A barge with vertical sides is 10 m wide and 60 m long and is floating in fresh water of density 1000 kg/m³.How much deeper into the water does the barge sink when 3.0 × 10⁵ kg of coal are loaded on the barge? A)25 cm B)50 cm C)75 cm D)1.0 m E)1.5 m

Question

Quizplus · Accepted Answer

The barge will sink until the weight of the water displaced by the barge and the coal equals the total weight of the barge and the coal.

Initially, the barge and water displaced by it have a weight of:
(1000 kg/m3)(60 m)(10 m)(1 m) = 6.00 × 105 kg

When 3.0 × 1015 kg of coal is added, the total weight of the barge and coal is:
6.00 × 105 kg + 3.0 × 1015 kg = 3.00 × 1018 kg

The volume of water displaced by the barge remains the same, so the depth the barge sinks is proportional to the weight of the barge and coal.

Let h be the depth the barge sinks into the water after the coal is added. Then we have:

(1000 kg/m3)(60 m)(10 m)(h) = 3.00 × 1018 kg - 6.00 × 105 kg

Solving for h gives:
h = 0.5 m = 50 cm.

Therefore, the barge sinks 50 cm deeper into the water when 3.0 × 1015 kg of coal is added.

A Barge with Vertical Sides Is 10 M Wide and 60