What is the likely identity of a substance (see Table 10-1) if a sample has a mass of 9.38 g when measured in air and an apparent mass of 8.55 g when submerged in water?
A)Copper
B)Iron or steel
C)Aluminum
D) Lead
E)Concrete
F)Gold
assume a volume d.So the mass of the volume displaced is v*1g/cm^3
mass object=9.38
masssubmerged+masswaterdisp=9.38
8.55+v*1g/cm^3=9.38
solve for volume v
density=mass/volume=9.38/volume
then, compare that number with the mass of the elements/substances above.
To determine the likely identity of the substance, we need to first understand the concept of buoyancy and how it affects the apparent mass of an object when submerged in water.
When an object is submerged in a fluid, it experiences an upward force called buoyant force. The magnitude of this force is equal to the weight of the fluid displaced by the object. This buoyant force reduces the apparent weight of the object when submerged.
In this case, the substance has a mass of 9.38 g when measured in air and an apparent mass of 8.55 g when submerged in water. The difference in mass (9.38 g - 8.55 g = 0.83 g) represents the weight of the water displaced by the object.
By comparing the density of the object with the densities of common substances, we can determine the likely identity of the substance.
Let's go through the options:
A) Copper: The density of copper is approximately 8.96 g/cm^3.
B) Iron or steel: The density of iron is approximately 7.87 g/cm^3, and the density of steel varies depending on its composition.
C) Aluminum: The density of aluminum is approximately 2.70 g/cm^3.
D) Lead: The density of lead is approximately 11.34 g/cm^3.
E) Concrete: The density of concrete varies depending on its composition, but it typically ranges from 2.30 g/cm^3 to 2.60 g/cm^3.
F) Gold: The density of gold is approximately 19.32 g/cm^3.
Comparing the densities, we can see that the density of the substance must be less than the density of water, which is approximately 1 g/cm^3.
Therefore, the likely identity of the substance is C) Aluminum. Aluminum has a lower density than water, so it would displace less mass and result in a smaller apparent mass when submerged.
To determine the likely identity of the substance, we need to compare the mass of the sample in air to its apparent mass when submerged in water.
In this case, the mass of the sample in air is 9.38 g, and its apparent mass when submerged in water is 8.55 g.
The difference in mass between the sample in air and when submerged in water is due to buoyancy. When an object is submerged in a fluid, it experiences an upward force called buoyant force, which reduces its effective weight.
To find the buoyant force, we can use Archimedes' principle, which states that the buoyant force on an object immersed in a fluid is equal to the weight of the fluid displaced by the object.
By subtracting the apparent mass (8.55 g) from the actual mass (9.38 g), we find that the difference is 0.83 g.
Since the apparent mass is less than the actual mass, this indicates that the buoyant force is less than the weight of the substance. This suggests that the substance is denser than water since a denser substance displaces less water and experiences less buoyancy.
Based on the provided options, the most likely identity of the substance is lead (option D). Lead is a dense metal with a density higher than that of water. When submerged in water, it would experience a small but noticeable loss of weight due to the buoyant force being slightly less than the weight of the lead sample.
To be more certain about the substance's identity, one could confirm this by comparing the density of lead with the density of the other options listed in Table 10-1. The substance with a density closest to the calculated density of the sample would be the likely identity.