Question

A Great Lakes ore freighter has a mass of 46000 tons. It is designed to safely carry 36000 tons of iron ore, when it is in Lake Ontario. How much ore (in tons) could it carry as safely on the ocean? Assume that safety depends only on maintaining the water line at the same position.

Answer 1

den1=density of the lake water (1000kg/m^3)
den2=density of sea water (1029kg/m^3)
A=Area of ship
g=gravity 9.8
h=amount of ship under water
m1=mass of ship (in tons)
m2=mass of ore in the Lake (in tons)
m3=mass of ore in ocean

den1*g*A*h=(m1+m2)*g
den1*A*h=m1+m2
A*h=(m1+m2)/den1 (A*h remains constant)

A*h = (46000+36000)/1000

82000 tones = 74389149 kgs

A*h = (74389149kg)/1000
A*h = 74389.14
now:
den2*g*A*h=(m1+m3)g
den2*A*h=m1+m3
m3=den2*A*h-m1 (use the A*h calculated earlier)

m3 = 1029* 74389.14 - 46000

m3 = 76500383.9

m3 = 84327.23846303 tones