Joel Kolberg
Jacob Diener
Erica Oldre
Amanda Stern
Center of Gravity
The center of gravity is a geometric property of any selected object. It is also explained as by the Army Field Manual 100-5 stating that it "is the hub of all power and movement upon which everything depends." In any object the center of gravity exists and may be determined by the equilibrium equation. This property determines at what point, balance might occur in an object. It is also called the center of mass because all of the mass in the object can balance on this specific point. The balance point of an object may be found by calculus or by experimenting.
Using experiments one must find the line of symmetry and then from that line find the points at which that object balances. Another experiment to find the center of gravity is to hang an object from any point and then from that same point drop a weighted string. Then trace along the line on the string and then repeat these two steps from a different point. The location where the two lines intersect is the center of gravity. Yet to find the center of gravity mathematically, one must find the centroid of the item. The centroid is the basic idea behind the center of gravity. In order to find the center of gravity, data points from the figure must first be ordered by the x-values in a table lowest to highest. The data is then divided into three equal parts. The median points from these three data sets will be separated into a summary point from each section. The average of these summary points is then taken and will result in the centroid. The centroid simply finds the center of gravity. The center of gravity of an object is only the same as its center of mass when that object is a sphere of uniform density.
The concept of the center of gravity was first concocted by Newton and was an extension of Kepler’s third law {(m1+m2) P2=(d1+d2)3=R3}. Where P is the planetary orbital period, R is the total separation between the centers of the two objects, and D is the distance from the fulcrum to the center of a selected object.
The center of gravity can be found in anything from basic geometric shapes such as squares, triangles, rectangles, and other polygons, to buildings, aircraft, watercraft, and other everyday items. The center of gravity can be applied even to sports. Where one wants a good center of gravity so that they won’t fall or trip while they run or compete. Balance is how things are able to stand and not come crashing down on the earth.
The center of gravity is used to balance a lot of common day things such as train cars, in jeeps just to make sure they don’t roll over too easy,
The center of gravity of an aircraft is the point where all of the weight of the aircraft is considered to be located. Where the weight is placed in the airplane is a factor that has a tremendous effect on how well the airplane will fly. This is because the center of gravity of the airplane must be maintained within certain limits given by the manufacturer, in order for the aircraft to be flown safely. If the center of gravity gets too far forward or too far backward the aircraft will be out of balance and difficult, if not impossible, to control. The use of the center of gravity is used often for the flight of airplanes. It is very essential that planes and other flying vehicles have that equilibrium because if they don’t it can be catastrophic.
Gravitational Force is everywhere and plays an integral role in designing buildings, bridges, and machines. When thinking of gravitational force and an object’s center of gravity we assume all of the mass to be concentrated in a very small point. This point is the point at which gravity exerts a force. When building complex structures- a lot of thought, calculations, and time have to invested so that the center of gravity of each piece is in equilibrium- that is, so that the net torque of the system is zero.
The United States Air Force uses the center of gravity a great deal. They need it for their plains and jets. With out the proper balance in the plains they would be unable to fly well and it could cause the plain to be unable to be controlled. The Air Force would also need to have their aircraft carriers balanced so that they don’t tip over in the ocean.
Bibliography
http://pw1.netcom.com/~jrosgood/wc4.htm
http://www.journaloftheoretics.com/Comments/c3-3.htm
http://mathworld.wolfram.com/CenterofGravity.html
http://www.paf.mil.ph/af_review/vol02/STRAT&CG.HTM
http://csep10.phys.utk.edu/astr161/lect/history/newtongrav.html