Our group conducted water quality tests in the Greenbrier River today. These tests included dissolved oxygen, conductivity, total dissolved solids and pH. A fellow teacher made the mistake of asking why certain a rock would sink but a "larger" piece of wood would float; physics to the rescue.
Remember folks that fluid dynamics plays an important part of our daily life. And for you AP students, fluid dynamics accounts for roughly 12% of the AP Physics B exam. As such, let us entertain one of the key concepts of this study.
Archimedes principle simply states that an object is buoyed up by a force equal to the weight of the fluid it displaces. Quantitatively this can be written as Fb = mgf (force buoyancy is equal to mass times gravity of displaced fluid). However, we should remember that mass is equal to density times volume. Thus, we can think of the buoyant force as being equal to the density of the fluid times gravity times volume. The force the object applies downward is equal its mass times gravity (mg). If the object floats, the buoyant force must be equal to the weight of the object (mg). We can set theses forces equal and the density substitution and arrive at this:
volume fluid density of obj
___________ = ________________
volume obj density of fluid
This equation will serve you well, as test writers routinely will as you to determine the volume of the object submerged. It is equal to the volume of the dispaced fluid represented in this equation; I assure you this will be asked. Let' see an example of what to expect.
A wooden cube with a density of 650 kg/m^3 floats in fresh water. If an edge of the cube is 200 cm, what level or height of the cube is submerged?
Wood clearly floats well due to its density. It is no wonder most of us have seen logs travelling by way of water. And, its nothing more than a little physics making our lives easier.
Remember folks that fluid dynamics plays an important part of our daily life. And for you AP students, fluid dynamics accounts for roughly 12% of the AP Physics B exam. As such, let us entertain one of the key concepts of this study.
Archimedes principle simply states that an object is buoyed up by a force equal to the weight of the fluid it displaces. Quantitatively this can be written as Fb = mgf (force buoyancy is equal to mass times gravity of displaced fluid). However, we should remember that mass is equal to density times volume. Thus, we can think of the buoyant force as being equal to the density of the fluid times gravity times volume. The force the object applies downward is equal its mass times gravity (mg). If the object floats, the buoyant force must be equal to the weight of the object (mg). We can set theses forces equal and the density substitution and arrive at this:
volume fluid density of obj
___________ = ________________
volume obj density of fluid
This equation will serve you well, as test writers routinely will as you to determine the volume of the object submerged. It is equal to the volume of the dispaced fluid represented in this equation; I assure you this will be asked. Let' see an example of what to expect.
A wooden cube with a density of 650 kg/m^3 floats in fresh water. If an edge of the cube is 200 cm, what level or height of the cube is submerged?
Wood clearly floats well due to its density. It is no wonder most of us have seen logs travelling by way of water. And, its nothing more than a little physics making our lives easier.
Interesting post and provides physics based questions for your students.
ReplyDeleteHowever, I saw no relationship to many of the experiences of the day (Gaudineer Knob and Durbin) and the only reference to the water testing is in the blog title post.
Perhaps a good physics connection would be in the expansion of steam to move the locomotive pistons or discussions of the mechanical advantage in geared locomotives (Shay and Climax).