A Boat of bottom area 2m2 is pushed by a force of 500N.It moves with a constant V of 10ms-1.If the mass of the boat is 50kg and the coefficient of viscosity of water is 1*10-3, what is the depth of the pond.
To find the depth of the pond, we need to consider the forces acting on the boat. In this scenario, there are three significant forces acting on the boat: the weight of the boat, the buoyant force, and the viscous drag force.
1. Weight of the boat:
The weight of an object can be calculated using the formula: Weight = mass * acceleration due to gravity (W = m * g).
Given the mass of the boat as 50 kg and assuming the acceleration due to gravity is approximately 9.8 m/s², the weight is:
W = 50 kg * 9.8 m/s² = 490 N.
2. Buoyant force:
The buoyant force is the upward force exerted on an object submerged in a fluid. It can be calculated using the formula: Buoyant force = density of the fluid * volume of the fluid displaced * acceleration due to gravity (Fb = ρ * V * g).
Since the boat is floating, the buoyant force is equal to the weight of the boat:
Fb = W = 490 N.
3. Viscous drag force:
The viscous drag force is the resistance experienced by the boat due to the viscosity of the water. It can be calculated using the formula: Drag force = coefficient of viscosity * velocity * area (Fv = η * V * A).
Given the coefficient of viscosity of water as 1 * 10⁻³ and the velocity of the boat as 10 m/s, and the bottom area of the boat as 2 m², the drag force is:
Fv = 1 * 10⁻³ * 10 m/s * 2 m² = 0.02 N.
Now, let's consider the forces acting in the vertical direction:
Upward forces: Buoyant force = W = 490 N.
Downward forces: Weight of the boat = 490 N.
Since the boat is in equilibrium, the upward forces must balance the downward forces.
Therefore, the depth of the pond can be calculated using the formula:
Depth of the pond = (Weight of the boat - Buoyant force) / (Density of the fluid * g).
Given:
Weight of the boat (W) = 490 N.
Buoyant force (Fb) = 490 N.
Density of water (ρ) = 1000 kg/m³ (approximately).
Acceleration due to gravity (g) = 9.8 m/s².
Depth of the pond = (490 N - 490 N) / (1000 kg/m³ * 9.8 m/s²)
Depth of the pond = 0 m.
Therefore, the depth of the pond is 0 meters, indicating that the boat is floating on the water surface rather than being submerged.