A dense plastic toy of mass 2.8 kg is floating
just beneath the surface of a pond.
What is the buoyant force on it?
Answer in units of N.
Upthrust = weight of object
= 2.8*g N
To calculate the buoyant force on the plastic toy, we can use Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object.
The buoyant force (B) can be calculated using the formula:
B = ρ * V * g
Where:
ρ is the density of the fluid (water) in kg/m³,
V is the volume of the fluid displaced by the object in m³,
g is the acceleration due to gravity (approximately 9.8 m/s²).
In this case, since the plastic toy is floating just beneath the surface of the pond, we assume it displaces a volume of water equal to its own volume.
To find the volume of the plastic toy (V), we need to know its density. Let's assume it is made of a common plastic material with a density of 1000 kg/m³.
Therefore, the buoyant force (B) can be calculated as:
B = ρ * V * g
B = (1000 kg/m³) * V * (9.8 m/s²)
Since we don't have the volume of the plastic toy, we cannot determine the exact buoyant force.
To determine the buoyant force on the plastic toy, we need to use Archimedes' principle, which states that the buoyant force acting on an object submerged or floating in a fluid is equal to the weight of the fluid displaced by the object. The buoyant force can be calculated using the formula:
Buoyant force = Density of the fluid * Volume of the displaced fluid * Acceleration due to gravity
First, we need to determine the volume of fluid displaced by the toy. Since the toy is floating just beneath the surface of the pond, it is in equilibrium, meaning that the weight of the toy is equal to the buoyant force acting on it.
The weight of the toy can be calculated using the formula:
Weight = Mass * Acceleration due to gravity
Given that the mass of the toy is 2.8 kg, and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight of the toy.
Weight = 2.8 kg * 9.8 m/s^2
Next, we need to find the density of the fluid, which in this case is water. The density of water is approximately 1000 kg/m^3.
To calculate the volume of the displaced fluid, we can use the buoyancy formula:
Volume of displaced fluid = Mass of the toy / Density of the fluid
Volume of displaced fluid = 2.8 kg / 1000 kg/m^3
Now that we have the volume of the displaced fluid, we can calculate the buoyant force using the buoyancy formula mentioned earlier.
Buoyant force = Density of the fluid * Volume of the displaced fluid * Acceleration due to gravity
Substituting the values we have:
Buoyant force = 1000 kg/m^3 * (2.8 kg / 1000 kg/m^3) * 9.8 m/s^2
Calculating the result will give you the buoyant force on the plastic toy, expressed in units of Newtons (N).