Physics 24 Center of Gravity

Have you ever picked up a long board? How is it different to pick it up in the middle from picking up one end?
Have you ever watched a waitress balance a tray on one hand?
How do you balance an object on a small point?materials for project 24
Question: How does an object balance?
Materials:
Cardboard from a box
Marker
Scissors
Scale
Spoon
Procedure:
marking the rectangle

The best way I’ve found for cutting out a rectangle rather than a trapezoid is to measure out across twice, once toward the top and once toward the bottom so the line is straight across the piece of cardboard.

Cut out a square 15 cm on a side, a circle 15 cm diameter, a 15 cm x 20 cm rectangle [These can be a little bigger or smaller.]
rectangle cut out

The rectangle is cut out by cutting down the line. The entire piece of cardboard was a rectangle and could have been used that way.

Mass the shapes

Massing the rectangle.

Massing the rectangle.

Balance each geometric shape on your fingertip marking the place your finger is

Balancing point of rectangle

The rectangle is longer than its width. This makes finding the balancing point harder as both the length and width must be balanced.

Record where the point is in your Observations

balancing point of rectangle

Finding the balancing point for the rectangle took some moving around and a couple of tries to mark it accurately. I marked the first one and tried balancing from that point and found the point was a little further over.

Mark a line straight across each geometric shape going through the marked point
Cut each shape in two on the line
Mass each piece

massing half rectangle

The mass of the split cardboard rectangle is roughly half the total mass.

Balance the spoon on your finger marking the balancing point
Observations:
Balancing points of the geometric shapes

massing squaare

The mass of the entire cardboard square is 14.32 g.

Masses of the geometric shapes
Masses of the two pieces of each shape:
Balancing point of the spoon
Conclusions:
Is the balancing point always in the measured middle of the object? Why do you think so?
Compare the mass of the object on either side of the balancing point of the cardboard shapes.

massing half square

The mass of half the cardboard square is 7.16 g , exactly half of the total mass.

Does mass determine the balancing point of an object?
If you could cut the spoon at the balancing point, how do you think the masses of the two pieces would compare?
Another name for this balancing point is the center of gravity. Why is this a good name for the balancing point?

center of gravty of square

Finding the center of a square without measuring first can take some shifting around but the square finally balances on the tip of my finger.

What I Found Out:
My rectangle was 15 cm x 20 cm. The square was 14 cm x 14 cm. The diameter of the circle was 10 cm.
massing circle

The mass of the entire cardboard circle is 6.41 g.

The rectangle would sort of balance when my finger was close to the center of the rectangle. It balanced the best, the flattest when my finger was in the center. The same was true for the square and the circle.

mass of half circle

Dividing a circle in half even with a center point isn’t easy but still the half is about half the total mass.

The spoon was different. The balancing point was closer to the spoon bowl than to the end of the handle. The balancing point is not always in the middle of a shape.
When I cut the cardboard shapes into two pieces, the two pieces had similar masses. The square halves were the same. The others were tenths of a gram different.

center of gravity of  circle

It’s easier to see the circle balances at a point in the center. This is the circle’s center of gravity.

The balancing point seems to be where the mass is the same all around it. If I cut the spoon at the balancing point, I would expect the masses of the two pieces to be very close to the same.
Gravity creates weight. As the balancing point is at the place in an object where the mass and the weight will be the same on all sides, it is at the center of the gravitational pull on the object, the center of gravity.