## Problems 1

### Understanding the Past & Present, Predicting the Future

Numerous students of science have brought chuckles to their teachers by saying: I understand the science.  I just can't do the problems.

Scientists attempt to understand the world.  They determine if that understanding is valid or not by using that understanding to make PREDICTIONS and then checking to determine it the predictions are correct.  Precise mathematical quantities are considered better predictions than vague word descriptions.  Science can't actually PROVE their understanding is TRUE.  The best scientists can do is to check predictions.  So solving problems and making predictions are essential to establish the VALIDITY of the scientific theories.  This checking against reality is the part of science that distinguishes it from philosophy.  Beyond just being a part of science, checking the predictions is the very aspect of science that makes science so valuable to civilization.  Without doing the problems (i.e., making and checking predictions) you really haven't achieved the skills that makes doing science so important.

The following problems are intended to focus your thinking, help you understand our world, and to make predictions that are verifiable.  Keep your thoughts and predictions for these problems in your journal.  Include sufficient information so you can later refer back to your journal to refresh your thoughts and memories.

1. Ponder the most significant events of your life.  Which senses were involved in what you know about those events?  Are there any significant memories of your life that don't involve any of your senses?
2. One way to imagine a volume is to consider it filled with cubic blocks.  In science it often helps to draw diagrams to help visualize the situation being considered.  Consider using small blocks 1 cm on an edge to construct larger shapes.
1. How many little building cubes would be needed to build a larger cube 3 cm on each edge.
2. How many cubes would be needed to fill a rectangular box 30 cm long, 15 cm wide, and 10 cm tall.
3. How many cubes would be needed to fill a rectangular box 30 cm long, 15 cm wide, but only 9.2 cm tall.  Presume we can use partial portions of blocks as needed.
3. Consider a graduated Imhoff Cone used by environmental scientists to measure the amount of sediment in water.  Why are the divisions NOT evenly spaced?  What would be the advantage of using a graduated cone rather than a graduated cylinder?
4. Scales abound on measuring devices of all kinds.  It is crucial to become skilled at gaining all the knowledge possible from a scale while not exaggerating what is knowable.  Estimate the positions of the arrows below as accurately as you can.
It is usually possible to determine one more digit than the available scale marks.  Using fewer digits discards available information.  Using additional digits is little more than bragging, providing no additional information of significance, but obscuring what is justifiably known.
5. Three people measure the same video scene length as 6.7 seconds, 6.6 seconds, and 7.1 seconds.  What single value would best represent the scene length?
6. A fourth person measures the video scene in the previous problem and reports it is about 7 seconds long.  Does this measurement add significant information?  Now what would be the best single value for the scene length?
7. One single measurement of the volume of soda in a can is 355 mL.  Independent measurements of ten cans of soda give three measures of 354 mL, four measures of 355 mL and three measures of 356 mL.  Is there any significant difference in the second set of measurements compared to the single measurement?  How could the value of the average of the set indicated added precision?  Generally the number of significant figures may increase during addition, decrease during subtraction, and have the precision of the least significant value after multiplication or division.
8. What is the volume of liquid in the graduated cylinder to the right?
9. If a metric bolt is added to this graduated cylinder causing the meniscus to rise to 9.5 mL, what must be the volume of the metal in the bolt?
10. Consider constructing a stair stoop out of cubic cement blocks 8 inches on a side.  If the stoop is to be solid, 6 steps high and 12 blocks wide, how many blocks will be needed?  (Don't forget the value of a drawing.)

If you need credit for this study, use complete sentences so that your thoughts and predictions are not just unintelligible words and numbers, but make sense to whomever is the reader.

You may have found the kind of question asked was a bit different from what you would expect for predictions.  Note that to scientists a prediction involves more than a simple for cast about the future.  Scientists are concerned as much about HOW they know something, how ACCURATELY they know, and how PRECISELY.

created 12/7/2002
revised 11/20/2003
by D Trapp