You are on a supply run to an offshore drilling rig. On board is the cargo listed. What is the height above the main deck of the center of gravity of the cargo?
I. Drill casing - 50 lengths stowed in a block 8 feet
high. Each pipe weighs 326 lbs.
II. Crated valves - 10 crates stowed 2 high. Each crate
is 36" L X 30" W X 15" H and weighs 1020 lbs.
III. Dry stores - 14 containers stowed 2 high. Each
container weighs 2 long tons and measures
6'L X 6'W X 6'H.
IV. Anchors - 4. Each one on deck. The center of
gravity of each anchor is 9" from the deck and each
weighs 6120 lbs.
A. 3.6 feet
B. 4.2 feet
C. 4.4 feet
D. 4.9 feet
I. Drill casing - 50 lengths stowed in a block 8 feet
high. Each pipe weighs 326 lbs.
II. Crated valves - 10 crates stowed 2 high. Each crate
is 36" L X 30" W X 15" H and weighs 1020 lbs.
III. Dry stores - 14 containers stowed 2 high. Each
container weighs 2 long tons and measures
6'L X 6'W X 6'H.
IV. Anchors - 4. Each one on deck. The center of
gravity of each anchor is 9" from the deck and each
weighs 6120 lbs.
A. 3.6 feet
B. 4.2 feet
C. 4.4 feet
D. 4.9 feet
To solve this we need to calculate a "Weighted Average" of the cargo on deck.
ReplyDeleteFirst we need to identify each weight and its center of gravity above the deck:
I. Drill casing - 50 lengths stowed in a block 8 feet
high (so the VCG is half the height or 4 feet or 48 inches). Each pipe weighs 326 lbs. (so 50 pipes x 326 lbs = 16,300 pounds)
II. Crated valves - 10 crates stowed 2 high. Each crate
is 36" L X 30" W X 15" H (so the VCG is half the height = 15 inches) and weighs 1020 lbs. (so 10 x 1020 pounds = 10,200 pounds)
III. Dry stores - 14 containers stowed 2 high. Each
container weighs 2 long tons (so 14 x 2 LT = 28 LT or 62,720 pounds) and measures
6'L X 6'W X 6'H. (so the VCG is 6 feet or 72 inches)
IV. Anchors - 4. Each one on deck. The center of
gravity of each anchor is 9" (so the VCG is 9 inches) from the deck and each
weighs 6120 lbs. (so 6120 pounds x 4 = 24,480 pounds)
Now that we have identified the each groups weights and VCGs we can do the Weighted Average Calculation. By the way at one time this was called the Theory of Moments method, however you cannot look up "Theory of Moments" on the internet, but you can find "Weighted Average" if you want to learn more about it.
Solution by Weighted Average Method:
Item Weight VCG Vertical Moment
I. 16,300 lb x 48 inches = 782,400 inch pounds
II. 10,200 lb x 15 inches = 153,000 inch pounds
III. 62,720 lb x 72 inches = 4,515,840 inch pounds
IV. 24,480 lb x 9 inches = 220,320 inch pounds
Total Weight = 113,700 lb
Total Moment = 5,671,560 inch pounds
VCG of Deck Cargo = Total Moment/Total Weight
= 5,671,560 inch pounds / 113,700 lb
=49.88 inches or 4.16 feet or 4.2 feet, The best answer is B.
Please note: I used pounds and inches because in this problem it was just as easy to use these units instead of converting them to tons and feet.
One may ask if this question is designed to test your skill of the Weighted Average Method or Units Conversion or your reading skills!
B. 4.16 ft
ReplyDelete