How does oil affect the buoyant force of a block of wood versus water?

[agw]

Hi, I'm having trouble with a conceptual problem:

Homework Statement

There is a block of wood in a jar with water; it is floating. If I pour oil into the container, obviously the oil sits at a layer above the water. The wooden block touches the water, oil and air now. Did the volume of the block in air decrease/increase/stay the same after adding oil?

Homework Equations

FB = ρvg

The Attempt at a Solution

I thought that since the block is still floating, that the force of gravity (Fg) and the buoyant force (FB) are still balanced. With this, you can see that the block of wood displaces the same weight of fluid. Since oil is less dense than water, (a smaller ρ), "v" (in this equation FB = ρvg) must increase since FB is unchanged.

Do have the concepts wrong? Is this a correct explanation of what would happen?
Thank you!

 

[Jolb]

I think you are getting the concept of buoyancy just fine, but you're missing what the question is asking for. They're asking about how much of the block is sticking up into the air, as opposed to how much of the block is submerged in the oil/water.

Think of it like this: if the block floats when there is only water and air, then it must displace a certain volume v such that the displaced volume's weight cancels the gravitational force on the block. If instead the block first sinks through some oil, then a greater displaced volume of oil is required for the same buoyant force. [We know the oil is lighter than the water since the oil forms a layer on top of the water.] So the block has to sink lower down into the oil to get the same buoyant force (or, equivalently, sinking a given distance into oil provides less buoyant force than sinking the same distance into water)--and hence less of the block sticks up into the air.