What is the apparent weight of a 36 kg block of aluminum (density 2700 kg/m3) completely submerged in a fluid with density 1300 kg/m3?

To find the apparent weight of the block of aluminum completely submerged in the fluid, we need to consider the buoyant force acting on the block. The apparent weight of an object in a fluid is equal to its actual weight minus the buoyant force.

The buoyant force is given by the formula:

Buoyant force = density of the fluid × volume of the displaced fluid × acceleration due to gravity

In this case, the block of aluminum is completely submerged in the fluid, which means it displaces a volume of fluid equal to its own volume. The volume of the block can be calculated using its density and mass:

Volume of the block = mass of the block / density of the block

Applying the given values, we can calculate the volume of the block:

Volume of the block = 36 kg / 2700 kg/m3

Next, we calculate the buoyant force:

Buoyant force = density of the fluid × volume of the block × acceleration due to gravity
= 1300 kg/m3 × (36 kg / 2700 kg/m3) × 9.8 m/s2

Finally, we can find the apparent weight by subtracting the buoyant force from the actual weight of the block:

Apparent weight = actual weight - buoyant force
= mass of the block × acceleration due to gravity - buoyant force

Substituting the values:

Apparent weight = 36 kg × 9.8 m/s2 - (1300 kg/m3 × (36 kg / 2700 kg/m3) × 9.8 m/s2)

Therefore, the apparent weight of the 36 kg block of aluminum completely submerged in the fluid with a density of 1300 kg/m3 is the answer to the calculation.