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Introductory Mechanics Experimental Laboratory
Specific Gravity
Goals: Observe the buoyancy principle of an object in a fluid. Use the principle to find the specific gravity.
APPARATUS Specific gravity is a measure of the density of a material compared to water. The appara- tus to do this consists of a metal overflow cup with a side spigot and a beaker. If the overflow cup is filled to its limit, then an object lowered into the water will cause some of the water to spill out the side spigot. This water can be collected in the beaker and weighed.
The objects in this laboratory will be weighed by a spring scale. The spring scale mea- sures the weight of an object in newtons (N). There are two sping scales available, one with a maximum reading of 2.5 N and one with a maximum reading of 20 N. An object with a weight of more than 2.5 N must be read with the 20 N scale. If the weight is below 2.5 N switch to the 2.5 N scale.
THEORY Though they are often treated interchangeably, weight and mass are different physical properties. Mass ( m ) is a fundamental measure of the amount of matter. Weight ( w ) is a measure of the force exerted by a mass. On the surface of the earth the conversion factor is the acceleration of gravity ( g = 9.8 m/s^2 ). Thus, an object on earth has a weight related to its mass by EQ 1.
(EQ 1)
Density (ρ the greek letter “rho”) is defined as the mass ( m ) of an object divided by the volume ( V ) of the object (EQ 2). The density of a material depends on the phase it is in and the temperature. (The density of liquids and gases is very temperature dependent.) Water in the liquid state has a density (ρ w ) of about 1 g/cm^3 = 1000 kg/m^3.
(EQ 2)
w = mg
ρ m V =^ ----
2 Specific Gravity
The density of an object can be used to identify the material of the object, and to predict its behavior when placed in a fluid, either liquid or gas. If the density of an object is greater than the fluid it will sink, and if it is less than the density of the fluid it will rise. Water is the most commonly used fluid to compare material for density measurement.
The specific gravity ( SG ) is the ratio of a material’s density compared to water (EQ 3). The official specfic gravity is defined using water at 4oC. Because it is the ratio of two densities with the same units (g/cm 3 ), it has no units itself. Note that since water has a density of 1 g/cm 3 , the specific gravity is the same as the density of the material mea- sured in g/cm 3.
(EQ 3)
When an object is in a fluid there is a buoyant force acting on the object due to the pres- sure of the fluid. The buoyant force is equal to ρ w gV where g is the acceleration of grav- ity and V is the volume of the object in the liquid. Since ρ w V is equal to the mass of the water displaced by the object, this quantity is also exactly equal to the weight of the water. This is called the buoyancy (or Archimedes) principle: the buoyant force on a body immersed in a fluid is equal to the weight of the fluid displaced by the object.
If the numerator and denominator of EQ 3 is multiplied gV , and EQ 1 and 2 are used, we get EQ 4.
(EQ 4)
The last step in the equation used the buoyancy principle for the denominator. Here wout is the weight of the object out of the water, and w (^) in is the weight in water.
DATA COLLECTION Part A - Heavier than water
1. Weigh the beaker used to catch water from the overflow can, and record the value of the mass ( m 0 ) in grams. 2. Weigh each of the metal cubes (aluminum, brass, steel, lead) with a spring scale. Record these weights ( wout ) in newtons. 3. Fill the overflow can with water so that water just begins to spill out. 4. Use the spring scale to lower one metal cube into the water in the overflow can until it is completely submerged. The water should be collected in the beaker. 5. Record the weight (in newtons) of the cube while it is submerged ( w (^) in ). 6. Weigh the beaker including the water ( m 1 ) and record the mass difference due to the water m (^) w = m 1 - m 0 in grams. 7. Repeat steps 3 through 6 for each of the other metal cubes.
SG ρ ρ w =^ ------
SG ρ gV ρ w gV
-------------- w w (^) water
w (^) out w (^) out – w (^) in = = =-------------------------
