Example 14.5 Eureka! AM Archimedes supposedly was asked to determine whether a crown made for the king consisted of pure gold. According to legend, he solved this problem by weighing the crown first in air and then in water as shown in Figure 14.11. Suppose the scale read 7.84 N when the crown was in air and 6.84 N when it was in water. What should Archimedes have told the king? b طلب من أرخميدس التأكد من أن تاج الملك مكون من الذهب الخالص وفقا للأسطورة، أجاب أرخميدس على هذا الطلب بوزن التاج في الهواء ثم وزنه في الماء (الشكل) افترض أن وزن التاج في الهواء ٧,٨٤ نيوتن ووزنه في الماء ٦,٧٤ نيوتن بماذا أخبر أرخميدس الملك؟ F= B+ T₂-F=0 B=F-T B = PwgV. للحل نحسب كثافة تاج الملك ونقارنها بكثافة الذهب. Substance Air Air (at 20°C and atmospheric pressure) Aluminum p (kg/m³) 1.29 1.20 m mcg mcg mcgpw Pe= = = V V.g (B/pm) B mcgpw E-T 2.70 x 10 Benzene 0.879 x 10' Brass 8.4 x 10' Copper 8.92 x 10 Ethyl alcohol 0.806 X 10 (7.84 N)(1 000 kg/m³) Fresh water 1.00 x 10 Pe 7.84 x 103 kg/m³ Glycerin 1.26 x 10 7.84 N-6.84 N Gold 19.3 x 10 Helium gas 1.79 x 10-1 Hydrogen gas 8.99 x 10 From table 14.1, Archimedes should have reported that the king had been cheated! Ice 0.917 x 10
Example 14.5 Eureka! AM Archimedes supposedly was asked to determine whether a crown made for the king consisted of pure gold. According to legend, he solved this problem by weighing the crown first in air and then in water as shown in Figure 14.11. Suppose the scale read 7.84 N when the crown was in air and 6.84 N when it was in water. What should Archimedes have told the king? b طلب من أرخميدس التأكد من أن تاج الملك مكون من الذهب الخالص وفقا للأسطورة، أجاب أرخميدس على هذا الطلب بوزن التاج في الهواء ثم وزنه في الماء (الشكل) افترض أن وزن التاج في الهواء ٧,٨٤ نيوتن ووزنه في الماء ٦,٧٤ نيوتن بماذا أخبر أرخميدس الملك؟ F= B+ T₂-F=0 B=F-T B = PwgV. للحل نحسب كثافة تاج الملك ونقارنها بكثافة الذهب. Substance Air Air (at 20°C and atmospheric pressure) Aluminum p (kg/m³) 1.29 1.20 m mcg mcg mcgpw Pe= = = V V.g (B/pm) B mcgpw E-T 2.70 x 10 Benzene 0.879 x 10' Brass 8.4 x 10' Copper 8.92 x 10 Ethyl alcohol 0.806 X 10 (7.84 N)(1 000 kg/m³) Fresh water 1.00 x 10 Pe 7.84 x 103 kg/m³ Glycerin 1.26 x 10 7.84 N-6.84 N Gold 19.3 x 10 Helium gas 1.79 x 10-1 Hydrogen gas 8.99 x 10 From table 14.1, Archimedes should have reported that the king had been cheated! Ice 0.917 x 10
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter15: Fluids
Section: Chapter Questions
Problem 34PQ
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Question
Transcribed Image Text:Example 14.5
Eureka! AM
Archimedes supposedly was asked to determine whether a crown
made for the king consisted of pure gold. According to legend, he
solved this problem by weighing the crown first in air and then
in water as shown in Figure 14.11. Suppose the scale read 7.84 N
when the crown was in air and 6.84 N when it was in water. What
should Archimedes have told the king?
b
طلب من أرخميدس التأكد من أن تاج الملك مكون من الذهب الخالص وفقا للأسطورة، أجاب أرخميدس على هذا الطلب بوزن التاج في الهواء ثم وزنه في
الماء (الشكل) افترض أن وزن التاج في الهواء ٧,٨٤ نيوتن ووزنه في الماء ٦,٧٤ نيوتن بماذا أخبر أرخميدس الملك؟
F= B+ T₂-F=0
B=F-T
B = PwgV.
للحل نحسب كثافة تاج الملك ونقارنها بكثافة الذهب.
Substance
Air
Air (at 20°C and
atmospheric pressure)
Aluminum
p (kg/m³)
1.29
1.20
m mcg
mcg
mcgpw
Pe=
=
=
V V.g (B/pm) B
mcgpw
E-T
2.70 x 10
Benzene
0.879 x 10'
Brass
8.4 x 10'
Copper
8.92 x 10
Ethyl alcohol
0.806 X 10
(7.84 N)(1 000 kg/m³)
Fresh water
1.00 x 10
Pe
7.84 x 103 kg/m³
Glycerin
1.26 x 10
7.84 N-6.84 N
Gold
19.3 x 10
Helium gas
1.79 x 10-1
Hydrogen gas
8.99 x 10
From table 14.1, Archimedes should have reported that the king had been cheated!
Ice
0.917 x 10
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