According to legend, the following challenge led Archimedes to the discovery of his famous principle: Hieron, king of Syracuse, was suspicious that a new crown that he had received from the royal goldsmith was not pure gold, as claimed. Archimedes was ordered to determine whether the crown was in fact made of pure gold, with the condition that only a nondestructive test would be allowed. Rather than answer the problem in the politically most expedient way (or perhaps extract a bribe from the goldsmith), Archimedes thought about the problem scientifically. The legend relates that when Archimedes stepped into his bath and caused it to overflow, he realized that he could answer the challenge by comparing the volume of water displaced by the crown with the volume of water displaced by an amount of pure gold equal in weight to the crown. If the crown was made of pure gold, the two volumes would be equal. If some other (less dense) metal had been substituted for some of the gold, then the crown would displace more water than the pure gold. A similar method of answering the challenge, based on the same physical principle, is to compute the ratio of the actual weight of the crown, Wactual, and the apparent weight of the crown when it is submerged in water, Wapparent. See whether you can follow in Archimedes' footsteps. The figure shows what is meant by weighing the crown while it is submerged in water. (Figure 1) Part A Take the density of the crown to be pc. What is the ratio of the crown's apparent weight (in water) Wapparent to its actual weight Wactual? Express your answer terms of the density of the crown pc and the density of water pw. ▸View Available Hint(s) IVD] ΑΣΦ Wapparent Wactual Submit Previous Answers Part B Complete previous part(s) Provide Feedback ?
According to legend, the following challenge led Archimedes to the discovery of his famous principle: Hieron, king of Syracuse, was suspicious that a new crown that he had received from the royal goldsmith was not pure gold, as claimed. Archimedes was ordered to determine whether the crown was in fact made of pure gold, with the condition that only a nondestructive test would be allowed. Rather than answer the problem in the politically most expedient way (or perhaps extract a bribe from the goldsmith), Archimedes thought about the problem scientifically. The legend relates that when Archimedes stepped into his bath and caused it to overflow, he realized that he could answer the challenge by comparing the volume of water displaced by the crown with the volume of water displaced by an amount of pure gold equal in weight to the crown. If the crown was made of pure gold, the two volumes would be equal. If some other (less dense) metal had been substituted for some of the gold, then the crown would displace more water than the pure gold. A similar method of answering the challenge, based on the same physical principle, is to compute the ratio of the actual weight of the crown, Wactual, and the apparent weight of the crown when it is submerged in water, Wapparent. See whether you can follow in Archimedes' footsteps. The figure shows what is meant by weighing the crown while it is submerged in water. (Figure 1) Part A Take the density of the crown to be pc. What is the ratio of the crown's apparent weight (in water) Wapparent to its actual weight Wactual? Express your answer terms of the density of the crown pc and the density of water pw. ▸View Available Hint(s) IVD] ΑΣΦ Wapparent Wactual Submit Previous Answers Part B Complete previous part(s) Provide Feedback ?
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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![According to legend, the following challenge led Archimedes to the
discovery of his famous principle: Hieron, king of Syracuse, was
suspicious that a new crown that he had received from the royal
goldsmith was not pure gold, as claimed. Archimedes was ordered to
determine whether the crown was in fact made of pure gold, with the
condition that only a nondestructive test would be allowed. Rather than
answer the problem in the politically most expedient way (or perhaps
extract a bribe from the goldsmith), Archimedes thought about the
problem scientifically. The legend relates that when Archimedes stepped
into his bath and caused it to overflow, he realized that he could answer
the challenge by comparing the volume of water displaced by the crown
with the volume of water displaced by an amount of pure gold equal in
weight to the crown. If the crown was made of pure gold, the two volumes
would be equal. If some other (less dense) metal had been substituted for
some of the gold, then the crown would displace more water than the
pure gold.
A similar method of answering the challenge, based on the same physical
principle, is to compute the ratio of the actual weight of the crown,
Wactual, and the apparent weight of the crown when it is submerged in
water, Wapparent. See whether you can follow in Archimedes' footsteps.
The figure shows what is meant by weighing the crown while it is
submerged in water.
(Figure 1)
Part A
Take the density of the crown to be pc. What is the ratio of the crown's apparent weight (in water) Wapparent to its actual weight Wactual?
Express your answer terms of the density of the crown pc and the density
water pw-
View Available Hint(s)
IVD] ΑΣΦ
Wapparent
Wactual
Submit
Previous Answers
Part B Complete previous part(s)
Provide Feedback
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Transcribed Image Text:According to legend, the following challenge led Archimedes to the
discovery of his famous principle: Hieron, king of Syracuse, was
suspicious that a new crown that he had received from the royal
goldsmith was not pure gold, as claimed. Archimedes was ordered to
determine whether the crown was in fact made of pure gold, with the
condition that only a nondestructive test would be allowed. Rather than
answer the problem in the politically most expedient way (or perhaps
extract a bribe from the goldsmith), Archimedes thought about the
problem scientifically. The legend relates that when Archimedes stepped
into his bath and caused it to overflow, he realized that he could answer
the challenge by comparing the volume of water displaced by the crown
with the volume of water displaced by an amount of pure gold equal in
weight to the crown. If the crown was made of pure gold, the two volumes
would be equal. If some other (less dense) metal had been substituted for
some of the gold, then the crown would displace more water than the
pure gold.
A similar method of answering the challenge, based on the same physical
principle, is to compute the ratio of the actual weight of the crown,
Wactual, and the apparent weight of the crown when it is submerged in
water, Wapparent. See whether you can follow in Archimedes' footsteps.
The figure shows what is meant by weighing the crown while it is
submerged in water.
(Figure 1)
Part A
Take the density of the crown to be pc. What is the ratio of the crown's apparent weight (in water) Wapparent to its actual weight Wactual?
Express your answer terms of the density of the crown pc and the density
water pw-
View Available Hint(s)
IVD] ΑΣΦ
Wapparent
Wactual
Submit
Previous Answers
Part B Complete previous part(s)
Provide Feedback
?
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