Materials Included In Kit

Additional Materials Required

Prelab Preparation

1. Place the tip of a nail into the hole in the center of a wood block. Hammer this “support nail” straight into the block until it is secure. Note: Make sure the nail is driven in vertically. The nail head must be level.
2. Repeat with each of the wood blocks.
3. Place sets of 10 nails into resealable bags for distribution to the student groups.

Safety Precautions

The nails are sharp. Use care when handling. Wear safety glasses. Remind students to wash their hands thoroughly with soap and water before leaving the laboratory.

Disposal

All materials may be stored for future use.

Lab Hints

• Enough materials are provided in this kit for eight groups of students. All materials are reusable. Both parts of this activity can reasonably be completed in one 50-minute class period. The prelaboratory assignment may be completed before coming to lab.
• To balance the nails on the support nail, follow these steps.
  1. Lay one nail horizontally on the table.
  2. Place eight nails at right angles across the first nail so each adjacent nail head is facing the opposite direction (see Figure 1).
     {12773_Hints_Figure_1}
  3. Lay the tenth nail across the other nails, lining it up with the first horizontal nail and with its nail head at the opposite end (see Figure 2).
     {12773_Hints_Figure_2}
  4. Pick up the nails by carefully holding the ends of the horizontal nails together and place the center of the bottom nail on the support nail in the wood block (see Sample Observations).
• Set a time limit for Part I. Unless students have seen the “trick” they may become frustrated after several unsuccessful attempts. Following is a list of hints you may want to employ. Use your best judgment as to how much help to give.

  Balance one nail horizontally on the support nail.
  Remove the one nail and lay it on the lab counter or desk.
  Try to arrange eight nails across the one that is lying down so there is an equal distribution of mass on either side of the first nail.
  How can you use the final nail to hold the others in place? How will it need to be oriented in relationship to the first nail?

• Consider allowing more time for the exploration phase (Part II) than the challenge phase (Part I). If more challenge time is desired, the activity may be conducted over two class periods.

Teacher Tips

• This is a fun activity to develop and reinforce critical thinking and problem-solving skills as well as cooperative learning. It may also be used as part of a physical science unit on forces.
• In general, guided-inquiry activities are most successful if students understand that the activity replaces the lecture. Students are more likely to take responsibility for learning when they are actively engaged in the process of “constructing knowledge.” Guided-inquiry activities simulate the scientific method—students make observations, search for patterns or relationships, and try to identify guiding principles that will explain the results.
• Encourage student groups to share ideas rather than view this activity as a competition.
• Allow two groups to join together and see if they can balance two systems of ten nails each on one support nail.
• If time permits, allow students to investigate their questions.
• To demonstrate the difference between balancing and hanging, use the Balancing Bird and the Fascinating Finger Balance, both available from Flinn Scientific (Catalog Nos. AP9301 and AP6640, respectively). The Balancing Bird balances on its base of support and the Finger Balance hangs from its base of support.

Answers to Prelab Questions

1. Look at the figures of the two gymnasts. Which one is balanced? Which one is hanging in balance? How do you know?
   {12773_PreLab_Figure_1}

   The gymnast in Figure B is balanced because his center of gravity is above his support (the rings). The gymnast in Figure A is hanging because his center of gravity is below his support.

2. What clues are given in the Background and Activity Overview sections to help you solve the “hanging nails” challenge?

   The nails will be hanging, not balancing, so the center of gravity of the nail system must be below the head of the support nail. In order for the nails to be in equilibrium, the center of gravity of the total system must be in line with the support nail.

3. If you were to balance a nail horizontally on your finger, would you expect the center of gravity to be in the exact middle of the nail, closer to the head of the nail, or closer to the point? Explain your answer, and then try it!

   Since the head of the nail has more mass than the point, the center of gravity would be closer to the head of the nail.

Sample Data

Part I. Hanging Nails Challenge
Draw the system of nails once all ten are hanging in balance on the support nail.

Answers to Questions

Part I. Hanging Nails Challenge

1. Describe or use arrows to show the directions of the opposing forces acting on the nails and why they are in equilibrium.

   The support nail is pushing up on the bottom horizontal nail and vice versa. The heads of the nails are pushing from opposite directions on the top horizontal nail, keeping it in place. As gravity pulls the hanging nails down, their shafts push in opposite directions against the bottom horizontal nail, keeping it in place. All the forces acting on the nails cancel each other and the center of gravity of the system is in line with the support nail, so the system hangs in equilibrium.

2. When the 10-nail system is in equilibrium, is its center of gravity above or below the head of the support nail? How can you tell?

   The center of gravity is below the head of the support nail because most of the mass of the nail system is below this point.

3. Why is the title, “Hanging Nails Challenge,” more appropriate for this activity than “Balancing Nails Challenge”?

   Since the center of gravity of the nail system is below its point of support, the nails are hanging. They would be balancing if the center of gravity were above the point of support.

4. How is the position of the nails when nine are in equilibrium different than with 10?

   The shafts of the nails are more aligned when nine are in equilibrium. The four nails on one side hang down more vertically than the three on the other side. When ten are in equilibrium, their shafts are more spread out in a fan shape, with the outermost nails on opposite sides hanging at the same angle; the next two toward the center hang at the same angle, etc.

5. What effect does the stepwise removal of one nail at a time have on the way the nail system hangs? Describe and explain any patterns you observe.

