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. 50 drums of cement. Each drum weighs 600 pounds and
is stowed on end. Each drum measures 28 inches in
diameter and is 32 inches high.
II. Two reels of 1 inch diameter wire rope. Each reel
contains 3000 linear feet of wire weighing 1.55
pounds per linear foot. The tare weight of each reel
is 450 pounds. The reels are stowed on the flat and
are 36 inches high.
III. Twelve pallets of general supplies. Each pallet
measures 8'L X 4'W X 3'H. The pallets are stowed
singly and weigh 580 pounds each.
IV. Twelve crates of machine parts and pipe fittings.
Each weighs 880 pounds. Each crate measures
8'L X 3'W X 4'H and is stowed singly.
A. 1.50 feet
B.1.96 feet
C. 2.21 feet
D. 2.78 feet
I. 50 drums of cement. Each drum weighs 600 pounds and
is stowed on end. Each drum measures 28 inches in
diameter and is 32 inches high.
II. Two reels of 1 inch diameter wire rope. Each reel
contains 3000 linear feet of wire weighing 1.55
pounds per linear foot. The tare weight of each reel
is 450 pounds. The reels are stowed on the flat and
are 36 inches high.
III. Twelve pallets of general supplies. Each pallet
measures 8'L X 4'W X 3'H. The pallets are stowed
singly and weigh 580 pounds each.
IV. Twelve crates of machine parts and pipe fittings.
Each weighs 880 pounds. Each crate measures
8'L X 3'W X 4'H and is stowed singly.
A. 1.50 feet
B.1.96 feet
C. 2.21 feet
D. 2.78 feet
I drew a blank on this one. It seems vaguely familiar, but...nothing.
ReplyDeleteTo 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. 50 drums of cement. Each drum weighs 600 pounds and
is stowed on end. (50x600 pounds = 30,000 pounds)Each drum measures 28 inches in
diameter and is 32 inches high. (If stowed on end the vertical center of gravity, VCG of the drums is half the height or 16 inches.
II. Two reels of 1 inch diameter wire rope. Each reel
contains 3000 linear feet of wire weighing 1.55
pounds per linear foot. (each reel's weight = 3000 ft x 1.55 lb/ft = 4650 lb)The tare weight of each reel is 450 pounds. (the total weight of each reel = 4,650 + 450 = 5,100 pounds. WE need to double this because there are two reels that weigh 10,200 pounds.)The reels are stowed on the flat and are 36 inches high. ( So the VCG of the reels is half their height or 18 inches)
III. Twelve pallets of general supplies. Each pallet
measures 8'L X 4'W X 3'H. The pallets are stowed
singly (so their VCG is half their height = 1.5 feet or 18 inches) and weigh 580 pounds each. (so their total weight = 12 x 580 = 6,960 pounds)
IV. Twelve crates of machine parts and pipe fittings.
Each weighs 880 pounds. (so their weight = 12 x 880 = 10,560 pounds.) Each crate measures 8'L X 3'W X 4'H and is stowed singly. (so their VCG is half their height = 2 feet or 24 inches)
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. 30,000 lb x 16 inches = 480,000 inch pounds
II. 10,200 lb x 18 inches = 183,600 inch pounds
III. 6,960 lb x 18 inches = 125,280 inch pounds
IV. 10,560 lb x 24 inches = 253,440 inch pounds
Totals 57,720 lb 1,042,320 inch pounds
VCG of Deck Cargo = Total Moment/Total Weight
= 1,042,320 inch pounds / 57,720 lb
=18.05 inches or 1.504 feet
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 additional comment. As I recall the there are many word multiple choice questions that do not require a calculation on a license exam for many subjects. You must be able to answer these easier questions. On the other hand there are multiple choice questions that require a calculation to find the correct answer. I took the time to write out the answer in detail so you can see the thought process it takes to do it.
ReplyDelete