What factors play a role in the formation of a crater? In this lab, you will actually drop a selection of projectiles into trays of sand in order to investigate what properties of the projectile affect the size and shape of the resulting crater. Right away we can identify a number of properties of the projectile that might affect the crater size and shape:

a) the shape of the impacting object

b) its mass

c) its density

d) the velocity of the projectile relative to the target when the impact occurs.

Obviously, the formation of craters will also depend on the characteristics of the surface that is struck (your fist makes a bigger dent in a pillow than it would in a brick wall). Some of the properties of the target that might be important include:

a) the strength of its surface (resistance to deformation)

b) the density of its surface

c) its gravity, which binds the surface to itself

d) the melting properties of the surface.

For today, we will only use the trays of sand as targets and so we will only investigate the first list of possible factors, those related to the projectile. But in thinking about planets, keep in mind the other list which in reality, plays an important role in the formation of craters in the solar system.

The height of the drop will be an important parameter to record in making these measurements. Notice that as you held the sphere in your hand ready to drop, its velocity was 0; however, it certainly had some non-negligible velocity relative to the sand when the impact occurred. This change in the sphere’s velocity, once you released it, is its acceleration. Acceleration is caused by gravity. The amount of acceleration depends on the height of the drop.

Two of the important parameters in cratering are the mass (m) and velocity (V) of the projectile. We know these variables are important, but it is not quite obvious how each of them affects the resulting crater. There are two physically meaningful quantities that we can think of that combine mass and velocity:

a) the momentum - mV

and

b) the kinetic energy - ½ mV².

The momentum measures the tendency that a moving body has to keep moving. It is a measure of the impulse, or integrated energy. Momentum is the important quantity that determines the change of path of a hockey player when he is hit by another hockey player. The kinetic energy, on the other hand, measures the work available to dig the crater.

You will address the question of how mass and velocity affect cratering by determining the way in which the crater diameter depends on both m and V. If all goes well, you should be able to distinguish whether the combined dependence goes as mV or ½ mV².

The objects available for experimentation have their properties labeled in cgs units (density in grams per cubic centimeter, for example). You should use centimeters, grams, and seconds as units in all of your calculations and plots. When you form a crater, record all properties in the tables provided so that your T.A. will know exactly what you have done.

You can quantitatively express the dependence of the diameter on the mass by determining the power to which the mass must be raised in order to produce a number proportional to the crater diameter, that is. . .

Similarly, we can see how the crater diameter depends on the impact velocity of the projectile, and we can determine the exponent b of this dependence

Since we cannot measure the impact velocity V, we need to use the fact that it depends on the height h from which the object was dropped.

V² = 2 g h

In this equation, g is the acceleration of gravity (980 cm/sec² at the surface of the Earth). Since we care only about the power of the dependence, we can ignore the constant g, remembering that it is constant as long as we keep our apparatus.

By determining the exponent c of the dependence of crater diameter on height

we can translate c directly into the power of V² on which the crater diameter depends.