A solid rectangular block measures 0.100m x 0.080m x 0.060m and float freely in a liquid of density 13546kg/m³. If the depth of liquid is 0.045m up the block largest side find the density of the block...
Don't know what to do
Show step
Yes
Hurray
find the volume of the block V = 0.100m * 0.080m * 0.060m
then its mass is Rho * V
find the mass of liquid displaced M = 13546 * 0.100m * 0.080m * 0.045m
which Archimedes says is the mass of the block.
then Rho = M/V
Sir Damon I got
Answer=10,159.5?
I still can't get my answer
Hurray my problem has been solved i got my answer
10,159.5
10159.5
To find the density of the block, we can use the principle of buoyancy. Buoyancy is the upward force exerted on an object immersed in a fluid, which is equal to the weight of the fluid displaced by the object.
The weight of the fluid displaced can be calculated using the formula:
Weight of fluid displaced = density of fluid x volume of the fluid displaced
In this case, the fluid is the liquid in which the block is immersed, and the volume of the fluid displaced is equal to the volume of the block that is submerged in the liquid.
First, let's calculate the volume of the block:
Volume of the block = length x width x height
Volume of the block = 0.100m x 0.080m x 0.045m
Now that we know the volume of the block, we can calculate the weight of the fluid displaced by the block using the formula mentioned earlier.
Weight of fluid displaced = density of fluid x volume of the fluid displaced
Weight of fluid displaced = 13546kg/m³ x volume of the block
Now, since the block is floating freely in the liquid, the buoyant force exerted on the block is equal to the weight of the fluid displaced. Therefore, the buoyant force can be calculated as:
Buoyant force = weight of fluid displaced
We can equate the buoyant force to the weight of the block to solve for the density of the block.
Now, the weight of the block can be calculated using the formula:
Weight of the block = density of the block x volume of the block
Since the block is in equilibrium and not sinking or rising, we can conclude that the weight of the block is equal to the buoyant force.
Setting the weight of the block equal to the buoyant force, we have:
Weight of the block = Buoyant force
density of the block x volume of the block = density of fluid x volume of the block
Now we have:
density of the block = (density of fluid x volume of the block) / volume of the block
Plugging in the values, we can calculate the density of the block:
density of the block = (13546kg/m³ x volume of the block) / volume of the block
Simplifying the equation, we find:
density of the block = 13546kg/m³
So, the density of the block is 13546kg/m³.