**Problem Statement:**A wooden crate has a mass of 2 kg and it is floating halfway submerged in water. What is the upward buoyant force exerted by water \(1000 \, \text{kg/m}^3\) on the crate?**Explanation:**To solve this problem, we need to apply Archimedes' principle, which states that the buoyant force on a submerged object is equal to the weight of the fluid displaced by the object.**Key Details:**1. **Mass of the Crate:** - The crate's mass is 2 kg.2. **Density of Water:** - The density of water is \(1000 \, \text{kg/m}^3\).3. **Submersion Level:** - The crate is floating halfway submerged.**Solution Steps:**- The weight of the crate (\(W\)) is given by: \[ W = \text{mass} \times \text{gravity} = 2 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 19.6 \, \text{N} \]- Because the crate is floating, the upward buoyant force (\(F_b\)) must be equal to the weight of the crate: \[ F_b = 19.6 \, \text{N} \]Thus, the upward buoyant force exerted by the water on the crate is \(19.6 \, \text{N}\).

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What is the upward buoyant force exerted by

Physics for Scientists and Engineers, Technology Update (No access codes included)

9th Edition

ISBN:9781305116399

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter14: Fluid Mechanics

Section: Chapter Questions

Problem 14.6OQ: A solid iron sphere and a solid lead sphere of the same size are each suspended by strings and are...

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Question

**Problem Statement:**

A wooden crate has a mass of 2 kg and it is floating halfway submerged in water. What is the upward buoyant force exerted by water \(1000 \, \text{kg/m}^3\) on the crate?

**Explanation:**

To solve this problem, we need to apply Archimedes' principle, which states that the buoyant force on a submerged object is equal to the weight of the fluid displaced by the object.

**Key Details:**

1. **Mass of the Crate:**
- The crate's mass is 2 kg.

2. **Density of Water:**
- The density of water is \(1000 \, \text{kg/m}^3\).

3. **Submersion Level:**
- The crate is floating halfway submerged.

**Solution Steps:**

- The weight of the crate (\(W\)) is given by:
\[
W = \text{mass} \times \text{gravity} = 2 \, \text{kg} \times 9.8 \, \text{m/s}^2 = 19.6 \, \text{N}
\]

- Because the crate is floating, the upward buoyant force (\(F_b\)) must be equal to the weight of the crate:
\[
F_b = 19.6 \, \text{N}
\]

Thus, the upward buoyant force exerted by the water on the crate is \(19.6 \, \text{N}\).

Expert Solution

Step 1

Given:

Mass of the wooden crate=2 kg

Let density of wood crate be D_wc=600 kg/cm³

Density of Water D_w=1000Kg/cm³

To Find:

Buoyant Force F_b=?

Step by step

Solved in 2 steps

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