Question

1. a piece of wood floats in ethanol but sinks in gasoline. give a range of possible densities for the wood.

Explanation:

Step1: Recall buoyancy - density relationship

An object floats in a fluid if its density ($
ho_{object}$) is less than the density of the fluid ($
ho_{fluid}$), and sinks if $
ho_{object}>
ho_{fluid}$.

Step2: Identify fluid densities

The density of ethanol is approximately $
ho_{ethanol}=0.789\ g/cm^{3}$, and the density of gasoline is approximately $
ho_{gasoline} = 0.70 - 0.78\ g/cm^{3}$.

Step3: Determine wood - density range

Since the wood floats in ethanol, $
ho_{wood}<
ho_{ethanol}=0.789\ g/cm^{3}$. Since the wood sinks in gasoline, $
ho_{wood}>
ho_{gasoline}$. Taking the upper - bound of gasoline density, we get that the density of the wood $
ho_{wood}$ satisfies $0.78\ g/cm^{3}<
ho_{wood}<0.789\ g/cm^{3}$.

Answer:

The density of the wood is in the range $0.78\ g/cm^{3}<
ho_{wood}<0.789\ g/cm^{3}$