EXAMPLE 9.8 A Red-Tag Special on Crowns GOAL Apply Archimedes\' principle to a s

Question

EXAMPLE 9.8 A Red-Tag Special on Crowns GOAL Apply Archimedes' principle to a submerged object. PROBLEM A bargain hunter purchases a "gold" crown at a flea market. After she gets home, she hangs it from a scale and finds its weight to be 7.84 N (Figure (a)) She then weighs the crown while it is immersed in water, as in Figure (b), and now the scale reads 6.86 N. Is the crown made of pure gold? Tair STRATEGY The goal is to find the density of the crown and compare it to the density of gold. We already have the weight of the crown in air, so we can get the mass by dividing by the acceleration of gravity. If we can find the volume of the crown, we can obtain the desired density by dividing the mass by this volume IN ng (a) When the crown is suspended in air, the scale reads Tair-g, the crown's true weight. (b) When the crown is When the crown is fully immersed, the displaced water is equal to the volume of the crown. This same volumeB is used in calculating the buoyant force. So our strategy is as follows: (1) Apply Newton's second law to the crown, both in the water and in the air to find the buoyant force. (2) Use the buoyant force to find the crown's volume. (3) Divide the crown's scale weight in air by the acceleration of gravity to get the mass, then by the volume to get the density of the crown immersed in water, the buoyant force B reduces the scale reading by the magnitude of the buoyant force, Twater mg

Explanation / Answer

weight of the bracelet in air = 0.105 N

weight of the bracelet in water = 0.078

buoyant force = weight of the bracelet in air - weight of the bracelet in water

buoyant force = 0.105 - 0.078

buoyant force = 0.027 N

volume of water = buoyant force / gravity * density of water

volume of water = 0.027 / 9.8 * 1000

volume of water = 0.0000027551 m^3

mass = 0.105 / 9.8

density = mass / volume

density = (0.105 / 9.8) / 0.0000027551

density = 3888.892 kg/m^3

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