A block of metal floats in oil of density 700Kg/m3 with 3/4 of volume in mass. Find the density of metal.
displacement mass: 3/4 V*700kg/m^3
because this also equals the mass of the metal...
density metal= massabaove/V= .75*700kg/m^3
Well, let us assume that the block has a volume of one cubic meter.
Then 0.75 cubic meter is in the oil.
The mass of the block is then 0.75 * 700 = 525 kg
so mass/volume =
525 kg/1m^3 = 525 kg/m^3
Thanks alot, bobpursley and Damon. But I didn't understand where did we get the mass 1cm'3. Please, help.
To find the density of the metal, we need to understand the concept of buoyancy.
Buoyancy is an upward force that acts on an object submerged in a fluid (liquid or gas). This force is equal to the weight of the displaced fluid. If the buoyant force is greater than the weight of the object, it will float; if it is less, the object will sink.
In this case, the block of metal is floating in the oil. This means that the buoyant force is equal to the weight of the block of metal. We can set up an equation to represent this:
Buoyant force = Weight of the block of metal
Now let's calculate the buoyant force:
Buoyant force = Density of oil * Volume of displaced oil * Acceleration due to gravity
Given that the density of oil is 700 kg/m^3 and 3/4 of the block of metal's volume is submerged, we can calculate the volume of displaced oil as follows:
Volume of displaced oil = (3/4) * Volume of the block of metal
Now, let's calculate the weight of the block of metal:
Weight of the block of metal = Density of metal * Volume of the block of metal * Acceleration due to gravity
Since the weight of the block of metal is equal to the buoyant force, we can set up an equation:
Density of oil * Volume of displaced oil * Acceleration due to gravity = Density of metal * Volume of the block of metal * Acceleration due to gravity
We can cancel out the acceleration due to gravity on both sides of the equation, and rearrange it to solve for the density of the metal:
Density of metal = (Density of oil * Volume of displaced oil) / Volume of the block of metal
Plug in the given values:
Density of metal = (700 kg/m^3 * (3/4) * Volume of the block of metal) / Volume of the block of metal
The volume of the block of metal cancels out, leaving us with:
Density of metal = 700 kg/m^3 * (3/4)
Now, let's simplify the expression:
Density of metal = 525 kg/m^3
Therefore, the density of the metal is 525 kg/m^3.