The motion of bodies launched through the air has interested people since ancient times. Aristotle (384 - 322 BCE) believed that the “natural” state of massive objects was to seek the center of the Earth. When a stone is launched, an impetus is given to it to disturb it from its natural condition. Gradually, this impetus is forgotten, and the stone falls as it seeks its natural place. Something of this spirit is captured in the seventeenth century drawing shown here of cannonball trajectories from a “practical” treatise on gunnery.
Archimedes of Syracuse (287 - 212 BCE) took a more practical approach. At the request of Hieron, the tyrant of Syracuse and a family friend, Archimedes interrupted his mathematical researches long enough to apply his understanding of levers and pulleys to the construction of remarkable catapults and cranes to defend the city against Roman attack. Archimedes’ catapults lobbed quarter-ton stones at the attacking Roman ships, quickly destroying the clumsy Roman siege engine. Work on the problem during the Middle Ages lay principally in perfecting the range and destructive power of catapults and trebuchets. For some insight into the engineering accomplishments of this period, see the recent article featuring pictures of a piano being lofted over the English countryside in Scientific American (“The Trebuchet,” Paul E. Cheveden, Les Eigenbrod, Vernand Foley, and Werner Soedel, July 1995, pp. 66 - 71).
Then Galileo (1564 - 1642) decided to investigate more carefully. Although the story of his dropping canonballs from the Tower of Pisa is inaccurate, Galileo did perform studies of the acceleration of spherical bodies rolling without slipping down planes. By inclining the planes at a small angle, he was able to slow down the motion enough to obtain quantitative measurements with his crude timing methods. From this research came the understanding that falling bodies (in the absence of air resistance) are uniformly accelerated. Consequently, the trajectory followed by a projectile in the absence of significant air resistance is a parabola.
Upon the foundation Galileo began, Isaac Newton (1642 - 1727) developed his mechanics, which allows one to predict the motion of bodies from the forces to which they are subject. In this experiment you will compare the motion of projectiles to the predictions of Newtonian theory.
Provided that air resistance is negligible, the theory of projectile motion is straightforward. You should be able to work it out for yourself, but you may consult Physics for Scientists and Engineers by Serway if need be. When objects move very fast or when they are very light, the drag force on the object may be comparable to or greater than gravity. In such cases, the range of a projectile is reduced and the trajectory (the path followed by the projectile) becomes more complicated. Obtaining a functional expression for the trajectory may be difficult or impossible. However, it is not too difficult to integrate the equations of motion numerically on a computer to investigate how different relationships between projectile speed and the drag force produce different trajectories. Excel, Maple, Mathematica, and DE Architect are possible platforms to use. We'll be happy to get you going with one of them; just ask.
Load the yellow plastic projectile balls by placing one in the barrel of
the launcher and compressing the spring with the black ramrod to the
desired click setting (there are three).
Pasco claims that the launchers are “repeatable,” but
this is of course a matter of degree. Your first job should be to
investigate how repeatable the launcher is at a particular setting.
Be very careful not to launch projectiles at other people.
Do not compress the styrofoam balls this way or you will destroy them!
Instead, use the ramrod to compress the launcher’s spring
slowly and carefully to the desired setting, then gently insert the
styrofoam ball.
The first experiment you should conduct is a trajectory experiment.
After you have made a forward prediction as described above, you may decide to attempt a fit to your data. With this approach, you assume that the trajectory has a certain functional form, in which the precise curve depends on one or more parameters (e.g., launch angle, launch speed, ...). You make guesses for those parameters and you let the computer find the set of parameters that agrees best with the data. You then attempt to reconcile the determined parameters, and their uncertainties, with the observations of the initial parameters that you made directly. See Fitting Data for more information on performing such a fit.
Many other experiments are possible with the available apparatus. Some sample experimental objectives are:
Once you have performed some of these, and have learned how the apparatus behaves, you might investigate the influence of air resistance on the motion of the light styrofoam balls. See the warnings and pitfalls below for care and handling of the styrofoam balls.
Are you keen to compete for the fabulous prize of the sincere and joyous admiration of your colleagues? Do you have projectile motion all figured out? Then take the Trash Can Challenge. I will place a target on the floor along the line of site of your launcher, set to the maximum velocity setting. You and your partner may make all the measurements you need to pinpoint the landing site of your projectile. You may then compute the desired launch angle, load the projectile, cross your fingers, and take one pull of the launcher arm. Full admiration for a swish; partial admiration for a rim shot!
There are a couple of ways to measure the launch speed of the projectile using the Timers and Photogates. Using a single photogate you can measure the transit time of the ball through the photogate beam. Or, using a pair of photogates you can start the clock when the ball breaks the first photogate beam and stop it when it breaks the second beam. Which way would be more accurate?
The time-of-flight pads send a digital pulse back to the timer when they are struck by a hard object. You may have to experiment a bit with them to be sure they are working for the impact velocity of your experiment. Noisy collisions seem to work better than quiet ones, and collisions in the middle work better than those at the edges of the plate.
You will summarize your findings in this experiment in an informal oral report. See the Reports page for further information.
Updated 9/11/00 by Peter N. Saeta .