Dropping stuff (in the spirit of Galileo and Letterman)

Physics of the Mundane

Adam Johnston

Special note: After a brief meeting in the warmth of the indoors, we will disperse outside.  Hope you brought a coat!

 

We know that Astuff@ falls Adown,@[1]  but we generally don=t get the opportunity to analyze the characteristics of such downward motion.  Usually, the problem is simply a matter of not having enough time to analyze the motion, since most dropped distances are only a few feet. 

 

What we need is a tall platform, say six stories high, from which to drop objects; and a wide open space from which to observe and analyze the motion.  Fortunately, we have both at our disposal.  From the sixth floor of the science lab building, the emergency exit leads immediately to the roof B an odd evacuation procedure, but a useful feature for our experiment.  The roof overlooks an open lawn at the south side of the building.  From this lawn, observers can analyze angles to measure the height of the building, time the journey of the falling object and analyze the motion overall.

 

Objectives:

1.      Determine whether all objects fall at equal rates (as claimed by Galileo) or at different rates (as claimed by Aristotle).

2.      Determine the acceleration of gravity.  As derived in class, this acceleration should be equal to:

where h is the height from which the object falls, and t is the time it takes for the object to have fallen this distance.  (Often we write agravity as just g.)  Note that if you measure distance in meters and time in seconds, your units for the acceleration of gravity will be meters/second/second, or m/s2.

 

3.      Graph the motion of the object.  Your graph should show distance on the vertical axis and time on the horizontal axis.  Explain what the graph tells you regarding the motion of various objects.  (For example, you might compare the falling motion of a tennis ball to that of a ping-pong ball.)

 

Equipment:

C     Stuff to drop from roof:  tennis balls, koosh balls, plastic bottles, parachuting rocket, miscellaneous balls and whatever else we can find.

C     High-tech angle measuring devices and tape measures.

C     Protractors and rulers.

C     Stop watches.

Suggestions:

C     To meet the above objectives, the class will need to work together.  Some people will need to time how long it takes for the object to fall the complete height, while an army of others should be timing how long it takes for the object to fall to different fractions of the total height.  (So, for example, Eratosthenes might be timing from the roof to the sixth story, Aristarchus might be timing from the roof to the fifth story, and so on . . .  We will have to share and compare data later.)  Still others will need to make sure that no innocent passers-by become targets of the freefalling objects.  And, of course, someone needs to drop the stuff from the roof.

C     You will need to measure the height of the building.  We can do this several different ways.  One way will be to use your high-tech angle measuring equipment and the tape measures, as discussed briefly in class.  Create a triangle that can be drawn to a known scale (you should use a ruler and a protractor for this) and measure the height of the building directly from your scale drawing.  This could also be your method for measuring the distance to the sixth floor, fifth floor, etc.


 

[1]Exactly what Astuff@ is and which direction is Adown@ are issues we won=t deal with quite yet.