How can I solve two fluid problems involving a raft and pressure?

[insideout]

Hey, these two questions are off a take home test I was given. I could use a good grade on them so could anyone give me a hand? thanks

A raft with a length of 8.0m, a width of 1.6m, a thickness of 0.11m, and a density of 690.0kg/m^3 is placed in a river. How far below the water's surface does the bottom of the raft sink? (recall that fresh water has a density of 1.00x10^3 kg/m^3)

The absolute pressure below the surface of a freshwater lake is 2.43 x 10^5 Pa. At what depth does this pressure occur? Assume that atmospheric pressure is 1.01 x 10^5 Pa and that the density of the water is 1.00 x 10^3 kg/m^3.

 

[AtticusFinch]

So the buoyant force is equal to the weight of the water displaced right? If the raft floats the buoyant force is equal and opposite of the weight of the raft.

Find the weight of the raft and find how much water must be displaced. Then you can find the volume of the raft needed to be below the surface and consequently, how far it sinks.

Your second question is easy. Remember what absolute pressure is and how pressure changes with depth in a fluid.

 

[insideout]

alright so i figured out the second one, but I am really at a loss for the first one. could someone show step by step how to do it? thanks :D

 

[AtticusFinch]

alright so i figured out the second one, but I am really at a loss for the first one. could someone show step by step how to do it? thanks :D

Buoyancy is equal to \rho_{water}gV_{dis}. Find the weight of the raft. Set that equal to the preceding equation and find the volume of water displaced. The raft has a constant area so find how far down the raft must go to displace the appropriate volume of water.