A rectangular parallelepiped with a square base d = 0.260 m on a side and a height h = 0.120 m has a mass m = 6.70 kg. While this object is floating in water, oil with a mass density ?o = 710 kg/m3 is carefully poured on top of the water until the situation looks like that shown in the figure. Determine the height of the parallelepiped in the water. This diagram illustrates a wooden block partially submerged in a container filled with two immiscible liquids: oil and water. Key Features:1. **Block Dimensions**: The block is represented as a cube with side length \( d \).2. **Liquid Layers**: - The upper layer consists of oil. - The lower layer consists of water.3. **Submersion Heights**: - \( h \): The height of the block submerged in the water. - \( h_o \): The height of the block submerged in the oil. - \( h_w \): The exposed height of the block above the water's surface.This setup can be used to study principles such as buoyancy, density differences between the two fluids, and the equilibrium of floating objects. The forces acting on the block include the buoyant forces from both the oil and the water, as well as the gravitational force on the block.

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Answered: A rectangular parallelepiped with a…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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A rectangular parallelepiped with a square base d = 0.260 m on a side and a height h = 0.120 m has a mass m = 6.70 kg. While this object is floating in water, oil with a mass density ?_o = 710 kg/m³ is carefully poured on top of the water until the situation looks like that shown in the figure. Determine the height of the parallelepiped in the water.

This diagram illustrates a wooden block partially submerged in a container filled with two immiscible liquids: oil and water.

Key Features:

1. **Block Dimensions**: The block is represented as a cube with side length \( d \).

2. **Liquid Layers**:
- The upper layer consists of oil.
- The lower layer consists of water.

3. **Submersion Heights**:
- \( h \): The height of the block submerged in the water.
- \( h_o \): The height of the block submerged in the oil.
- \( h_w \): The exposed height of the block above the water's surface.

This setup can be used to study principles such as buoyancy, density differences between the two fluids, and the equilibrium of floating objects. The forces acting on the block include the buoyant forces from both the oil and the water, as well as the gravitational force on the block.

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