# Center of Gravity Toss

### Introduction

In this demonstration, students will observe the motion of an irregularly shaped object as it spins around its center of mass. The path of the spinning object reveals that the net force of gravity pulls down on the object at its center of mass. The center of mass of the irregularly shaped object will remain stable and follow a simple parabolic trajectory when the object is tossed into the air.

### Concepts

• Center of gravity
• Stability
• Newton’s laws of motion
• Parabolic motion

### Background

Gravity is the attractive force between all objects. The most familiar gravitational force is that of the Earth, which pulls all objects down and is more commonly referred to as an object’s weight. The more massive the objects are, the greater the gravitational force that exists between them.

{12508_Background_Figure_1}

According to Isaac Newton’s (1642–1727) laws of gravitation, the Earth attracts every tiny particle of mass of every object and pulls them toward the center. For any specific object (composed of many tiny particles), the center of gravity of the object is the location where all the individual gravitational forces acting on the individual particles add up and result in one net downward force. At this point we can assume all of the mass of the object is concentrated, and therefore this point is also referred to as the center of mass. The location of the center of gravity, especially for an irregularly shaped object, is critical for the overall stability and balance of an object on the Earth’s surface. An object is most stable on the Earth’s surface when the object’s center of gravity is at its lowest point and is centered about the object’s support base.

In general, when a force acts on an object, it can be assumed that the force acts on the center of mass of the object. If a force is specifically applied to an object at a position other than its center of mass (i.e., to the left, right, up or down) from the center of mass, then this force will cause the object to rotate about its center of mass. This is observed when the irregularly shaped foam object is thrown and spun—it rotates about its center of mass, and the center of mass follows a smooth parabolic trajectory as it travels through the air (see Figure 1).

### Materials

Binder clips, 2*
Fishing sinker*
Foam shape*
Nail*
Pushpins, 5*
Scissors
String, 2 m*
Velcro® dots, hooks, 4*
*Materials included in kit.

### Safety Precautions

The materials in this demonstration are considered safe. The foam object is soft and will not break or damage items in the classroom. However, do not throw the foam object at anyone.

### Disposal

Save the materials for future demonstrations.

### Prelab Preparation

1. Peel two Velcro dot hooks from the strip. The two remaining Velcro dots can be used as replacements, if necessary.
2. Press the two sticky sides together so that the Velcro hooks are on the outside.
3. Cut a piece of string approximately 50 cm (20") long.
4. Tie the fishing sinker to one end of the string.
5. Tie a “looping knot” at the other end of the string (see Figure 2).
{12508_Preparation_Figure_2}

### Procedure

1. Show the foam shape to the students.
2. Toss the foam object forward with a backspin so the students can see the irregularly shaped object wobble as it travels along its trajectory (see Figure 1 in the Background section).
3. Ask students if there was a point on the object that appeared to follow a stable parabolic path during its motion. Toss the object again, if necessary.
4. Attach the center of the binder clip to the very edge of one corner of the foam object (see Figure 3).
5. Slide the “looping knot” onto the nail and then slide the nail through the wire loops on the binder clip.
6. Hold the nail parallel to the ground and high enough to allow the foam object, and string and sinker to hang freely (see Figure 3). Make sure the string does not get “hung up” on the foam.
{12508_Procedure_Figure_3}
Once the foam object and string stop swinging and come to rest, have a student place two pushpins into the foam object along the path of the vertically hanging string.
1. With the pushpins in place, repeat steps 4–6 at a different corner on the foam object. The student should place a third pushpin at the crossing point between the path of the vertically hanging string and the imaginary line between the two pushpins that are stuck in the foam. (This third pushpin should be the center of gravity of the foam object.)
2. As a check, repeat steps 4–6 at a third corner. The path of the string should cross the location of the third pushpin (the center of mass).
3. Remove the “center of mass” pushpin and replace it with the Velcro dot. Note: Position the Velcro dot as close as possible to the location of the (removed) “center of mass” pushpin.
4. Remove the two remaining pushpins and the binder clip.
5. Repeat step 2 so students can observe the spinning, thrown irregularly shaped object in motion.
6. Is there a point that appears to follow a stable parabolic path?

### Student Worksheet PDF

12508_Student1.pdf

### Teacher Tips

• This kit contains enough materials to perform the demonstration indefinitely. Extra pushpins, Velcro dots and pinch clips are provided.
• Make sure clip is attached to as little foam as possible, and that the bottom of the clip is centered on the foam edge and remains parallel to the floor. This will help to eliminate any “extra mass” from affecting the center of mass of the foam object.
• Not all foam shapes will look exactly the same from kit to kit.
• Use a paper cutter to change the shape of the object, if desired. Draw the desired shape before cutting—measure twice, cut once.
• Attach different size pinch clips or clothespins to one or two corners of the foam shape to change the location of the center of mass.

### Science & Engineering Practices

Obtaining, evaluation, and communicating information
Developing and using models

### Disciplinary Core Ideas

MS-PS2.A: Forces and Motion
MS-PS2.B: Types of Interactions
HS-PS2.A: Forces and Motion
HS-PS3.B: Conservation of Energy and Energy Transfer

### Crosscutting Concepts

Energy and matter
Structure and function
Cause and effect
Stability and change
Systems and system models

### Performance Expectations

MS-PS2-4: Construct and present arguments using evidence to support the claim that gravitational interactions are attractive and depend on the masses of interacting objects
HS-PS2-4: Use mathematical representations of Newton’s Law of Gravitation and Coulomb’s Law to describe and predict the gravitational and electrostatic forces between objects.

### Sample Data

Observations
Describe the motion and “travel” of the irregularly shaped object after it was tossed into the air:

The object wobbled as it spun. There is a point on the foam that appears to be a “center point” that the rest of the object spins around.

The center of gravity dot remained stable and traveled in a smooth curve (parabola) as it flew through the air.

1. Define the center of mass of an object.

See Background information for an appropriate definition.

2. Describe a process or procedure for locating the center of mass of an irregularly shaped object.

Hang the object and string from one corner and draw a vertical line through the object. Repeat the same steps at a different corner. The point where the lines intersect should be the center of mass of the object.

3. Can the center of mass ever be located outside the physical object? Explain with an example.

Yes. If all the mass is located on an outside edge of an object such as a tire, then the center of mass will be located at the center of the tire and not physically on the tire.

4. When the irregularly shaped foam sheet was spun and tossed into the air, what was the shape of the path that the center of mass followed? Draw the shape that the center of mass follows.

The center of mass followed a stable parabolic trajectory.

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