Physics Boyancy Problem: A seagoing crane lifts a sealed safe from a sunken ship in the Great Lakes...?

Question

A seagoing crane lifts a sealed safe from a sunken ship in the Great Lakes. The average density of the safe is 5.3 grams/cc and its mass is 120 kg. What is the tension in the ifting cable when the safe is still submerged?

Answer 1

The forces acting on the safe after it is off the floor of the lake are the tension in the cable and the bouyant force (in the upward direction) and the weight of the safe in the down ward direction. If the safe is not accelerating, then the sum of the forces up equals the sum of the forces down, according to Newton's 2nd Law or:

T + Fbuoyant = weight

The weight of the safe is 120kgx9.8m/s/s = 1176N

The Bouyant force exerted on the safe is equal to the weight of the water displaced. The volume of the safe is 120/0.00533 =22642 cc's which means it displaces 22642 g of water or 22.6 kg of water. Which means the WEIGHT of the water displaced or the Fbouyant = 22.6 x 9.8 = 221.9 N

T + 221.9 = 1176

So T = 954.1 N

Answer 2

Assume the density of the water in the Great Lakes to be 1g/cc

The volume of the safe is
120/.0053 cc

So it displaces

22.6 kg

The resultant tension of the cable while the safe is submerged is:

22.6*9.81 N
=222 N

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Answer 3

5.3 grams/cc = 5.3 kg/L
Volume of safe = mass/density = 120/5.3 L
Water displaced = 120/5.3 L
Mass of water displaced = 120/5.3 kg
Tension in the string = (120 - 120/5.3) x 9.81 N
(Assuming water specific gravity = 1 and ignoring accelerating force in the string)