A frog in a hemispherical pod finds that he
just floats without sinking in a fluid with a
density of 1.33 g/cm3.
If the pod has a radius of 5 cm and negligible
mass, what is the mass of the frog?
Answer in units of kg.
densityfluid*volume=massfrog*g
change all things to kg, meter
To find the mass of the frog, we need to understand the concept of buoyancy and the conditions for an object to float in a fluid.
Buoyancy is the upward force exerted by a fluid on an object immersed in it. For an object to float, the buoyant force acting on it must be equal to or greater than its weight. If the buoyant force is less than the weight, the object will sink.
In this case, the frog is floating in the fluid, which means the buoyant force acting on the frog is equal to its weight. The buoyant force can be calculated using Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object.
To calculate the buoyant force, we need to determine the volume of the fluid displaced by the frog. The pod in this case is a hemisphere with a radius of 5 cm. The volume of a hemisphere is given by the formula (2/3)πr³, where r is the radius. Plugging in the radius of 5 cm, we find:
Volume of hemisphere = (2/3)π(5 cm)³
Next, we need to convert the volume from cubic centimeters (cm³) to cubic meters (m³) since the density of the fluid is given in grams per cubic centimeter (g/cm³). There are 100 centimeters in 1 meter, so we divide the volume by (100 cm)³ to convert it to cubic meters.
Volume of hemisphere = (2/3)π(5 cm)³ / (100 cm)³
Now, we can calculate the mass of the fluid displaced by the frog using the formula:
Mass = Density x Volume
The density of the fluid is given as 1.33 g/cm³. Convert the density to kilograms per cubic meter by dividing it by 1000.
Density of fluid = 1.33 g/cm³ / 1000 kg/g
Now, multiply the density by the volume to find the mass of the fluid displaced:
Mass of fluid displaced = Density of fluid x Volume
Finally, since the buoyant force acting on the frog is equal to its weight, the mass of the frog must be equal to the mass of the fluid displaced.
Therefore, the mass of the frog is equal to the mass of the fluid displaced.
Perform the calculations to find the mass of the frog.