Calculating Boat Submersion and Fish Capacity

In summary, the problem involves finding the amount that a rectangular boat will sink into fresh water when a 98kg person jumps in. To solve this, we use Archimedes' principle and realize that the buoyant force must equal the weight of the displaced water. Knowing that the boat and person weigh a total of 173kg, we can calculate the volume of water that must be displaced and therefore the amount that the boat will sink. For part b, we can also use this information to determine the number of 2kg fish that can be caught before the boat sinks. However, the wording of the problem may be vague and may require the use of the total weight of the boat and person for part a.
  • #1
daisyi
32
0
okay, here's the problem as stated:

A rectangular boat is 2m long and 0.8m wide and 0.2m high and weights 75kg. If the boat is in fresh water, find (a) the amount that it will sink into the water when Squink (98kg) jumps in, and (b) the number of 2kg fish he can catch before the boat sinks.

If I can get the first part figured out, the second part sh ouldn't be that difficult, but I can't for the life of me figure out the first part.

any help would be greatly appreciated!
 
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  • #2
buoyant force

Welcome to PF!

Think of Archimedes' principle: The buoyant force that the water exerts on the boat equals the weight of the displaced water. Then realize that for the boat to float in equilibrium the bouyant force must equal the weight of whatever is floating.

So... how much additional water must the boat displace to support the added weight of Squink? And how far does the boat have to sink in the water to displace that much water?
 
  • #3
so the bouyant force must equal a total of 173kg in order to support the boat and Squink. To find the amount the boat had to sink in order to support the extra weight, it is necessary to first find the amount of the boat under water before the extra weight was added and then subtract that from the amount the boat is under water afterwards.

the only way I could figure to measure how far the boat is under water is by dividing the volume of the boat by the density of water, thereby getting 99.9% of the boat underwater before Squink. After Squink it would be 99.83% of the boat is under water.

Calculating these amounts with the .20cm height of the boat gives a difference of .06cm, which is not the correct answer according to the packet.

Is my logic completely off here or what?
 
  • #4
daisyi said:
so the bouyant force must equal a total of 173kg in order to support the boat and Squink.
That's correct.
To find the amount the boat had to sink in order to support the extra weight, it is necessary to first find the amount of the boat under water before the extra weight was added and then subtract that from the amount the boat is under water afterwards.
No. It's easier than that. How much additional water (in kg) must be displaced to support an additional mass of 98 kg? Answer: 98 kg! Now, how much volume is that? (What's the density of water?) Since the boat is rectangular, what height along its side will give you that volume of water? (Volume = area X height; what's the area of the boat bottom?)
 
  • #5
thanks so much :)

figured that one out, and easily figured out the fish problem.

the problem in the packet did, however, require the use of the total weight of the boat and Squink. it didn't seem like it would from the way it was worded, but it did.

Thanks again!
 
  • #6
daisyi said:
the problem in the packet did, however, require the use of the total weight of the boat and Squink. it didn't seem like it would from the way it was worded, but it did.

Thanks again!
Part b certainly requires the total weight, but not part a. (Unless they meant the total amount that the boat sinks in the water for part a. It was worded vaguely. I was interpreting it to mean just the added amount that it will sink when Squink jumps on.)

And you are welcome!
 
Last edited:

1. How does the weight of a boat affect its ability to float?

The weight of a boat affects its ability to float because it determines the buoyancy force acting on the boat. The buoyancy force is equal to the weight of the water displaced by the boat. If the boat is too heavy, it will displace less water and have a lower buoyancy force, making it more difficult for the boat to float.

2. Can a boat sink if too much weight is added to it?

Yes, a boat can sink if too much weight is added to it. As mentioned before, the buoyancy force is determined by the weight of the water displaced by the boat. If the weight of the boat (including any added weight) exceeds the weight of the water it displaces, the boat will sink.

3. How does the shape of a boat affect its ability to float with weight?

The shape of a boat plays a significant role in its ability to float with weight. Boats with wider hulls have a larger surface area, which allows them to displace more water and have a higher buoyancy force. Additionally, the shape of the hull can also affect the stability of the boat, which can impact its ability to stay afloat with added weight.

4. Is there a maximum weight a boat can carry while still remaining afloat?

Yes, there is a maximum weight that a boat can carry while still remaining afloat. This weight is determined by the boat's buoyancy force, which is based on the weight of the water it displaces. If the weight of the boat and its cargo exceeds this buoyancy force, the boat will sink.

5. How does the distribution of weight on a boat affect its stability?

The distribution of weight on a boat can significantly impact its stability. If the weight on one side of the boat is greater than the other, it can cause the boat to tip over. Additionally, the distribution of weight can also affect the center of gravity of the boat, which can impact its overall stability and ability to remain afloat.

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