Your friend of mass 150 can just barely float in fresh water. Find her volume.

You must provide the units of her weight as well as a number. Is it pounds?

If she "barely floats", her volume is the same as that of an equal mass of liquid water.

Water weighs 62.4 lb/ft^3

150 lb of water would occupy 2.40 ft^3

To find the volume of your friend, we need to use the fact that she can just barely float in fresh water.

When an object floats, the buoyant force acting on it is equal to the weight of the object. The buoyant force is given by the formula:

Buoyant force = density of the liquid × volume of the submerged portion of the object × acceleration due to gravity

The weight of your friend is equal to her mass multiplied by the acceleration due to gravity:

Weight = mass × acceleration due to gravity

Since she can just barely float, the buoyant force equals her weight:

Buoyant force = Weight

So, we have:

density of the liquid × volume of the submerged portion × acceleration due to gravity = mass × acceleration due to gravity

Since the density of fresh water is approximately 1000 kg/m³, and the acceleration due to gravity is approximately 9.8 m/s², we can simplify the equation:

1000 kg/m³ × volume of the submerged portion × 9.8 m/s² = 150 kg × 9.8 m/s²

Now, we can solve for the volume of the submerged portion:

volume of the submerged portion = (150 kg × 9.8 m/s²) / (1000 kg/m³ × 9.8 m/s²)

volume of the submerged portion = 150 kg / 1000 kg/m³

volume of the submerged portion = 0.15 m³

Since the volume of the submerged portion is equal to the volume of your friend, her volume is 0.15 m³.

To find the volume of your friend, we can use Archimedes' principle, which states that the buoyant force experienced by an object submerged in a fluid is equal to the weight of the fluid displaced by the object.

To start, we need to find the weight of your friend. We can use the formula:

Weight = mass x gravitational acceleration

By plugging in the given information, we have:

Weight = 150 kg x 9.8 m/s^2 (gravitational acceleration) = 1470 N

Since your friend is just barely floating, the buoyant force acting on her is equal to her weight.

Next, we need to determine the density of fresh water. The density of fresh water is typically considered to be about 1000 kg/m^3.

Now let's apply Archimedes' principle:

Buoyant force = weight of the fluid displaced
Buoyant force = density of fluid x volume of the fluid displaced x gravitational acceleration

As the buoyant force is equal to the weight, the equation becomes:

Weight = density of fluid x volume of the fluid displaced x gravitational acceleration

Rearranging the equation for volume:

Volume = Weight / (density of fluid x gravitational acceleration)

Plugging in the values we have:

Volume = 1470 N / (1000 kg/m^3 x 9.8 m/s^2) ≈ 0.15 cubic meters

Therefore, the volume of your friend is approximately 0.15 cubic meters.