Center of Gravity

Although most real objects are spread out in space, they act as if the mass were concentrated at a single point. In a uniform gravitational field, such as the classroom, the center of gravity and center of mass are located at the same point.

1. Cut out an irregularly-shaped object from a folder.

2. Use a pin to make three holes at various places near the edge of the object.

3. Create a hook from a small paper-clip. Cut heavy thread 4 cm longer than your object's widest point. Tie a large paper clip to one end of the string and make a small loop at the other.

4. Push the hook through one of the holes and suspend the mass on a string. The object and suspended mass should swing freely.

5. While holding the object by the hook, mark the location of the string with a pencil.

6. Repeat steps 4 and 5 for the other holes in the object.

7. The point at which your lines cross is the location of the center of gravity for your object.

Questions

1. Can the center of gravity of a system be outside of the substance itself?

2. Where is the center of gravity for...
...a CD?
...a horseshoe?
...two identical chocolate candies placed 1 cm apart?

3. Where is the center of gravity for a meter-stick? How can you find it?

4. Mathematically, the center of gravity is a weighted average of the mass distribution in an object:

Center of gravity =

(weight 1) (distance 1) + (weight 2) (distance 2) + ...

weight 1 + weight 2 + ...

An airplane has a center of mass of 2,000 kg located 3.0 meters from the front of the plane. The pilot sits 1.0 meters from the front and has a mass of 10 kg. The cargo has a mass of 400 kg and is located 2.0 meters from the front. How far from the front of the plane is the center of gravity?

A. Draw a diagram.

B. Solve the problem.

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