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

  • Thread starter NYCHE89
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In summary, in order for a barge 150 ft. long and 30 ft. wide to carry a payload of 10-ton light tanks without sinking more than an additional 1 ft, the buoyant force must be equal to or greater than the weight of the tanks. Based on the given equation for buoyant force, a total of 12 light tanks can be loaded onto the barge without exceeding the maximum sinking depth.
  • #1
NYCHE89
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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.
 
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  • #2
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.
 
  • #3
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.
 

1. What is the definition of buoyancy?

Buoyancy is the upward force exerted by a fluid (such as water) on an object immersed in it. This force is equal to the weight of the fluid that the object displaces.

2. How does buoyancy affect the weight of an object?

Buoyancy reduces the effective weight of an object in a fluid. For example, if an object weighs 10 pounds on land and is placed in water, it will weigh less than 10 pounds due to the upward force of buoyancy.

3. What is the formula for calculating buoyancy?

The formula for calculating buoyancy is Fb = ρVg, where Fb is the buoyant force, ρ is the density of the fluid, V is the volume of the displaced fluid, and g is the acceleration due to gravity.

4. How does the shape of an object affect its buoyancy?

The shape of an object can greatly affect its buoyancy. Objects with a larger volume and a lower density will experience a greater buoyant force. This is why objects with a larger surface area, such as a barge, will float more easily than dense objects with smaller surface areas, such as a brick.

5. What is the difference between positive and negative buoyancy?

Positive buoyancy occurs when the buoyant force is greater than the weight of an object, causing it to float. Negative buoyancy occurs when the weight of an object is greater than the buoyant force, causing it to sink. Neutral buoyancy occurs when the weight and buoyant force are equal, causing an object to neither sink nor float.

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