A frog in a hemispherical pod finds that he just floats without sinking in a fluid of density 1.30 g/cm3. If the pod has a radius of 3.00 cm and negligible mass, what is the mass of the frog?
density= mass/volume
mass= density*volume
the volume of a sphere is 4/3 PI r^2, so the volume of a hemisphere is half that.
To find the mass of the frog, we need to use the concept of buoyancy. Buoyancy is the upward force exerted by a fluid on an object immersed in it. It is equal to the weight of the fluid displaced by the object.
To solve this problem, we can start by calculating the volume of the fluid displaced by the frog. Since the frog is floating without sinking, the weight of the frog is equal to the weight of the fluid displaced.
The volume of a hemisphere is given by the formula: V = (2/3) * π * r^3, where r is the radius.
Given that the radius of the pod is 3.00 cm, we can substitute the value into the formula to find the volume of the fluid displaced.
V = (2/3) * π * (3.00 cm)^3
V = (2/3) * π * 27.00 cm^3
V ≈ 56.54 cm^3
Now, let's calculate the weight of the fluid displaced using the density of the fluid. The formula for weight is given by: weight = density * volume * gravity, where the density of the fluid is given as 1.30 g/cm^3 and the acceleration due to gravity is approximately 9.8 m/s^2.
First, we need to convert the volume from cm^3 to m^3:
V = 56.54 cm^3 = 56.54 * 10^(-6) m^3
Now, we can substitute the values into the formula to find the weight of the fluid displaced:
weight = 1.30 g/cm^3 * 56.54 * 10^(-6) m^3 * 9.8 m/s^2
weight ≈ 0.0071 kg
Since the weight of the frog is equal to the weight of the fluid displaced, we can conclude that the mass of the frog is approximately 0.0071 kg, or 7.1 grams.