A piece of metal, when weighed in air, has a weight of 20.7 N. When completely submerged in blood (ĉ = 1060 kg/m3), the metal has a weight of 12.7 N. Based on the values from table 11.1 in the text, what is the most likely metal?
Here is the answer but I need help with the steps of equations to use.
Aluminum (closest density to the calculated 2740 kg/m3 of the metal)
weightinblood=20.7-volumeblood*1060
solve for volume blood
density=20.7/volumeblood
To determine the most likely metal, we can use the concept of buoyancy and Archimedes' principle. Archimedes' principle states that an object submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the object.
Let's start by calculating the buoyant force acting on the metal when it is submerged in blood. We can use the equation:
Buoyant force = Weight of the fluid displaced by the metal
Given that the weight of the metal when submerged is 12.7 N and the density of blood (ƒâ) is 1060 kg/m³, we can rearrange the equation to solve for the weight of the fluid displaced:
Weight of the fluid displaced = Buoyant force = 12.7 N
Next, we need to determine the volume of the metal. We can use the equation:
Volume of metal = (Weight of the metal in air) / (Density of the metal)
Given that the weight of the metal in air is 20.7 N and the density of the metal is unknown, we rearrange the equation to solve for the density:
Density of the metal = (Weight of the metal in air) / (Volume of metal)
Now, let's substitute the known values into the equation to calculate the density of the metal:
Density of the metal = 20.7 N / (Volume of metal)
Finally, we can compare the calculated density of the metal to the values from table 11.1 in the text to determine the most likely metal. In this case, the closest density to the calculated 2740 kg/m³ is aluminum.
Therefore, based on the values from table 11.1 in the text, the most likely metal is aluminum.