Northern Illinois University
Physics 150
Lab 9 Recitation
Specific Gravity
Pressure/Specific Gravity
Definition of...
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Density = mass/volume
Specific Gravity = ratio of an object's (or material’s) density to the density of water
Pressure = Force per unit surface area
Weight = Force on an object due to gravity, evaluated by multiplying the object's mass
by the acceleration due to gravity.
Mass = a fundamental property of material; a measure of inertia
Experimental Fact: All fluids (water, molasses, air, etc.) exert pressure in all directions.
Typical atmospheric pressure (the pressure that results from the volume of air "piled" up on top
of the face of the Earth) exerts a little less than 15 pounds (force) per square inch. The fact that
we are able to extend our arms straight outward and support this much pressure (15 pounds per
square inch times approximately 100 square inches would result in us having to "lift" over 1500
pounds!) should be seen as evidence that the pressure is exerted in all directions, up against the
underside of our arms as well as down on the top of them.
You're no doubt familiar with the phenomenon of the "thinning" of air at higher altitudes.
Have you ever stopped to think why this is so? The "thinner" nature of air is simply a result of
less air being "piled up" on top of you. Less air means less fluid pushing down which in turn
means less pressure. Conversely, air is most dense at sea level.
Taking this concept a step further, let's apply it to water. Like air, water is a fluid. The higher
we stack the water on top of something, the greater the pressure on that something. This explains
why a scuba diver's breathing air must be compressed to a high pressure. In order to force it into
the lungs of the grateful diver, the air must be of a pressure at least as great as that applied to the
outside of the diver by the "stack" of water on top of him or her.
We should conclude that the lower we go in a fluid, be it water or air, the greater the pressure
is on us due simply to the weight of the fluid on top of us.
Buoyancy
Possibly you've had the opportunity to experience the ease with which large floating objects
can be lifted in water. These objects, too heavy to move on dry land, become maneuverable once
in water. Why exactly is this true?
We must conclude that, somehow, objects weigh less in water than they do on land. But how
can that be? After all, it's the same object. Well if the mass hasn't changed, something must be
helping us. Something must be pushing up on the object. And indeed something is! It is called
buoyant force and we need to figure out where it comes from.
If we accept that the pressure experienced by a submerged object is, according to our
previously stated definition, a force per unit area, we can evaluate the pressure. Remembering
first the difference between mass and weight (mass is a fundamental property--the same
anywhere versus weight which is a force, the product of mass times gravity), we note that the
buoyant force on an object is merely the weight of the "piled up" fluid. If we multiply that
weight times the surface area of our submerged object, we find the pressure:
Pressure = Force ÷ Area
Force = Weight of the column of fluid above the surface area
It may be subtle, but you can at this point spot the source of the buoyant force. Noting that the
pressure is a function of the weight of the fluid column above an object, it stands to reason that
the force is greater at greater depths. Combine this with the previously agreed upon phenomenon
of exertion of pressure in all directions, you can conclude that the force pushing up on the
bottom of an object is greater than the force pushing down on top of the object. This difference,
however slight, is the source of what we call buoyant force.
Further, if we evaluate the difference between the force on the top and the force on the bottom,
we find that it exactly equals the weight of the displaced fluid! In other words, if we know the
volume of our submerged object, we could use the definition of density to convert to the mass of
the fluid being displaced (the fluid into which we've placed our object). By multiplying the
resulting number by the acceleration of gravity, we have the weight of the displaced fluid and the
buoyant force on the object! This is known as Archimedes Principle, named after the great Greek
scientist.
Floater or Sinker?
If the only forces acting on an object placed in a fluid are weight (mass x the acceleration of
gravity) acting downward and buoyant force acting upward, it stands to reason that if the weight
is less than buoyant force, the object will float. Conversely, if buoyant force is less than weight,
the object will sink. Expressed in ratio form, we note that if an object (made from a particular
material) has a specific gravity that is less than one, it floats. If the specific gravity is greater
than one, it is a sinker. Note that we speak here of a generic "hunk" of material. We can, of
course, fashion the material into a shape that will enable it to float. Ever heard of a cement
canoe? The key to understanding why this is so is to remember that the buoyant force on an
object is equal to the weight of the fluid displaced. Can an object be shaped so that it displaces
water efficiently?