A frog in a hemispherical pod just floats without sinking into a pond with density 1.35 g/cm^3. If the pod has radius 6 cm and negligible mass, what is the mass of the frog?
wouldn't one need the thickness of the pad? And what has the density given? The pond water, or the frog?
?????
In this scenario, we assume that the hemispherical pod is made of a material with negligible density, meaning its mass can be considered negligible. The density given (1.35 g/cm^3) refers to the density of the pond water.
Since the frog is floating in the pod without sinking, the buoyant force acting on the frog must be equal to its weight. The buoyant force is calculated using Archimedes' principle:
Buoyant force = Weight of the fluid displaced
Buoyant force = Density of the fluid × Volume of the fluid displaced × Acceleration due to gravity
In this case, the weight of the fluid displaced is the weight of the frog. To find the mass of the frog, we can use the formula:
Weight of an object = mass × acceleration due to gravity
We can set up the following equation:
Density of the fluid × Volume of the fluid displaced × Acceleration due to gravity = mass × acceleration due to gravity
Since the acceleration due to gravity cancels out, we can simplify the equation:
Density of the fluid × Volume of the fluid displaced = mass
Now, let's calculate the volume of the fluid displaced by the frog. The pod is a hemisphere, so its volume can be calculated using the formula:
Volume of a hemisphere = (2/3) × π × (radius)^3
Substituting the given radius (6 cm) into the formula, we get:
Volume of the pod = (2/3) × π × (6 cm)^3
Now, we can substitute the density of the fluid (1.35 g/cm^3) and the calculated volume of the pod into the equation to find the mass of the frog:
mass = (1.35 g/cm^3) × [(2/3) × π × (6 cm)^3]
To solve this problem, we do not need the thickness of the pod or the density of the frog. Here's how you can find the mass of the frog:
Step 1: Determine the volume of the hemisphere pod.
The volume of a hemisphere is given by the formula: V = (2/3)πr^3, where r is the radius of the hemisphere. In this case, the radius is given as 6 cm.
V = (2/3)π(6 cm)^3
V ≈ 905.14 cm^3
Step 2: Calculate the mass of the water displaced by the pod.
Since the pod floats without sinking, it displaces an amount of water equal to its own weight. The weight of the water displaced can be found using the formula: W = V × ρ × g, where V is the volume of the pod, ρ is the density of the water, and g is the acceleration due to gravity.
Given that the density of the pond water is 1.35 g/cm^3 and the acceleration due to gravity is approximately 9.8 m/s^2, we need to convert the density to kg/m^3 and the volume to m^3:
Density of water (ρ) = 1.35 g/cm^3 = 1350 kg/m^3 (since 1 g/cm^3 = 1000 kg/m^3)
Volume of pod (V) = 905.14 cm^3 = 0.00090514 m^3
Now we can calculate the weight of the water displaced:
W = V × ρ × g
W = 0.00090514 m^3 × 1350 kg/m^3 × 9.8 m/s^2
W ≈ 11.61 N
Step 3: Calculate the mass of the frog.
Since the pod and the frog together displace the same amount of water, the weight of the frog will be equal to the weight of the water displaced, which we found to be approximately 11.61 N. Since weight can be converted to mass by dividing by the acceleration due to gravity (g), we can calculate the mass of the frog as follows:
Mass of frog = Weight of frog / g
Mass of frog = 11.61 N / 9.8 m/s^2
Mass of frog ≈ 1.18 kg
Therefore, the mass of the frog is approximately 1.18 kg.
Fg=Fb
m . g = d . V . g
m = d . V
m = (1,35 . 1000 kg per m cube) 2/3 pay ( .06 m )cube
m = 41 kg