   Each time a nail is removed the center of gravity shifts slightly upward and the system becomes less stable. When an even number of nails are hanging, the two outer nail heads push in opposite directions on the ends of horizontal nails. This causes the horizontal nails to rotate somewhat and the hanging nails spread out in a fan shape. When an odd number of nails are hanging, the two outer nail heads are pushing in the same direction on the top horizontal nail. Their shafts are pushing on the same side of the bottom horizontal nail, in the opposite direction as the force on the top nail. These forces keep the horizontal nails aligned. The side with the greater number of nails hangs lower than the side with the fewer nails.

6. Excluding balancing just one nail, what is the minimum number of nails necessary for the system to remain in equilibrium? Why do you think this is so?

   Five total nails, two horizontal and three hanging, was the minimum number we were able to use and keep the system in equilibrium. With fewer nails, there was not enough opposing force to keep the horizontal nails from rotating. Note to teacher: Balancing five nails is very difficult. The center hanging nail must be exactly over the support nail and the other two closer to the ends of the horizontal nails. Balancing six nails is a little easier if the two pairs of hanging nails are away from the center support.

7. List three other questions related to the Hanging Nails Challenge that could be answered by experimentation. Choose one and describe how you would investigate that question.

   Does the size of the nails affect the stability of the system? What effect does the number of nails have on the angle at which they hang? Do the heads of the nails need to alternate, or will different arrangements also work? Does the placement of the hanging nails on the horizontal nail affect the angle at which they hang?

References

The Experimentals, http://www.abc.net.au/science/experimentals/experiments/ (Accessed March 2009).

Introduction

The challenge is to arrange 10 nails so they will hang in perfect balance on the head of one other nail. No other materials may be used! Once this challenge is mastered, careful observations naturally lead to certain questions—how, what if, why? The answers to these questions are sought in further experimentation, which leads to more observations and further questions. Observation and experiment—twin pillars of problem solving.

Concepts

• Problem solving
• Observation and experiment
• Center of gravity
• Balanced forces

Background

Scientists use many different strategies to solve problems. Sometimes specific steps (e.g., making observations, developing a hypothesis, designing an experimen) are followed to find the answer to a question. Other times a trial-and-error method may be used. Trial and error involves testing multiple possibilities. Before testing begins, the problem must first be specified and then analyzed. Analyzing a problem includes learning background information, looking beyond the obvious, and brainstorming with others about possible solutions. Even if a tested solution fails, valuable knowledge has been gained—learning what does not work! This knowledge is then used to develop new possibilities to test. Problem solving is not a rigid path; it is a dynamic process of discovery.

To solve the hanging nails challenge, some knowledge about center of gravity may be helpful. According to Newton’s laws of gravitation, the Earth attracts every tiny particle of mass of every object and pulls them toward the center of the Earth. For any specific object, the center of gravity of the object is the point where all the individual gravitational forces acting on the individual particles add up and result in one net force. It is the point where we can assume all of the mass of the object is concentrated. The location of the center of gravity is critical for the overall stability and balance of an object on the Earth’s surface.

The above holds true for a system of objects as well. Think of a mobile in which several objects are in balance by a series of rods and string, all hanging from a central point. In this case, the system is hanging in balance, not balancing above a point. If a system’s center of gravity is positioned over the system’s base of support, the system is said to be balanced. If the center of gravity of a system is below its base of support, the system is hanging. In either case, all the forces acting on the system are in equilibrium. If a system’s mass shifts in such a way as to move the center of gravity beyond the point of support, the object will be unstable. The position of the center of gravity of an object or system is important in determining its stability. In general a system with its center of gravity fairly low is more stable than a system with a high center of gravity.

Experiment Overview

The purpose of this activity is to arrange 10 nails so they are hanging in balance on the head of another nail. No other materials such as tape or glue may be used, just the supporting nail and the other 10 nails. Once the “hanging nails” are in equilibrium, the properties of the system will be investigated to determine how different variables affect the balance of forces.

Materials

Prelab Questions

1. Look at the figures of the two gymnasts. Which one is balanced? Which one is hanging in balance? How do you know?
   {12773_PreLab_Figure_1}
2. What clues are given in the Background and Activity Overview sections above to help you solve the “hanging nails” challenge?
3. If you were to balance a nail horizontally on your finger, would you expect the center of gravity to be in the exact middle of the nail, closer to the head of the nail, or closer to the point? Explain your answer, and then try it!

Safety Precautions

The nails are sharp. Use care when handling. Wear safety glasses. Wash hands thoroughly with soap and water before leaving the laboratory. Please follow all laboratory safety guidelines.

Procedure

Part I. The Hanging Nails Challenge

1. As a group, brainstorm possible ways to arrange the nails so they will be in equilibrium on the head of the support nail.
2. Test an idea. If it doesn’t work, try another idea or go back to brainstorming. Here’s one hint: try arranging the nails on the table or desk in a balanced system before placing them on the support nail.
3. If success is not achieved after the time allotted by your instructor, he or she may give you some hints to help solve the problem.
4. Once the nails are hanging in balance, draw the arrangement on the Hanging Nails Challenge Worksheet.

5. Keeping the nails hanging in balance, see what happens if one nail is carefully removed. Note: The system of nails may need to be held in place as one is removed. Describe any shift in position of the remaining nails on the worksheet. Look at the system of nails from different angles. Draw a sketch if you prefer and answer Question 4 on the worksheet.
6. Repeat step one, observing any change in position of the remaining nails.
7. Continue to remove one nail at a time until the system is no longer in equilibrium and the remaining nails fall. As each nail is removed, note any change in position of the remaining nails. Answer Questions 5 and 6 on the worksheet.
8. Reset the original 10 nails on the support nail as in Part I. Join another group and see how many nails can be added to the system and still remain in equilibrium.
9. Complete the Hanging Nails Challenge Worksheet.

Student Worksheet PDF

12773_Student1.pdf