A copper (Cu) weight is placed on top of a 0.24 kg block of wood (density = 0.60 103 kg/m3) floating in water. What is the mass of the copper if the top of the wood block is exactly at the water's surface?
I will be happy to critique your thinking.
well i'm thinking to find the mass I need to find the volume of copper but i don't have any info to find that so i have no idea what to do
Density of wood is ρ₁=600 kg/m³,
density of water is ρ₂=1000 kg/m³,
m=0.24 kg,
M=?
The volume of the wooden block is
V=m/ρ₁=0.24/600=4•10⁻⁴ m³.
Mg+mg=F(buoyancy)
Mg+mg= ρ₂•V•g
M= ρ₂•V- m =1000•4•10⁻⁴-0.24=0.16 kg
To find the mass of the copper, we need to consider the buoyant force acting on the wood block.
The buoyant force is equal to the weight of the water displaced by the wood block. When the wood block is floating, the buoyant force is equal to the weight of the block.
Given that the density of the wood block is 0.60 * 10^3 kg/m^3 and the volume of the block can be calculated as its mass divided by its density, we can find the volume of the wood block:
Volume of the wood block = mass of the wood block / density of the wood block
Volume of the wood block = 0.24 kg / (0.60 * 10^3 kg/m^3)
Volume of the wood block = 0.24 kg / 600 kg/m^3
Volume of the wood block = 0.0004 m^3
Since the wood block is floating and its top is exactly at the water's surface, the volume of water displaced by the wood block is equal to the volume of the wood block.
Now, we can find the mass of the copper (Cu) by using the formula:
Mass = density * volume
The density of copper is a constant value and can be found. It is approximately 8,960 kg/m^3.
Mass of the copper = density of copper * volume of the displaced water
Mass of the copper = 8,960 kg/m^3 * 0.0004 m^3
Mass of the copper ≈ 3.584 kg
Therefore, the mass of the copper is approximately 3.584 kg.