A frog in a hemispherical bowl, as shown below, just floats in a fluid with a density of 1.29 ✕ 103 kg/m3. If the bowl has a radius of 5.30 cm and negligible mass, what is the mass of the frog?
To find the mass of the frog, we need to understand the forces acting on it in the given situation.
First, let's consider the forces acting on the frog:
1. Buoyant Force: When an object is immersed in a fluid, it experiences an upward force called the buoyant force. This force is equal to the weight of the fluid displaced by the object.
2. Weight of the Frog: The frog experiences a downward force due to its weight, which depends on its mass.
In this case, since the frog is floating, the buoyant force is equal to the weight of the frog. Therefore, we can equate these two forces to find the mass of the frog.
Let's calculate the buoyant force:
The volume of the fluid displaced by the frog is equal to the volume of the hemisphere that is submerged in the fluid. The volume of a hemisphere is given by the formula:
V = (2/3) * π * r^3
Where:
V = Volume of the hemisphere
π = Pi (approximately 3.14159)
r = Radius of the hemisphere
Now, let's substitute the given values:
V = (2/3) * π * (0.0530 m)^3
V ≈ 0.0039723 m^3
We know that the density of the fluid is 1.29 * 10^3 kg/m^3.
The weight of the fluid displaced is given by:
Weight = Density * Volume * Acceleration due to gravity
Weight = (1.29 * 10^3 kg/m^3) * (0.0039723 m^3) * 9.8 m/s^2
Weight ≈ 50.79 N
Since the frog is floating and the buoyant force is equal to its weight, the mass of the frog is given by:
Mass = Weight / Acceleration due to gravity
Mass = 50.79 N / 9.8 m/s^2
Mass ≈ 5.19 kg
Therefore, the mass of the frog is approximately 5.19 kg.