Maximum Capacity of a Flat-Bottomed Rowboat

[enceladus_]

Homework Statement

A rectangular, flat-bottomed rowboat has a mass of 120 kg when empty. It's 3 meters long, 1 meter wide, and .24 meters deep. How many 85 kg people could it hold before swamping?

Homework Equations

d=m/v ?

The Attempt at a Solution

I need to determine the average density, then compare to the density of water. I know the density of water...I know this isn't that hard. I need the average density of the boat + x people.

 

[haruspex]

What volume of water is displaced just before swamping?

 

[cepheid]

Remember Archimedes' principle? The buoyant force on the boat is equal to the weight of the water that is displaced by the boat. And the amount of water displaced by the boat is equal to the submerged volume of the boat. The submerged volume is l*w*x, where l*w = 3 m², and x is the depth by which it is submerged. So, when x is equal to 0.24 inches, you start taking on water and you sink.

For it to be balanced (floating), the weight of the displaced water (buoyant force) has to be equal to the combined weight of the boat + people.

(density of water)*(l*w*x) = (weight of boat + people)

 

[enceladus_]

(3*1*.24)(1000 kg/m3) = 720 kg/m3

85 * 7 = 595 kg

595 + 120 = 715 kg

My answer is 7 people, but I know from the video that my answer is wrong...

Is the mass of the displaced fluid more than the mass of the object...

 

[haruspex]

Your answer looks right to me.

 

[enceladus_]

The answer they have is:

"It could hold 6 people, 590 kg, not counting the boat."

Could they have messed up? 85 * 6 = 510 kg.

 

[haruspex]

The answer they have is:

"It could hold 6 people, 590 kg, not counting the boat."

Could they have messed up? 85 * 6 = 510 kg.

Maybe, or is it a matter of one rower and six passengers?

 

[enceladus_]

I don't think so. A rower is not mentioned in the problem. That is so weird though. I can't believe that there would be a mistake like that.

 

[cepheid]

Sounds like either a typo or arithmetic error on the part of "them", whoever they are. After all, they got the. 590 kg part right.

 

[enceladus_]

Thank you all very much. I appreciate your time and wisdom very much!