A barge with vertical sides is 10 m wide and 60 m long and is floating in fresh water of density $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ How much deeper into the water does the barge sink when $3.0 \times 10 ^ { 5 } \mathrm {~kg}$ of coal are Ioaded on the barge?
A) 1.0 m
B) 1.5 m
C) 50 cm
D) 75 cm
E) 25 cm

Question

A barge with vertical sides is  10 m wide and  60 m long and is floating in fresh water of density $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ How much deeper into the water does the barge sink when $3.0 \times 10 ^ { 5 } \mathrm {~kg}$ of coal are Ioaded on the barge?
A)  1.0 m 
B)  1.5 m
C)  50 cm
D)  75 cm
E)  25 cm

Quizplus · Accepted Answer

The barge sinks deeper by an amount that displaces an additional volume of water equal to the mass of the coal divided by the density of water. The volume of water displaced by the coal is $3.0 \times 10^5 \, \text{kg} / 1000 \, \text{kg/m}^3 = 300 \, \text{m}^3$. The area of the barge is $10 \, \text{m} \times 60 \, \text{m} = 600 \, \text{m}^2$. The depth increase is $300 \, \text{m}^3 / 600 \, \text{m}^2 = 0.5 \, \text{m}$ or 50 cm.

A Barge with Vertical Sides Is 10 M Wide 1000 kg/m31000 \mathrm {~kg} / \mathrm { m } ^ { 3 }1000 kg/m3

A Barge with Vertical Sides Is 10 M Wide $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$