Calculating Boat Submersion and Fish Capacity

[daisyi]

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!

 

[Doc Al]

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 buoyant 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?

 

[daisyi]

so the buoyant 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?

 

[Doc Al]

so the buoyant 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?)

 

[daisyi]

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!

 

[Doc Al]

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!