How many tanks can a 150 ft. barge carry without sinking more than 1 ft?

[NYCHE89]

Homework Statement

A barge 150 ft. long and 30 ft. wide is to carry a payload of 10-ton light tanks over water. If the barge is to sink no more than an addictional 1 ft, how many tanks can be loaded?

Homework Equations

The Attempt at a Solution

Buoyant Force = fluid density x volume submerged x gravity
= (1 g/cm^3 x 1kg/1000g) x (4500 ft^3 x 28.317L/1ft^3 x 1000cm^3/1L) x 9.8 m/s^2
= 1,248,779.7 N

I've gotten this far and don't know what to do next. Also, this may be completely wrong.

 

[mgb_phys]

It might be easier to restate this as: "It receives an upthrust equal to the weight of water displaced."
Or the extra weight of cargo equals the weight of the water.
There no need to explicitly include g - especially if you can't decide which units to use.

 

[nvn]

NYCHE89: Nice work! Your equation and answer for buoyancy force, Fb, is correct. g = 9.807 m/s^2. Now, the weight of each light tank is Pt = 88 964.4 N. Therefore, see if you can now figure out how many light tanks would have a total weight not exceeding Fb. Try it.