Question 52

[matthew]

Dear Dr. Ferdinand,

You mentioned in the solns. that the volume displaced equals the area of the tank and the height. Can you please show this by equations? I can't seem to see the connetion.

Thinking... I understand that pressure is force over area and buoyant force is density times volume displaced times gravity, and pressure is also delta h times gravity times density, but where does area come in?

[matthew]

okay I got problem I asked, but still dont't know why we are using the 10^3 instead of 1kg/m^3? Otherwise everything else made sense.

Basically this problem wants you to be able to remember the buoyant force formula, the pressure (force over area) and pressure depth eqn and put them equal to each other. The rest is just plug and move on.

[admin]

8 - 20% of Physical Sciences real MCAT CBT questions involve calculations. Sometimes it will just be "plug and chug" but sometimes you have to visualize the problem in order for it to make sense.

The passage and some previous questions have already established the relationship with the height of the water and the pressure below. Well, let's consider what happens when some wood falls into the tank. We are told that it displaces a certain volume of water. In other words, the water level of the tank must rise a bit. Once we can figure out by what height h the water rises, then we can plug and chug to determine by how much the pressure increases at the bottom.

So we know the volume of water displaced but we need the height. Well, a cylindrical tank is circular when you look at it from the top (area of a circle) and it has depth (height h). The volume in the tank, therefore, is the area of a circle (pi r^2) times h.

Known values:

Volume change: 0.5 m^3
pi : 3.14
Radius r of the tank (see passage): 8 m

Thus height h can be calculated.