Bottle Balance Beam

Introduction

A gymnast falls off a balance beam. A football player gets knocked over by a lineman. A ballerina can’t complete a twirl. A painter falls off a ladder. Center of gravity can be more than just an abstract concept!

Concepts

• Center of gravity
• Gravity
• Balance

Background

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. For irregularly shaped objects or moving objects, the center of gravity at a particular moment may be critical for balance and stability. The location of the center of gravity is critical for the overall stability and balance of an object on the Earth’s surface.

As an object’s mass shifts, its center of gravity also changes. If the center of gravity is positioned over an object’s base of support, the object will be balanced. If an object’s mass shifts in such a way as to move the center of gravity beyond the base of support, the object will be unstable. The position of the center of gravity of an object is important in determining its stability. An object with a broad base and with the center of gravity fairly low is more stable than an object with a narrow base and a high center of gravity.

Materials

Safety Precautions

This demonstration is considered safe. Follow all normal laboratory safety rules.

Disposal

Dispose of water in an appropriate sink and save the apparatus for many repeat demonstrations.

Procedure

1. Start by placing the empty bottle in the Balance Beam hole and trying to balance the apparatus on a flat, stable table top. When the bottle is empty, the apparatus will not balance and it will fall over.
2. Remove the empty bottle and fill it one-half full with water. Replace the cap and place the bottle back in the Balance Beam hole. Try to balance it. Determine the location of the center of gravity relative to the base. Note: An approximation of the center of gravity may be determined by placing a fingertip under the upper end of the beam, exerting a slight upward force, and then sliding the finger as far down the beam as possible while maintaining balance. The lowest point where the slight upward force of the finger can just hold the apparatus in balance is the center of gravity.
   {13871_Procedure_Figure_1_Bottle balance beam arrangement}
3. Continue adding water to the bottle and testing it until the apparatus balances. When it balances, identify the fact that the center of gravity is directly over the foot of the base of the apparatus. Use a plumb line or other vertical item to visually line up a straight line above the base. Show that the mass is equal on both sides of the plumb line and that the resultant force is centered on the foot of the base of the apparatus.
4. When the bottle is balanced, use your hand and press down on the bottle cap. What happens to the bottle? Set the bottle back up, and this time press down on the bottom of the bottle. What happens to the bottle? Get the apparatus to fall in both directions and discuss what happens in terms of the center of gravity shift.
5. Discuss other items relative to their center of gravity. See Answers to Questions for suggestions.
6. Dispose of water in an appropriate sink and save the apparatus for many repeat demonstrations.

Student Worksheet PDF

13871_Student1.pdf

Teacher Tips

• This kit contains one Balance Beam (wooden board) and one empty 2-L bottle with a screw-on cap.
• The bottle will balance when it is full.
• This kit can also be used as an innovative density demonstration. Obtain two clean 2-L bottles. Take one bottle and fill it half full with clear water and the remaining half with blue kerosene. Tightly cap the bottle. The blue kerosene will float on top of the clear water. Next, fill the second bottle half full with water that has been dyed blue (try to match the color of the blue kerosene), and fill the remaining half with clear mineral oil. Tightly cap the bottle. The clear mineral oil will float on top of the blue water. Set up and display the Bottle Balance Beam with one of the bottles. After a few days, replace this bottle with the second bottle. Do this when the students are not present. See how long it takes for the students to notice the color flip. This will initiate questions and discussion on density. At this point it may be beneficial to present both bottles to the students simultaneously. The bottles may be stored properly and reused for years. Note: Do not allow students to open the bottles—they contain flammable liquids. The caps may be glued onto the bottles to prevent opening, spilling or tampering.

Answers to Questions

1. When the empty bottle is placed in the hole in the balance beam, where is the center of gravity? Why does the bottle fall in the direction it does?

   When the bottle is empty and placed in the Balance Beam hole, the center of gravity is not over the base, but slightly above the hole. Most of the weight is beyond the base, so the bottle and beam fall forward.

2. When the bottle is one-half full with water and placed back in the Balance Beam hole, where is the location of the center of gravity relative to the base? Explain why the apparatus still falls over.

   The center of gravity is now closer to the base, but still beyond it, so the apparatus falls forward again.

3. When the apparatus balances where is the center of gravity? Explain why the bottle and beam stay balanced.

   The center of gravity is directly over the foot of the base of the apparatus. The mass is equal on both sides of the base, therefore the resultant force is centered on the foot of the base of the apparatus.

4. What happens to the bottle when a force is exerted on the cap? What happens when a force is exerted on the bottom of the bottle? Explain what happens in terms of the center of gravity shift.

   Pressing down on the bottle cap increases the force on the upper part of the beam, and the apparatus falls in the direction of the applied force. Pressing down on the bottom of the bottom has the reverse effect, and the apparatus falls in the opposite direction. Each time a force is applied, the center of gravity shifts beyond the base of the beam, causing the apparatus to fall in the direction of the shift.

5. When a person is standing on two feet, where is his or her center of gravity? Where is the center of gravity when standing on one foot? What happens if the person’s weight shifts and his or her center of gravity shifts outside of the base?

   When a person stands on two feet, the center of gravity is along the midline of the body, between the feet. When standing on one foot, the center of gravity shifts over the one foot and correspondingly, the person must shift his or her body to remain stable. If the body shifts too far in either direction, causing the center of gravity to move beyond the base foot, the person becomes unstable and may fall down.

6. Why do football players in the line try to “stay low to the ground”?

   Football players in the line try to stay low to the ground to become more stable. The lower the mass is to the ground, the harder it is to displace, and the harder it would be to knock the player down.

References

Thanks to Robert Farber, Central High School, Philadelphia, PA, for sending this idea to Flinn Scientific.