Question

1. A cubical block of wood (of unknown density), 10.0 cm on a side, floats at the interface between oil and water with its lower surface 1.50 cm below the interface. The density of the oil is 790 kg/m3 . (The density of water is 1000 kg/m3 .) What is the gauge pressure at the upper face of the block

Answer 1

The gauge pressure at the upper face of the block can be determined using the concept of buoyancy.

Step-by-step explanation:

The gauge pressure at the upper face of the block can be determined by using the concept of buoyancy. Buoyancy force is equal to the weight of the fluid displaced by the object. Since the block is floating, the weight of the block is equal to the buoyancy force.

To calculate the density of the wood, we need to find the height of the submerged part of the block. Given that the lower surface of the block is 1.50 cm below the interface, the height of the submerged part is 8.50 cm (10.0 cm - 1.50 cm).

Using the formula for buoyancy force: Buoyancy force = weight of displaced fluid

the gauge pressure at the upper face of the block can be calculated.

Answer 2

To calculate the gauge pressure at the upper face of a cubical block at the oil-water interface, consider the pressures exerted by the oil and the displaced water, where the weight of the block is equal to the buoyant force due to the water. Pressure is calculated using the given density of oil, the known density of water, and gravitational acceleration.

Step-by-step explanation:

To find the gauge pressure at the upper face of the cubical block floating at the interface between oil and water, we must consider the pressures exerted by both the oil and the water on the block. The pressure due to the oil layer must first be calculated:

Pressure due to oil (Poil) = height of oil layer above the block × density of oil × gravitational acceleration

Poil = (10 cm - 1.5 cm) × 10-2 m/cm × 790 kg/m3 × 9.8 m/s2

Now, considering that the block is only 1.50 cm deep in the water, only the displaced water contributes to the buoyant force, which equals the weight of the block:

Buoyant force = weight of displaced water = volume of displaced water × density of water × gravitational acceleration

Since the block is in equilibrium, the buoyant force due to the water also equals the weight of the block. Therefore, we can deduce that the pressure on the upper face of the block is equal to the pressure due to the oil layer (Poil).

However, to provide a comprehensive answer, one would need to perform the actual calculations using the formulas provided above to determine the gauge pressure.