Question

LEARN MORE REMARKS Because the density of gold Is 1.93 x 104 kg/m", the crown is elther hollow, made of an alloy, or both. Despite the mathematical complexity, it is certainly conceivable that this was the method that occurred to Archimedes. Conceptually, it's a matter of realizing (or guessing) that equal weights of gold and a silver-gold alloy would have different scale readings when immersed in water because their densities and hence their volumes are different, leading to differing buoyant forces. QUESTION True or False: The magnitude of the buoyant force on a completely submerged object depends on the object's density. O True False PRACTICE IT 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 7.53 N (Figure (a)). She then weighs the crown while it is immersed in water, as shown in Figure (b), and now the scale reads 6.70 N. What is the density of the crown? kg/m3 Is the crown made of pure solid gold? Yes NO EXERCISE HINTS: GETTING STARTED I'M STUCK! The weight of a metal bracelet is measured to be 0.11700 N in air and 0.08300 N when immersed in water. Find its density. kg/m3 Need Help? Read It Talk to a Tutor

Answer 1

Yes , Buoyant force does depends on density of object.

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PRACTICE IT

We need to find the buoyant force on crown. It is just the difference between weight in air and weight in water

so,

F = 7.53 - 6.70

F = 0.83 N

so,

we know

F = pgV

where V is volume, p is density of fluid

Volume of crown = 0.83 / 1000 * 9.8

V = 8.469e-5 m³

and

mass can be found as ( using weight in air)

m = 7.53 / 9.8 = 0.76836 kg

so,

density = mass / volume

density = 0.76836 / 8.469e-5

density = 9072.7 kg / m³

as we can see this is much less than density of gold, so she was looted. IT'S NOT GOLD

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EXERCISE

We need to find the buoyant force on crown. It is just the difference between weight in air and weight in water

so,

F = 0.117 - 0.083

F = 0.034 N

so,

we know

F = pgV

where V is volume, p is density of fluid

Volume of crown = 0.034 / 1000 * 9.8

V = 3.469e-6 m³

and

mass can be found as ( using weight in air)

m = 0.117 / 9.8 = 0.011938 kg

so,

density = mass / volume

density =3441.56 kg/m³