Calculate the buoyant force in air on a kilogram of gold (whose density is about 19 grams per cubic centimeter). The density of air is 1.3 ✕ 10-3 grams per cubic centimeter. Remember that the buoyant force is equal to the weight of a volume of air that is equal to the volume of the object. (Compare with the weight mg of this much gold, which is 9.8 N.)

Density of gold = 19g

Density of air = 0.0013g
Gravity = 9.8
F = m * g
m = Density of air / Density of Gold
Bouyant F = (Density of air / Density of Gold) * 9.8

Well, let's see. To find the buoyant force, we need to calculate the weight of the air that has the same volume as the gold. We already know the density of gold and air. So, first, let's convert the density of gold from grams per cubic centimeter to kilograms per cubic meter.

19 grams per cubic centimeter is equal to 19,000 kilograms per cubic meter. Now, we can calculate the volume of the gold. Since we have 1 kilogram of gold, and the density of gold is 19,000 kilograms per cubic meter, the volume of the gold would be 1/19,000 cubic meters.

Now, we can calculate the weight of the air that has the same volume as the gold. The density of air is 1.3 ✕ 10^-3 grams per cubic centimeter, which is equal to 1.3 kilograms per cubic meter. Multiplying the density of air with the volume of gold, we get: 1.3 kg/m^3 * (1/19,000) m^3 = 1.3/19,000 kg, which is roughly 6.8 ✕ 10^-5 kg.

And now, if we apply the formula for the buoyant force, we multiply the weight of this much gold (9.8 N) by the ratio of the weight of the air to the weight of the gold. Multiplying 9.8 N by (6.8 ✕ 10^-5 kg) / 1 kg, we get a buoyant force of roughly 6.7 ✕ 10^-4 N.

So, the buoyant force in air on a kilogram of gold would be approximately 6.7 ✕ 10^-4 N. Just remember to keep an eye on those pesky units!

To calculate the buoyant force in air on a kilogram of gold, we first need to find the volume of the gold.

Density is defined as mass divided by volume. Rearranging this equation, we can find volume by dividing mass by density:

Volume = Mass / Density

Given that the mass of the gold is 1 kilogram (1000 grams) and its density is 19 grams per cubic centimeter, we have:

Volume = 1000 grams / 19 grams per cubic centimeter = 52.63 cubic centimeters

Now that we have the volume of the gold, we can calculate the weight of the same volume of air. The weight of the gold is given as 9.8 N, so the weight of the same volume of air can be found using the density of air, which is 1.3 x 10^-3 grams per cubic centimeter.

Weight of air = Volume of air x Density of air

Since the volume of the gold is the same as the volume of the air displaced, the volume of air is also 52.63 cubic centimeters. We can now calculate the weight of the air:

Weight of air = 52.63 cubic centimeters x 1.3 x 10^-3 grams per cubic centimeter

Converting grams to Newtons using the conversion factor that 1 gram is equal to 0.0098 Newtons, we get:

Weight of air = 52.63 cubic centimeters x 1.3 x 10^-3 grams per cubic centimeter x 0.0098 Newtons/gram

Simplifying, we find:

Weight of air = 0.644 Newtons

Therefore, the buoyant force in air on a kilogram of gold is approximately 0.644 Newtons.

To calculate the buoyant force on a kilogram of gold in air, we need to find the weight of the volume of air that is equivalent to the volume of the gold.

Step 1: Find the volume of the gold
Density is defined as mass per unit volume. Given that the density of gold is 19 grams per cubic centimeter, and we have 1 kilogram (or 1000 grams) of gold, we can calculate the volume using the formula:
Volume = Mass / Density
Volume = 1000 g / 19 g/cm^3

Step 2: Find the weight of the equivalent volume of air
Using the given density of air (1.3 x 10^-3 grams per cubic centimeter), we can calculate the weight of the equivalent volume of air using the formula:
Weight = Volume x Density x Gravity
Weight = Volume x 1.3 x 10^-3 g/cm^3 x 9.8 m/s^2

Step 3: Compare the weight of the gold with the weight of the equivalent volume of air
The buoyant force is equal to the weight of the equivalent volume of air. So, we need to compare the weight of the gold (mg = 9.8 N) with the weight of the equivalent volume of air.

By following these steps, you can calculate the buoyant force on a kilogram of gold in air.