Challenge One

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HOW MANY BOOKS CAN A SHEET OF PAPER HOLD WHEN THE PAPER IS NOT FLAT ON THE TABLE?

stack of books Individual students or preferably groups of students are given one sheet of copy paper and that paper must support at minimum several small books.  NO PART OF ANY OF THE BOOKS USED FOR TESTING THE STRENGTH OF THE PAPER STRUCTURE CAN TOUCH THE TABLE.  If students request some tape, they can have only 2 cm. (almost an inch) of tape. They can not have any other material such as string, wire, elastic bands, etc. to hold their structure together.  When all groups have made their structure, test each structure one at a time.  Use one kind of small book so each trial is equal.  Record the number of books for each person or group to determine the paper structure that worked best.  Ask students to analyze all the structures and determine why that particular paper structure worked best.

ANSWERS:

A. Carefully fold one sheet of copy paper in half lengthwise and be sure the corners meet perfectly.  Then fold that folded paper lengthwise in half the same way.  Bend this paper so you make a paper cylinder or tube that is approximately 5 cm (2 inches) high and 2.5-4 cm (1-1.5 inches) in diameter.  Tape it. PUT ONE BOOK ON THE TUBE AT A TIME CAREFULLY AND BE SURE EACH BOOK IS GOING TO BE BALANCED IN THE PILE BEFORE YOU REMOVE YOU HAND.  A hollow tube is very strong.  Bones are hollow tubes and that shape is one of the reasons for their unusual strength.

B. Fold the paper as in number one but bend the final folded paper into a square-shaped object instead of a cylinder or tube.  Tape it.  It is so similar to a tube that it gives it some strength.

C. Crumble the paper and flatten it.  Some students will use this solution and it should be accepted as a correct answer to the original question.  However, it has nothing to do with long bone structure. 
 


CHALLENGE #2:

CAN YOU COLLAPSE OTHER TUBES?

A.  CAN YOU COLLAPSE A TUBE FROM A ROLL OF TOILET PAPER?

When you are doing this experiment you hold your two hands in front of your chest.  The palms of your hands should be parallel to each other.  The palms of the hands must face one another and the fingers must face away from you. Another person places the circular ends of the toilet paper tube between your two hands and against the palm of each hand.  The tube should now be parallel to the floor.  The palms of the hands and the fingers must be held straight and firm at all times.  The experiment will not work properly if this arrangement is changed in any way. Press against the ends of the tube with the palms of your hands without bending your palms or fingers. Could you crush the tube?  Why?  What will happen if you use the tube of a roll of paper towels? Try it.  Why do you get these results? 

Caution
1). A tube is usually good for only one or two students.  Some students will bend their hands and ruin the tube. 
2). The teacher should provide all toilet paper rolls.  Other faculty members can supply them but no rolls should come from students.

B.  CAN YOU COLLAPSE A SHORT PIECE OF A DRINKING STRAW?

Cut a piece of a drinking straw so it is 2.5 cm (1 inch) long.  Hold the open ends of the piece of straw against the pad of your thumb and the pad of your index finger of the same hand.  Try to collapse the tube by pushing the open ends of the straw.  Do not push too hard or for too long a time because it will begin to hurt.  Can you collapse the piece of drinking straw?  Why?  Can you find another material that demonstrates the strength of a cylinder?    
 


CHALLENGE #3:

WHAT IS ANOTHER WAY A SHEET OF PAPER CAN HOLD A PILE OF BOOKS WITHOUT THE BOOKS TOUCHING THE TABLE?

Try to find a second way to use a single sheet of copy paper to hold a few books.  NO PART OF ANY OF THE BOOKS USED FOR TESTING THE STRENGTH OF THIS PAPER STRUCTURE CAN TOUCH THE TABLE.  Students can not have tape, string, wire, or elastic bands.  They can only have a single sheet of copy paper.

ANSWER:

Fold a narrow side of the sheet of paper like an accordion or paper fan.  The folds should be approximately 1.5 cm (0.5 inch) high.   Folds should always be the same height.  When you complete folding the paper, it will look like a paper fan.  Place the folded paper on the table so it looks like a row of mountains and place one book on it.  Place additional books on it slowly.  It will not hold as many books as the tube. 

The folds form a triangular shape of paper and the triangle is the strongest geometric shape.  An examination of the interior part of the bones of human legs would show there is solid bone material that form structures called struts.  Many of these hard structures (or struts)  form triangles.  These struts provide considerable strength to the bones so they can withstand gravitational forces on your body. 

Which bones in your body oppose gravity?  They are called anti-gravity bones.

FURTHER INQUIRIES:

o   Does the height of the fold affect the strength of the structure?

o   Would the structure hold more books if you had use the whole sheet of paper?

o   Would the structure hold more books if you cut it in half lengthwise to make it narrower?

o   What other way can you make the structure stronger?

o   What are the names of the bones in your body that oppose gravity? They are called anti-gravity bones.

 


CHALLENGE #4:

WHAT HAPPENS WHEN YOU COMBINE THE CYLINDER WITH THE FOLDED PAPER?

QUESTION A: 
WHAT DO YOU PREDICT WILL HAPPEN TO THE STRENGTH OF YOUR STRUCTURE IF YOU COMBINE THE TUBE AND FOLDED PAPER?  HOW ARE YOU GOING TO TEST YOUR HYPOTHESIS?

Make the tube and folded paper as presented in section 1A and 3.  Take the fan-shaped folded paper and cut it so it is no more than 5cm or 2 inches wide.  Squeeze it together and place it inside the paper cylinder.  The folded paper must never be higher than the cylinder before you begin testing this combined structure.  Trim it so it is no longer than the height of your cylinder.  Follow the strength testing procedures stated in Section 1.  Be sure to use the same books and add them one at a time.

QUESTION B: 
WHAT HAPPENS IF YOU GLUE PAPER ONTO THE TOP AND BOTTOM SURFACES OF THE PREVIOUS STRUCTURE?

Cut a sheet of paper lengthwise in half.  Fold one of the halves into the accordion-shape as explained in section 03.  Place the accordion shaped paper flat on the table so the points on one side are touching the table and the points on the other side are facing upward.  Cut 2 pieces of paper to be equal in size to the area of the accordion shaped object.  They must be the same length and width as the folded paper. Put a very small amount of white glue along all the points facing upward.  Let the glue dry for 1-2 minutes and put one of the pieces of paper that equals it size on it.  Let it dry for a few minutes. Then turn it over and repeat these procedures with the other piece of paper.  Let the glue dry for a day and trim the top and bottom pieces of paper if necessary. Test it with the books you used in section 01 or 03 the next day. 

What have you made?  Is it strong?  Study the structure of a long bone and compare its structure with the structure of the paper object you made.  What are their similarities?  How are they different?  Which one would be stronger?

Could you make one of these constructions that would not collapse if the students in your class stood on it one at a time? 

©2010 Elinor W. Semel   All rights reserved.