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? Figure 14.11 (Example 14.5) (a) When the crown is suspended in air, the scale reads its true weight because T1 = Fg (the buoyancy of air is negligible). (b) When the crown is immersed in water, the buoyant force B changes the scale reading to a lower value T2 = Fg - B.
Added by Christy J.
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- The weight of the crown in air (W_air) is given as 7.84 N. Show moreā¦
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Adi S.
It is said that Archimedes discovered his principle during a bath while thinking about how he could determine if King Hieroās crown was actually made of pure gold. While in the bathtub, he conceived the idea that he could determine the average density of an irregularly shaped object by weighing it in air and also in water. If the crown weighed 3.55 kgf (= 34.8 N) in air and 3.25 kgf (= 31.9 N) in water, determine if the crown is made of pure gold. The density of gold is 19,300 kg/m3. Discuss how you can solve this problem without weighing the crown in water but by using an ordinary bucket with no calibration for volume. You may weigh anything in air.
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