43. •. A solid block is attached to a spring scale. When the block is suspended in air, the scale reads 20.0 N; when it is completely immersed in water, the scale reads 17.7 N. What are (a) the vol- ume and (b) the density of the block?
43. •. A solid block is attached to a spring scale. When the block is suspended in air, the scale reads 20.0 N; when it is completely immersed in water, the scale reads 17.7 N. What are (a) the vol- ume and (b) the density of the block?
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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Part a and b. Show all work
![**Problem Statement:**
43. A solid block is attached to a spring scale. When the block is suspended in air, the scale reads 20.0 N; when it is completely immersed in water, the scale reads 17.7 N. What are (a) the volume and (b) the density of the block?
**Solutions:**
To solve this problem, we can use the principle of buoyancy and Archimedes’ principle.
**Concepts Involved:**
- **Weight in Air:** The force exerted by gravity on the block, measurable by the spring scale.
- **Buoyant Force:** The upward force exerted by water on the block when immersed.
- **Weight in Water:** The apparent weight of the block when it is submerged, reduced due to the buoyant force.
**Formulas:**
- **Buoyant Force:** \( F_b = \text{Weight in air} - \text{Weight in water} \)
- **Volume of Block:** \( V = \frac{F_b}{\text{Density of water} \times g} \), where \( g = 9.8 \, \text{m/s}^2 \).
- **Density of Block:** \( \rho = \frac{\text{Weight in air}}{V \times g} \).
**Execution:**
1. Calculate Buoyant Force:
\[ F_b = 20.0 \, \text{N} - 17.7 \, \text{N} = 2.3 \, \text{N} \]
2. Calculate Volume of the Block:
\[ V = \frac{2.3 \, \text{N}}{1000 \, \text{kg/m}^3 \times 9.8 \, \text{m/s}^2} \]
\[ V \approx 2.35 \times 10^{-4} \, \text{m}^3 \]
3. Calculate Density of the Block:
\[ \rho = \frac{20.0 \, \text{N}}{2.35 \times 10^{-4} \, \text{m}^3 \times 9.8 \, \text{m/s}^2} \]
\[ \rho \approx 857.14 \, \text{kg/m}^](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F587f9f8f-b9b6-467a-a476-89151f1449a5%2F8caeda48-9744-4871-9cdc-7784191e2868%2Fxfxewhs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
43. A solid block is attached to a spring scale. When the block is suspended in air, the scale reads 20.0 N; when it is completely immersed in water, the scale reads 17.7 N. What are (a) the volume and (b) the density of the block?
**Solutions:**
To solve this problem, we can use the principle of buoyancy and Archimedes’ principle.
**Concepts Involved:**
- **Weight in Air:** The force exerted by gravity on the block, measurable by the spring scale.
- **Buoyant Force:** The upward force exerted by water on the block when immersed.
- **Weight in Water:** The apparent weight of the block when it is submerged, reduced due to the buoyant force.
**Formulas:**
- **Buoyant Force:** \( F_b = \text{Weight in air} - \text{Weight in water} \)
- **Volume of Block:** \( V = \frac{F_b}{\text{Density of water} \times g} \), where \( g = 9.8 \, \text{m/s}^2 \).
- **Density of Block:** \( \rho = \frac{\text{Weight in air}}{V \times g} \).
**Execution:**
1. Calculate Buoyant Force:
\[ F_b = 20.0 \, \text{N} - 17.7 \, \text{N} = 2.3 \, \text{N} \]
2. Calculate Volume of the Block:
\[ V = \frac{2.3 \, \text{N}}{1000 \, \text{kg/m}^3 \times 9.8 \, \text{m/s}^2} \]
\[ V \approx 2.35 \times 10^{-4} \, \text{m}^3 \]
3. Calculate Density of the Block:
\[ \rho = \frac{20.0 \, \text{N}}{2.35 \times 10^{-4} \, \text{m}^3 \times 9.8 \, \text{m/s}^2} \]
\[ \rho \approx 857.14 \, \text{kg/m}^
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