A piece of metal with an irregular shape has a mass of 4.281kg. When weighed while submerged in water, the piece of metal has an apparent mass of 4.000kg. What is the density of the metal? (Ans: 1.52x10⁴ kg/m³)
so it displaces .281 kg of water ... 281 cm^3
density = mass / volume = 4281 g / 281 cm^3
4.281 - 4.000 = 0.281 kg of water displaced.
0.281kg * 1m^3/1000kg = 2.81*10^-4 m^3 = Vol. of water displaced = Vol. of metal submerged.
Density = 4.281kg/2.81*10^-4m^3 = 1.52 *10^4 kg/m^3.
To find the density of the metal, we can use the concept of buoyancy. When an object is submerged in a fluid, it experiences an upward buoyant force equal to the weight of the fluid displaced by the object. This buoyant force reduces the weight of the object, resulting in an apparent mass when weighed underwater.
The difference between the mass of the object in air and its apparent mass underwater is equal to the weight of the fluid displaced.
In this case, the mass of the metal in air is 4.281 kg, and its apparent mass underwater is 4.000 kg. The difference in these masses is 0.281 kg.
To find the density, we need the volume of the metal. The volume can be calculated using the formula:
Volume = (Mass in air)/(Density of water) = (4.281 kg)/(1000 kg/m³) = 0.004281 m³
Now we can find the density of the metal using the formula:
Density = (Mass in air)/(Volume) = 4.281 kg/0.004281 m³ = 1000 kg/m³
Therefore, the density of the metal is 1000 kg/m³ (or 1x10⁴ kg/m³ in scientific notation).
To find the density of the metal, we need to use the concept of buoyancy. When an object is submerged in a fluid, it experiences an upward force called buoyant force, which is equal to the weight of the fluid displaced by the object.
Here's how we can calculate the density of the metal:
Step 1: Find the weight of the metal
The apparent weight of the metal in water is given as 4.000 kg. This is the weight of the metal minus the buoyant force acting on it.
Weight of metal = apparent weight of metal in air - buoyant force
Weight of metal = 4.000 kg
Step 2: Find the weight of the displaced water
The buoyant force acting on the metal is equal to the weight of the water displaced by the metal.
Weight of water displaced = apparent weight of metal in air - weight of metal
Weight of water displaced = 4.281 kg - 4.000 kg
Weight of water displaced = 0.281 kg
Step 3: Calculate the volume of the submerged metal
The volume of the submerged metal can be calculated using the density of water and the weight of water displaced.
Density of water = 1000 kg/m³ (approximately)
Volume of submerged metal = weight of water displaced / density of water
Volume of submerged metal = 0.281 kg / 1000 kg/m³
Volume of submerged metal = 0.000281 m³
Step 4: Calculate the density of the metal
The density of the metal can be calculated using the mass of the metal and the volume of the submerged metal.
Density = mass of metal / volume of submerged metal
Density = 4.281 kg / 0.000281 m³
Density = 15209.964 kg/m³
Rounding off to the appropriate significant figures, the density of the metal is approximately 1.52 x 10⁴ kg/m³.