns for Slingshot Extension, Kinetic Energy, Crater Diameter, and (Crater Diameter)3. The last column should be there because the volume of the crater might be nearly proportional to the cube of the diameter- so you can test the dependence of the diameter and the volume on the impact energy.
On a single graph, plot the crater diameter and the diameter3 as functions of the energy. Draw lines if it seems appropriate to do so. Is the crater diameter or volume proportional to the energy?
Effect of Angle of Incidence
Most craters on the Moon are nearly circular, and yet it would seem likely that meteorites hit at all angles, with very few of them perfectly vertical. Explore this phenomenon by making craters with various angles of incidence.
Use a protractor to guide the slingshot and produce a crater with the projectile launched about 65 degrees to the surface. Sketch the map and cross-sectional views. Repeat this with the projectile launched about 40 degrees to the surface. Be extremely careful at these shallow angles that the projectile does not hit the wood box and ricochet into a person or a window- check that your "range" is clear at all times!
Write a few words about what you can conclude about the relationship between a projectile's angle of incidence and the resulting crater's shape and ejecta distribution.