Center of see-saw = 8 feet away from datum. Child 1 = 1 foot away from datum Child 2 = 15 feet away from datum
The see-saw: 30 lb. x 8 ft. = 240 ft. x lb. Child 1 = 40 lb. x 1 ft. = 40 ft. x lb. Child 2 = 60 lb. x 15 ft. = 900 ft. x lb.
1180 ft. x lb. ÷ 130 lbs = 9. 08 ft. The center of gravity is 9. 08 feet from the datum, or measured 9. 08 feet from the end of the left side of the see-saw, which is where the datum was placed.
For example, for people sitting on a seesaw, the center of gravity has to be somewhere on the seesaw, not to the left or right of the seesaw. It does not have to be directly on a person. This is still true with problems in two dimensions. Draw a square just large enough to fit all of the objects in your problem. The center of gravity must be inside this square.
The way we solved it, the datum is at the left end of the seesaw. Our answer was 9. 08 ft, so our center of mass is 9. 08 ft from the datum at the left end. If you pick a new datum 1 ft from the left end, you get the answer 8. 08 ft for the center of mass. The center of mass is 8. 08 ft from the new datum, which is 1 ft from the left end. The center of mass is 8. 08 + 1 = 9. 08 ft from the left end, the same answer we got before. (Note: When measuring distance, remember that distances to the left of the datum are negative, while distances to the right are positive. )
The way we solved it, the datum is at the left end of the seesaw. Our answer was 9. 08 ft, so our center of mass is 9. 08 ft from the datum at the left end. If you pick a new datum 1 ft from the left end, you get the answer 8. 08 ft for the center of mass. The center of mass is 8. 08 ft from the new datum, which is 1 ft from the left end. The center of mass is 8. 08 + 1 = 9. 08 ft from the left end, the same answer we got before. (Note: When measuring distance, remember that distances to the left of the datum are negative, while distances to the right are positive. )
For seesaw problems, all you care about is where the center of gravity is along the left-right line of the seesaw. Later, you might learn more advanced ways to calculate the center of gravity in two dimensions.
