Uncorking Work Problems

David Drymiller                Marie Sklodowska Curie Metro H.S.
                               4959 S. Archer Ave.
                               Chicago IL 60632
                               (312) 535-2120

Objectives:

     To solve problems about work, using the formula work = rate x time.
     To solve equations containing rational expressions.
     To strengthen basic skills learned in Algebra.  

Materials Needed:

     A large clear plastic bottle with 3 different sized holes drilled
         in the bottom
     3 corks to fill the holes
     A plastic storage crate
     A plastic container that fits into the storage crate
     A plastic funnel
     Stopwatches
     A pliers
     Rags to wipe up spills
     Saran wrap
     food coloring
     colored strips of paper

Strategy:
      
     The students perform the following demonstration for their classmates
under the direction of the classroom teacher.  No prior knowledge of the 
activity is needed by the students.

     Have the students fill the bottle with water and place it on the crate. 
Place the container in the crate to catch the water when the bottle is 
drained.  Place one colored strip of paper near the top of the bottle, but 
below the water level.  The other strip should be placed on the bottle near,
but not exactly at, the bottom.  Add food coloring to the water to make the
event easier to see.  Place a piece of Saran wrap on the top of the bottle 
to form a seal.  Using the pliers, remove the smallest cork.  Remove the
Saran wrap and start the stopwatches when the water level reaches the top
of the first colored strip.  Stop the stopwatches when the water level reaches
the top of the second colored strip.  Recork and refill the bottle.  Record
the time it takes to empty the bottle using the smallest hole.  (I got 127
seconds.) 
     Again drain the bottle as before but pull the middle sized cork and record 
the results.  (I got 65 seconds.)
     Now ask the question, "How long does it take to drain the bottle if both
the smallest and middle sized corks are pulled?"



     The formula, Work = Rate x Time is introduced and our discussion leads to 
the following chart, equation and prediction for the time.

                             Rate    x     Time    =   Work
           Smallest Hole     1/127         127          1
           Middle Size       1/65           65          1
           Both Together     1/t            t           1

                1/127  +   1/65  =   1/t
                65t    +   127t  =  65(127)
                           270t  =  65(127)
                              t  =  43 sec.

     Again drain the bottle by pulling both the small and middle sized corks
and record the result.  (I got 43 seconds---Perfection!)

     A variation of the above can be obtained by first draining the bottle by 
uncorking the middle and largest holes and predicting the time needed to drain 
the bottle using just the largest hole.  Here some error might appear in the 
timing of the event.