0.15 Phy1120: force -- center of gravity  (Page 5/8)

The pencil in this configuration is said to be in stable equilibrium. The key to success isthat you don't tip it so far that a vertical line through the C.G. moves outside the circle that defines the area of the supporting base of the pencil.

Balance it on its point

Assume that you rub the pencil lead back and forth a few times to slightly flatten the pointed end. If you were able to balance the pencil on that verysmall flattened surface, and then blow on the pencil very lightly, it would probably tip over and fall flat on the table. The smaller the flattened surface supporting the pencil, the easier it would be to cause it to tip over. Thepencil in that state would be said to be in unstable equilibrium.

Stability is important

Stability is very important for many things such as boats and airplanes. Usually, the lower the C.G., themore stable will be the object.

A high-wire artist

For example, a high-wire artist at the circus may carry a long flexible pole, perpendicular to the wire held near the center of the pole at about thigh height.In this case, the supporting surface is the feet on the wire.

The flex in the pole allows the ends of the pole, and conceivably a large portion of the pole to hang lower than the soles of the feet. This has the effect oflowering the C.G. of the combination of the person and the pole considerably. If the C.G. is below the supporting surface, which in this case is the soles of thefeet, the combination of the person and the pole will be very stable.

Cargo ships

The people that load cargo ships try to keep the C.G. of the loaded ship low in the hull of the ship. Sometimes they add extra weight called ballast very lowin the hull to get the C.G. as low as possible.

Cargo aircraft

The people that load large military cargo aircraft are very careful how they load the cargo in order to control the location of the C.G. of the aircraft tomaintain stability of the aircraft. The position of the C.G. relative to the axis of the wings is very important.

Children's toys

When my children were young, they had toys with a round bottom and something like a clown's head on the top. The toys had a heavyweight inside and very close to the bottom. This caused the C.G. to be very low in the toy. When the child pushed the toy over, it would return to an upright position. Thetoy was very stable.

An exercise involving the tipping point

Let's see if we can demonstrate stability or the lack thereof with a thought experiment. Begin by drawingtwo rectangles on your graph board side by side. Make each rectangle 2 units wide and five units tall.

Two boxes

Pretend that these rectangles represent side views of two cardboard boxes with dimensions of 2x2x5 ft. Assume that each box contains identical heavymaterial at one end and the remainder of the box is filled with very light packing material.Assume that the heavy contents are at the bottom of the left box and at the top of the right box. (The boxes and their contents are just alike, but one isupside down relative to the other.)