1) A frog in a hemispherical pod finds that he just floats without sinking in a fluid od density 1.35 g/cm^3. if the pod has a radius of 6.00 cm and negligible mass, what is the mass of the frog?
2) a small ferryboat is 4.00m wide and 6.00 m long. when a loaded truck pulls onto it, the boat sinks an additional 4.00 cm into the river. what is the weight of the truck?
any help would be great thank you. these are the only problems i cannot figure out, out of 45. Makes me irritated. thanks again.
2) a small ferryboat is 4.00m wide and 6.00 m long. when a loaded truck pulls onto it, the boat sinks an additional 4.00 cm into the river. what is the weight of the truck?
any help would be great thank you. these are the only problems i cannot figure out, out of 45. Makes me irritated. thanks again.
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) A frog in a hemispherical pod finds that he just floats without sinking in a fluid of density 1.35 g/cm^3. if the pod has a radius of 6.00 cm and negligible mass, what is the mass of the frog?
To float, the buoyant force must equal the weight of the frog.
The buoyant force is the weight of volume of the fluid which is displaced when the frog is in the hemispherical pod. The volume of a hemispherical pod = ½ * volume of sphere = ½ * 4/3 * π * r^3.
r = radius = 6.00 cm
Volume = ½ * 4/3 * π * 6.00^3 = 144 * π cm^3
Mass of fluid = volume * density = 144 * π * 1.35 = 610.7 grams = 0.6107 kilograms
Weight of fluid = mass * g = (0.6107 * g)
Weight of frog = mass of frog * g
mass of frog * g = (0.6107 * g)
mass of frog = 0.6107 Kg = 610.7 grams
2) a small ferryboat is 4.00m wide and 6.00 m long. when a loaded truck pulls onto it, the boat sinks an additional 4.00 cm into the river. what is the weight of the truck?
The weight of the truck caused the boat to move down 4.00 cm = 0.04 meters.
The volume of water which the boat displaced = 4.00 * 6.00 * 0.04 = 0.96 m^3
The buoyant force which is supporting the truck equals the weight of the 0.96 m^3 of water.
Weight = Volume * density * g
Density of water = 1000 kg/m^3
Weight of water = 0.96 * 1000 * 9.8 = 9408 N
Weight of Truck = 9408 N
Now let me show you, what is really supporting the weight of the truck!!
As you go deeper under water, the pressure increases.
Pressure = Density * ∆ depth * g
Pressure = 1000 kg/m^3 * 0.04 m * 9.8 m/s^2 = 392 N/m^2
As the boat moved 0.04 meters deeper, the pressure increased 392 N/m^2.
Pressure = Force ÷ area
Force = Pressure * area = 392 N/m^2 * (4 * 6) m^2 = 9408 N
This is the extra force which the water under the boat is exerting upward to support the extra weight of the truck.
So truck must weigh = 9408 N
To float, the buoyant force must equal the weight of the frog.
The buoyant force is the weight of volume of the fluid which is displaced when the frog is in the hemispherical pod. The volume of a hemispherical pod = ½ * volume of sphere = ½ * 4/3 * π * r^3.
r = radius = 6.00 cm
Volume = ½ * 4/3 * π * 6.00^3 = 144 * π cm^3
Mass of fluid = volume * density = 144 * π * 1.35 = 610.7 grams = 0.6107 kilograms
Weight of fluid = mass * g = (0.6107 * g)
Weight of frog = mass of frog * g
mass of frog * g = (0.6107 * g)
mass of frog = 0.6107 Kg = 610.7 grams
2) a small ferryboat is 4.00m wide and 6.00 m long. when a loaded truck pulls onto it, the boat sinks an additional 4.00 cm into the river. what is the weight of the truck?
The weight of the truck caused the boat to move down 4.00 cm = 0.04 meters.
The volume of water which the boat displaced = 4.00 * 6.00 * 0.04 = 0.96 m^3
The buoyant force which is supporting the truck equals the weight of the 0.96 m^3 of water.
Weight = Volume * density * g
Density of water = 1000 kg/m^3
Weight of water = 0.96 * 1000 * 9.8 = 9408 N
Weight of Truck = 9408 N
Now let me show you, what is really supporting the weight of the truck!!
As you go deeper under water, the pressure increases.
Pressure = Density * ∆ depth * g
Pressure = 1000 kg/m^3 * 0.04 m * 9.8 m/s^2 = 392 N/m^2
As the boat moved 0.04 meters deeper, the pressure increased 392 N/m^2.
Pressure = Force ÷ area
Force = Pressure * area = 392 N/m^2 * (4 * 6) m^2 = 9408 N
This is the extra force which the water under the boat is exerting upward to support the extra weight of the truck.
So truck must weigh = 9408 N