Penny+Velocity

Our **Lab Title:** Penny Velocity


 * Authors:** Branden, Peter, TJ, Jake


 * Goal:** To determine the terminal velocity of a penny and from that information prove whether it can penetrate a human skull when dropped from the sears tower.


 * Introduction:** It is often said that if a penny were dropped off of the Sears Tower then it could kill a person below through impact. Most people are mistaken in thinking that the penny constantly accelerates downward at 9.8 m/s/s. When means that the penny will be constantly gaining speed and since the Sear tower is extremely high, the penny will be able to gain an enormus amount of speed and thus go through a human skull. If this were the case, we could determine the potential energy with the equation mgh, and then find velocity using the equation Ke= .5mv^2. What most people forget about is the upward force of air resistance. The downward force of gravity causes an increase in speed, but as the speed increases, so does the air resistance. At some point the air resistance is as large as the force of gravity and the penny stays at a constant speed. This is called terminal velocity. We decided to test the theory by determining the terminal velocity of a penny,and testing it on an animal skull. We wanted to first ensure that a penny would reach terminal velocity in the distance between the sears tower's peak and the ground. From there, we analyze the penny's ability to penetrate a skull.


 * Methods:** Our first method was to drop a penny from different heights and find the velocity just before it hit the ground. We initially thought that we could use a force probe to find the speed, but we couldn't get the force probe outside, and we found it hard to drop the penny directly on it. We decided that we would videotape the dropping of the penny and use the logger pro dot diagram analysis to find the speed. And to find if the penny would reach terminal velocity from the height we dropped it from by examining the ditances between the dots on the logger pro dot diagram. Unfortunately the penny was too small, and was moving too fast, for the camera to detect. We needed to find a different way to find the terminal velocity.

We were thinking of all kinds of ways to find the speed. One idea that we had was to use an air supply machine to see at what speed the penny would not fall down the tube, and not be blown upward. We got the penny to hover (which was pretty awesome), but we could not find the speed of the air. As we were thinking of ways to find the speed of the air, we discovered a completely different way to find the terminal velocity of the penny (with a little help from Ms. Berlin aka the Iron Man finisher!!).

Terminal velocity is reached when air resistance and force of gravity are equal. If the penny were traveling horizontally and were attached to a string, then the picture above would represent the forces. When the angle is 45 degrees, the force of gravity is equal to the force of air resistance. If we were able to find the speed at which the penny would fly at an angle of 45 degrees, then we would know the terminal velocity.

For this, we were going to have to have the penny reach that angle and during that time, determine the speed it is moving. We decided that doing that in a car would be best. We glued a penny to a long piece of yarn, went out to the GBS parking lot on a very cold night (but we were ready to sacrifice for physics), and completed the experiment. We held the top of the string out of the window against the top of a protractor and let the end with the penny hang. As the car increased speed, the penny flew at a smaller angle from the horizontal. For the first few trials we were using a very long string, because we thought that it would be easier to see. But because the string was so long, and it was much lighter than the penny, the string was curving making our data very inaccurate. We fixed this problem by shortening the string to just a little bit longer than the length of the protractor. We found that this worked much better in displaying the actual angle of the penny. After many trials we decided that the speed of the car needed to be about 17mph. We did one more run traveling at 17mph the whole way, and it was perfect (as you can see from Branden's screaming in the video). The penny was 45 degrees from the horizontal. Although the speedometers in cars are not completely accurate, we knew that the terminal velocity of a penny is about 17mph. Next we tested whether a penny flying at 17mph would penetrate a skull. Thanks to the biology department we were able to use an animal skull about the size of a (coyote)(see picture below). Although this is not a human skull, we think that is a good object to use in place of one because otherwise we were going to use Peter's head. Also we believed that if anything, the skull would be weaker than a human skull, so if it didn't break we would know that it wouldn't break a human skull. We drove the car 17mph, holding the penny out the window, and had our dare devil (Peter) hold the skull. We drove the car to reach terminal velocity and drove it right by Peter on the same hit as the skull was being held. On our second try we directly hit the skull with the penny. After examining the skull, it was no different from before. There was no damage done. (see videos below) media type="custom" key="8042936"media type="custom" key="8042902"media type="custom" key="8042886"
 * Results:**

The videos above: The first one is a video of one of the trials we had. In this one, we had the longer string and as you can see, it was flawed data because the string was bring curved and so the correct de gree would not be found. So we thought that the solution would be to make the string shorter to not allow for it to curve like it did. And so the result is what you see in the second video. We reached the speed where the string was on the 45 degree mark. The last video is of the penny hitting the skull. The pictures: The first picture is the before picture of the skull The second picture is the after...there is no change.


 * Conclusion:** Our calculated terminal velocity for a penny was 17mph (7.60m/s) and a standard penny weighs 3.1 grams(.0031kg). This would make the maximum Kinetic Energy of a falling penny .0895 J. This is not enough kinetic energy to penetrate a hard skull as our results show. We know that terminal velocity would be reached before the penny reaches the ground because it reuires a relatively small distance (when compared to the sears towers height) to acheive terminal velocity. Although there could be some uncontrolable variables suck as wind, and the angle measurement cannot be exact, we believe that we have busted the myth that if a penny fell off of the Sears Tower it could kill a person below through our amazing knowledge of physics.