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1 0 	1 02 	1 03 	1 04 1 05 	1 06 	1 07 	1 08 
Crater Size (em) 

A meteoroid hitting the earth has a lot more energy than the ball bearing you just used, and it causes an explosion upon impact. There is still a relationship between the kinetic energy and crater size, however. A meteoroid hitting the earth can be moving at speeds up to 100 km/s. At these high speeds, the energy on impact is converted to other types of energy such as thermal, acoustic, and radiative energy. (There is not enough energy in our lab experiment to produce these effects.) As a large meteoroid hits the ground, it creates a shock wave in the rock and the rock bends under the pressure. 
Consider the famous meteor crater found near Flagstaff Arizona. It is 1.4 km across and 200 meters deep. Astronomers and geologists believe that about 1023 ergs was needed to produce this crater. We can make our own estimate of the energy needed to make the meteor crater in Arizona using our laboratory results. To do this we need to extrapolate the relationship we found in our lab experiment all the way up to a crater 1.4 km in size. The graph paper used to plot your lab data does not have enough range to plot 1.4 km, so we will use the graph in Figure 2 that extends to much higher energies and much larger crater sizes. 
On your graph on page 123, notice where your best fit line crosses the outside edges of the grid lines on the graph. Transfer these intercept points onto the graph on page 126. Connect them with a line. This is your best fit line from your ball bearing experiment transferred to a graph that covers a much larger range of energy and size. 
1. Now, extend your line all the way up and to the right on the graph to higher energies and larger crater sizes. Be sure the slope is the same as it was on the graph of your lab data! 
3.How does this compare with the energy geologists computed? (How may times more or less). 
4. What reasons might there be for any difference (ignoring problems in transferring your best fit line)? 
PRINT NAMES 	_ 
SIGNATURES 	_ 

3. Are the data points tight to the line (a strong correlation), show some dispersion about the line, or show a lot of dispersion about the line (a weak correlation).? 
4. Are there any points that do not follow the correlation? Can you think of a reason why? 
Once a correlation has been found you should test to see if it is valid outside the test region. One way to do this is through extrapolation (use our data to predict a value beyond the points plotted). Extend your line past your last data point to some value. See what the predicted value is and run the experiment to test the prediction. 
1. Calculate the energy for one of your ball bearings dropped from a height of 2.0 meters. Using your graph and your best fit line, predict the crater size for this case. SHOW YOUR WORK. 
Now check. Drop the ball bearing from 2.0 meters. What was the result for the diameter? 

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	2 	4 6 1 0 	20 	40 60 100 
Crater Diameter (em) 

Table 1: Crater Sizes at Different Heights (watch your significant figures and use scientific notation) 

Trial 	Ball Bearing 	Height (cm) 	Potential Energy 	Crater Diameter 	
	Mass 		(ergs) 	(cm) 	
1 					
2 					
3 					
4 					
5 					
6 					
7 					
8 					
9 					
Two numeric quantities are said to be correlated with one another if the value of one can be estimated from the value of the other. For example, the height and weight of people are correlated; tall people tend to weigh more than short people. It is extremely rare to find a person 6'6" tall who weights only 50 Ibs. Likewise, it would be unlikely to find a person 4' 6" who weighs 400 Ibs. 
One way to show a correlation is by graphing one quantity vs. another. If a pattern emerges from the data, suggesting one value can be used to predict the other, there exists a correlation. 
Graph your results on the Log-Log graph paper provided and draw a best fit line to your data points. 

 [ PE = m g h 
in units of ergs, where m is the mass of the object (in grams), h is the height (in centimeters), and g is the gravitational constant 981 cm/s2• 
This energy is then converted into kinetic energy as the object falls to the ground. Kinetic energy is the energy associated with motion and is expressed as: 
I KE = %xmv2 
(units are ergs), where m is the mass as before and v is the velocity of our object in cm/s. As the object falls it picks up speed and this implies it has more energy. Conservation of energy tell us that energy can not be created or destroyed so where did this energy come from? It comes from the gravitational potential energy it loses as it falls closer to the ground. It is the kinetic energy that creates the crater. 
Meteoroids out in space do not get their energy just from falling to the ground. They are already traveling at very high speeds as they speed around the solar system. We are using gravity to give our ball bearing 'meteoroids' kinetic energy because it is simple, convenient, and some of the energy of real meteoroids does come from falling down onto the Earth. 
1. Using the meter stick, ruler, a ball bearing, scale, and sand box, determine energy and crater size resulting from dropping a ball bearing from several different heights. Remember to keep track of the units carefully. Use the scale to get the mass of the ball bearing. The heights you choose should be between 12cm and 1 meter. 

Ball Bearing Size 	Diameter (mm) 	Mass (grams) 	
1 			
2 			
3