A metal cube, 19 cm on each side, has a density of 4800 kg/m3. If it is suspended totally submerged in water, find the tension in the string. Your Ancwor:
A metal cube, 19 cm on each side, has a density of 4800 kg/m3. If it is suspended totally submerged in water, find the tension in the string. Your Ancwor:
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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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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![**Problem Statement:**
A metal cube, 19 cm on each side, has a density of 4800 kg/m³. If it is suspended totally submerged in water, find the tension in the string.
Given:
- Side length of the cube = 19 cm
- Density of the metal = 4800 kg/m³
**Objective:**
- To find the tension in the string when the cube is submerged in water.
**Explanation:**
To calculate the tension in the string, consider the following steps:
1. **Calculate the volume of the cube:**
\[
\text{Volume} = \text{side length}^3 = (0.19 \, \text{m})^3
\]
2. **Determine the mass of the cube:**
\[
\text{Mass} = \text{Density} \times \text{Volume} = 4800 \, \text{kg/m}^3 \times \text{Volume}
\]
3. **Calculate the weight of the cube:**
\[
\text{Weight (W)} = \text{Mass} \times g
\]
(where \( g \) is the acceleration due to gravity, approximately \( 9.81 \, \text{m/s}^2 \)).
4. **Calculate the buoyant force (B):**
The buoyant force is equal to the weight of the water displaced by the cube.
\[
\text{Buoyant force (B)} = \text{Density of water} \times \text{Volume of cube} \times g
\]
(The density of water is approximately \( 1000 \, \text{kg/m}^3 \)).
5. **Determine the tension (T) in the string:**
Use the equilibrium condition for the forces:
\[
T = W - B
\]
This calculation will yield the tension in the string when the cube is fully submerged.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd1d700aa-072a-4ff7-be1d-cdca0f10aa9d%2Ff43cc823-9326-4cf0-8d0a-90e6e3a729c8%2Fr4fz1b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A metal cube, 19 cm on each side, has a density of 4800 kg/m³. If it is suspended totally submerged in water, find the tension in the string.
Given:
- Side length of the cube = 19 cm
- Density of the metal = 4800 kg/m³
**Objective:**
- To find the tension in the string when the cube is submerged in water.
**Explanation:**
To calculate the tension in the string, consider the following steps:
1. **Calculate the volume of the cube:**
\[
\text{Volume} = \text{side length}^3 = (0.19 \, \text{m})^3
\]
2. **Determine the mass of the cube:**
\[
\text{Mass} = \text{Density} \times \text{Volume} = 4800 \, \text{kg/m}^3 \times \text{Volume}
\]
3. **Calculate the weight of the cube:**
\[
\text{Weight (W)} = \text{Mass} \times g
\]
(where \( g \) is the acceleration due to gravity, approximately \( 9.81 \, \text{m/s}^2 \)).
4. **Calculate the buoyant force (B):**
The buoyant force is equal to the weight of the water displaced by the cube.
\[
\text{Buoyant force (B)} = \text{Density of water} \times \text{Volume of cube} \times g
\]
(The density of water is approximately \( 1000 \, \text{kg/m}^3 \)).
5. **Determine the tension (T) in the string:**
Use the equilibrium condition for the forces:
\[
T = W - B
\]
This calculation will yield the tension in the string when the cube is fully submerged.
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