Use the worked example above to help you solve this problem. A bargain hunter purchases a "gold" crown at a flea market. After she gets home, she hangs it on a scale and finds its weight to be 7.99 N (Figure (a)). She then weighs the crown while it is immersed in water, as shown in Figure (b), and now the scale reads 7.00 N.What is the density of the crown? kg/m3Is the crown made of pure solid gold?YesNo
Question
Use the worked example above to help you solve this problem. A bargain hunter purchases a "gold" crown at a flea market. After she gets home, she hangs it on a scale and finds its weight to be 7.99 N (Figure (a)). She then weighs the crown while it is immersed in water, as shown in Figure (b), and now the scale reads 7.00 N.What is the density of the crown? kg/m3Is the crown made of pure solid gold?YesNo
Solution
To solve this problem, we need to use the principle of buoyancy, which states that the buoyant force (or the decrease in weight when the object is submerged in water) is equal to the weight of the water displaced by the object.
First, we need to find the volume of the crown. We can do this by using the formula for buoyant force, which is the weight of the crown in air minus its weight in water.
Buoyant force = weight in air - weight in water = 7.99 N - 7.00 N = 0.99 N
Since the weight of water is 9.8 N for every liter (or 1000 cubic meters), we can find the volume of the crown by dividing the buoyant force by the weight of water.
Volume = buoyant force / weight of water = 0.99 N / 9.8 N/m^3 = 0.101 m^3
Next, we can find the density of the crown by dividing its weight in air by its volume.
Density = weight in air / volume = 7.99 N / 0.101 m^3 = 79.1 kg/m^3
The density of pure gold is 19,300 kg/m^3. Since the density of the crown is much less than this, the crown is not made of pure solid gold.
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