2. Pick up the 3/8" steel sphere. Drop the sphere into the sand, keeping track of the height from which you are dropping it, and then carefully measure the size of the crater. The important property of the resulting crater which we will investigate is its diameter, measured from rim peak to rim peak. How big is the crater?

crater diameter ____________ cm

3. If we change the shape but not the mass of the projectile, what do you think will happen to the crater?

We will experiment with this possibility in a few moments.

4. From how high did you drop the steel sphere?

height of drop ____________ cm

6. There is a second set of three identical-mass steel objects with the same shapes as the set you just used, but their mass is different from the first set. Repeat the above procedure for these objects and record the results:

What is more important in determining the diameter—the mass or the shape? Does the shape have any influence at all?

7. Now drop two spheres which have the same mass but different densities-the 13/32" steel sphere and the marble. Record the results:

Which is more important, the mass or the density?

9. You have been given (Graph #1) a piece of log-log graph paper. Let the numbers increasing to the right across the bottom of the sheet represent the mass. Label that axis "Projectile mass." Let the crater diameter be represented by the numbers increasing upward on the sheet. Label that axis "Crater diameter." Plot the six points tabulated in (8). Then measure the slope of the line to determine the exponent a.

where a = ____________.

10. Choose a steel ball and drop it from the following five heights. Use the stepladder for the last. Record your results on the following chart.

Plot the crater diameter versus height on a new sheet of log-log graph paper and, as before, measure the slope. Thus

where c = _____________

11. For this result to be consistent, c had better be independent of the mass chosen. Check this by repeating the measurements as done in (10) using a steel ball of different mass.

Plot the new points on the same piece of graph paper as you used for (10). Is the slope the same, within your estimate of the uncertainties?

12. You can combine the results for the exponents a and c from (8) and (10) to give:

where a = _____________

and c = _______________.

If a and c are equal, the crater diameter depends on the kinetic energy. If c = ½ a, the crater diameter depends on the momentum of the impacting object. Which conclusion do your results support?

13. The uncertainty can be estimated from the deviation of your plotted points from straight lines. How uncertain are the values of a and c?

Uncertainty assessment, based on scatter in results:

for a _____________________

for c _____________________

Do you think that the uncertainties are small enough so that a conclusion is warranted?

What are the major causes of uncertainty?

14. Now assume that you concluded that the kinetic energy is the relevant quantity. Thus

crater diameter = constant • (1/2 mV²)^d

where d is the exponent we are now after. Its value should be clear by now. Go back to a representative crater from your data tables and use the results to calculate the constant (whose units are cm per erg^d).

constant = __________________________

d = __________________________

15. The Barringer crater is a large meteorite crater in northern Arizona. You may remember seeing this crater in the movie "Starman." The crater’s diameter is 1.24 km. The crater resulted from what was probably the most recent large meteorite to hit the Earth, some 25,000 years ago. The impact probably occurred with a velocity of about 15 km/sec, a typical value for meteorite impacts. Based on the analysis of your experiments in this lab, and on the extremely bold assumption that your relationships can be extrapolated to the event that caused the Barringer crater to form, what was the kinetic energy of the impact?

kinetic energy = ____________________ ergs

What was the mass of the meteorite (before it was destroyed by the impact!)?

mass = ____________________ grams

Assume that the meteorite was an iron sphere with a density of 8 grams per cubic centimeter. What was its diameter?

diameter of meteorite = ____________________ cm.