Maximum Capacity of a Flat-Bottomed Rowboat

In summary, the conversation discusses the question of how many 85 kg people a rectangular rowboat can hold before swamping. The solution involves determining the average density of the boat and comparing it to the density of water. It is determined that the boat can hold 7 people, but the given answer states it can only hold 6 people, possibly due to a mistake in their calculation.
  • #1
enceladus_
58
0

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.
 
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  • #2
What volume of water is displaced just before swamping?
 
  • #3
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)
 
  • #4
(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...
 
Last edited:
  • #5
Your answer looks right to me.
 
  • #6
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.
 
  • #7
enceladus_ said:
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?
 
  • #8
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.
 
  • #9
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.
 
  • #10
Thank you all very much. I appreciate your time and wisdom very much!:smile:
 

Related to Maximum Capacity of a Flat-Bottomed Rowboat

1. What is Fluid Statics Boat Problem?

Fluid Statics Boat Problem is a physics problem that involves calculating the buoyant force acting on a boat that is partially submerged in a fluid, such as water. It is used to determine whether a boat will float or sink based on its weight and the weight of the fluid it displaces.

2. How is the buoyant force calculated in Fluid Statics Boat Problem?

The buoyant force can be calculated using Archimedes' principle, which states that the buoyant force acting on an object is equal to the weight of the fluid it displaces. In the case of a boat, the buoyant force is equal to the weight of the water that is displaced by the submerged part of the boat.

3. What factors affect the buoyant force in Fluid Statics Boat Problem?

The buoyant force is affected by the density of the fluid, the volume of the submerged part of the boat, and the gravitational force acting on the boat. As the density or volume of the fluid increases, the buoyant force also increases. However, as the gravitational force acting on the boat increases, the buoyant force decreases.

4. How can the stability of a boat be determined in Fluid Statics Boat Problem?

The stability of a boat can be determined by comparing the center of mass of the boat to the center of buoyancy. If the center of mass is below the center of buoyancy, the boat will be stable and will not overturn. However, if the center of mass is above the center of buoyancy, the boat will be unstable and may capsize.

5. Can Fluid Statics Boat Problem be applied to other objects besides boats?

Yes, the principles of Fluid Statics Boat Problem can be applied to any object that is partially or fully submerged in a fluid. This includes objects such as submarines, hot air balloons, and even human bodies in water. The same principles of buoyancy and stability apply to these objects, making Fluid Statics Boat Problem a versatile and useful tool in physics.

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