Physics for Scientists and Engineers with Modern Physics
Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Textbook Question
Chapter 1, Problem 17P

(a) Compute the order of magnitude of the mass of a bathtub half full of water. (b) Compute the order of magnitude of the mass of a bathtub half full of copper coins.

(a)

Expert Solution
Check Mark
To determine

The order of magnitude of the mass of a bath tub half full of water.

Answer to Problem 17P

The order of magnitude of the mass of a bath tub half full of water is 102kg .

Explanation of Solution

Section 1:

To determine: The volume of the half full water bathtub.

Answer: The volume of the half full water bathtub is 0.195m3 .

Assume length of a bathtub is 1.3m , breadth of a bathtub is 0.5m and the height of a bathtub is 0.3m . The density of water is 1000kg/m3 .

Formula to calculate the volume of the half full water bathtub is,

V=l×b×h2

  • l is the length of a bathtub.
  • b is the breadth of a bathtub.
  • h is the height of a bathtub.
  • V is the volume of volume of the half full water bathtub.

Substitute 1.3m for l , 0.5m for b and 0.3m for h to find V .

V=1.3m×0.5m×0.3m=0.195m3

Section 2:

To determine: The order of magnitude of the mass of a bath tub half full of water.

Answer: The order of magnitude of the mass of a bath tub half full of water is 102kg .

Assume length of a bathtub is 1.3m , breadth of a bathtub is 0.5m and the height of a bathtub is 0.3m . The density of water is 1000kg/m3 .

Formula to calculate the mass of half full water in the bathtub is,

m=ρV

  • m is the mass of the half full water in the bathtub.
  • ρ is the density of the water.
  • V is the volume of a bathtub.

Substitute 1000kg/m3 for ρ and 0.195m3 for V to find m .

m=(1000kg/m3)(0.195m3)=195kg

Since, the mass of half full of water is 195kg and can be rewrite as 1.95×102kg . So, the order of magnitude is 102kg .

Conclusion:

Therefore, the order of magnitude of the mass of a bath tub half full of water is 102kg .

(b)

Expert Solution
Check Mark
To determine

The order of magnitude of the mass of a bath tub half full of copper coins.

Answer to Problem 17P

The order of magnitude of the mass of a bath tub half full of copper coins is 103kg .

Explanation of Solution

Section 1:

To determine: The volume of the half portion of bathtub.

Answer: The volume of the half portion of bathtub is 0.195m3 .

Given information:

Assume length of a bathtub is 1.3m , breadth of a bathtub is 0.5m and the height of a bathtub is 0.3m . The density of copper is 8940kg/m3 .

Formula to calculate the volume of the half portion of bathtub is,

V=l×b×h2

  • l is the length of a bathtub.
  • b is the breadth of a bathtub.
  • h is the height of a bathtub.
  • V is the volume of volume of the half portion of bathtub.

Substitute 1.3m for l , 0.5m for b and 0.3m for h to find V .

V=1.3m×0.5m×0.3m=0.195m3

Section 2:

To determine: The order of magnitude of the mass of a bath tub half full of copper coins.

Answer: The order of magnitude of the mass of a bath tub half full of copper coins is 103kg .

Given information:

Assume length of a bathtub is 1.3m , breadth of a bathtub is 0.5m and the height of a bathtub is 0.3m . The density of copper is 8940kg/m3 .

Formula to calculate the mass of half full of copper coins in the bathtub is,

mc=ρcV

  • mc is the mass of the half full of copper coins in the bathtub.
  • ρc is the density of the copper.
  • V is the volume of a bathtub.

Substitute 8940kg/m3 for ρ and 0.195m3 for V to find m .

m=(8940kg/m3)(0.195m3)=17433kg

Since, the mass of half full of copper coins is 17433kg and can be rewrite as 1.74×103kg . So, the order of magnitude is 103kg .

Conclusion:

Therefore, the order of magnitude of the mass of a bath tub half full of copper coins is 103kg .

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Chapter 1 Solutions

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