Activity from the University of Michigan (March 2002)

Objective: To determine the guidelines affecting crater formation.

Procedure:

1. The size of a crater is related to the amount of energy the asteroid posses as it strikes the ground. The more energy it posses, the larger the crater's diameter. The relationship is not linear but rather a power law.

Where:

D is the crater's diameter
k is an unknown constant
E is the total energy of the asteroid (kinetic and potential)
n is some unknown power that describes how the diameter will depend on the amount of energy the asteroid holds.

2. First drop steel ball bearings at different heights. By doing so, the amount of energy can be determined by using the conservation of energy law.

Where for E=Mgh
E is the energy
M or m is the mass of the steel ball bearing
g is the gravitational acceleration of 9.8N/kg
h is the height at which the steel ball is dropped

3. Record the crater's diameter and the steel ball bearing's height in the following table:

Chose different vertical heights and record your observation in the table.

3. Calculate the mass of the steel ball bearing by:
a) obtaining its diameter
b) Find its volume using sphere volume equation: V=4/3(3.14)(radius)³
c) Find mass using density formula (density=mass/volume) Note: Density of the steel ball bearing is approx. 8000kg/m³

4. Now that the steel ball bearing's mass is obtained, calculate the E=mgh

5. Your goal is to find the value of n since it is a constant.

Plotting a diameter vs. energy graph would make finding n difficult, since the graph would be a curve.

Instead, a graph of log(diameter) vs log(energy) is required. By doing so, a straight line is obtained (If not, draw the line of "best fit"). Therefore n=slope of the line.

6. k is another unknown constant. In the D=kEⁿ equation, we know the D, E and n value, thus plugging in the data from the observation table allows us to solve for k.