How Much Water Does a 115578 Ton Cargoship Displace?

[Zaphbeebl]

Homework Statement

I've been working as part of a study group, but I doubt that the result we reached in class is correct, so would someone check our work?

The problem statement: A cargoship weighs in at 115578 ton and lies still in the ocean. The density of the saltwater is given at 1030 kg/m³
what is the area of the water displaced by the weight of the cargoship?

Homework Equations

This is the part where I'm somewhat uncertain, since we simply used math tools. This is also the area in which any help would be extremely usefull

The Attempt at a Solution

The attempt at this was:

converting the ships weight to kilograms: 115578 ton = 115578000 kg

Then dividing the weight by the density:
115578000kg/1030 (kg/m³) = 112211,65 m³

 

[mgb_phys]

correct, except you mean the VOLUME of water displaced, not AREA
And you have too many decimal places in you answer, you only know the density to an accuracy of four significant figures so your answer can only be that accurate.
eg 112200m^3

 

[kerimek]

Hello, thank you for reaching out for assistance. I would be happy to review your work and provide feedback.

Firstly, it is important to note that buoyancy is a force that acts on an object immersed in a fluid, in this case the cargoship in the ocean. This force is equal to the weight of the fluid displaced by the object. Therefore, in order to determine the area of water displaced by the weight of the cargoship, we must first calculate the buoyant force acting on the ship.

Using the given information, we can calculate the volume of the ship using the formula V = m/ρ, where V is volume, m is mass, and ρ is density. Converting the ship's weight to kilograms, we get 115,578,000 kg. Dividing this by the density of saltwater (1030 kg/m3), we get a volume of 112,211.65 m3.

Next, we can calculate the buoyant force using the formula 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 (9.8 m/s2). Plugging in the values, we get a buoyant force of approximately 1,098,000 N.

Now, to determine the area of water displaced by the weight of the cargoship, we can use the formula A = Fb/ρg, where A is the area, Fb is the buoyant force, ρ is the density of the fluid, and g is the acceleration due to gravity. Plugging in the values, we get an area of approximately 11,200 m2.

In conclusion, the area of water displaced by the weight of the cargoship is approximately 11,200 m2. I hope this helps clarify any doubts you may have had about your work. If you have any further questions or concerns, please do not hesitate to ask. Keep up the good work in your studies!