A baseball that lands in a lake (water) experiences a buoyant force of approximately 2N while submerged. A baseball’s mass is specified as 142-149g, or 5-5¼ oz., according to the official rules of baseball. What is the specific gravity of bromine if the same baseball experiences a buoyant force of 6.2N while submerged after landing in an open vat of liquid bromine at a nearby chemical factory?
The buoyant force exerted on an object by a fluid is given by the equation F=ρVg, where ρ is the density of fluid displaced by an object, V is the volume of fluid displaced, and g is gravitational acceleration. Specific gravity is the ratio of fluid density to density of water, and the student should know the density of water as 1 g/cm3 or 1000kg/m3.
The buoyant force in water is Fwater=ρwaterVbaseballg, and the buoyant force in bromine is Fbromine=ρbromineVbaseballg. Since specific gravity is ρbromine/ρwater, and all other variables are constant in the two buoyant force expressions, the specific gravity of bromine for this problem is equal to Fbromine/Fwater. 6.2N/2N equals SGbromine= 3.1.
a) 1.5, incorrect, This is the approximate weight of the baseball in newtons.
b) 3.1, correct.
c) 4, incorrect, This is the buoyant force in bromine divided by the ball’s weight in newtons.
d) 40, incorrect, This is the buoyant force in bromine divided by the ball’s mass in grams.