Question

(Figure 1) shows a container with a cross-section area of 15 cm^2 in which a layer of water floats on top of a layer of mercury. A 1.0 kg wood block with a cross-section area of 10 cm^2 floats on the water. The water depth, measured from the bottom of the block, is 25 cm. A pressure gauge at the bottom of the container reads 26 kPa.

A container with vertical walls is filled with a layer of mercury of height h at the bottom and a layer of water above it. A rectangular block of 1.0 kilogram floats on the water. The distance from the mercury layer to the bottom side of the block is 25 centimeters. The area of the horizontal cross section of the block is 10 square centimeters. The area of the bottom of the container is 15 square centimeters. A pressure gauge is located at the bottom of the container.
Part A
What is the depth dm of the mercury? Use ρw = 1000 kg/m3 as the density of water and ρm = 13,600 kg/m3 as the density of mercury.

Answer 1

To find the depth dm of the mercury, use the equation for pressure in a fluid: P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth. The depth of the mercury is 2.65 m or 265 cm.

Step-by-step explanation:

To find the depth dm of the mercury, we can use the equation for pressure in a fluid: P = ρgh, where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth.

In this case, the pressure gauge reads 26 kPa, which is equivalent to 26000 Pa. The density of water is ρw = 1000 kg/m³ and the density of mercury is ρm = 13600 kg/m³.

We can rearrange the equation to solve for h: h = P / (ρg).

Plugging in the values, we get: h = 26000 Pa / (1000 kg/m³ * 9.8 m/s²) = 2.65 m.

Converting this to centimeters, we get: dm = 265 cm.