If a object of radius 3 cm is attached to the ground in a 3 m deep sea, what is the vertical force in N with which the water (density = 1000 kg/m^3) presses on it?
To calculate the vertical force with which the water presses on the object, we can use the formula:
Force = Pressure × Area
First, let's calculate the pressure exerted by the water at a depth of 3 meters. The pressure at any given depth in a fluid is given by the equation:
Pressure = density × gravity × depth
Given:
Density of water (ρ) = 1000 kg/m³
Gravity (g) = 9.8 m/s²
Depth (h) = 3 m
Substituting these values into the equation, we can calculate the pressure:
Pressure = 1000 kg/m³ × 9.8 m/s² × 3 m = 29400 Pa
Next, let's calculate the area of the object. Since the object is a sphere, the area can be calculated using the formula:
Area = 4πr²
Given:
Radius (r) = 3 cm = 0.03 m
Substituting this value into the equation, we can calculate the area:
Area = 4π × (0.03 m)² = 0.01131 m²
Now we can calculate the vertical force:
Force = Pressure × Area = 29400 Pa × 0.01131 m² ≈ 332.34 N
Therefore, the vertical force with which the water presses on the object is approximately 332.34 N.
To calculate the vertical force exerted by the water on the object, you need to determine the weight of the water column directly above the object.
Here's how you can do it step by step:
1. Calculate the volume of the water column directly above the object. Since the object is a cylinder, you can use the formula for the volume of a cylinder: V = πr²h, where r is the radius and h is the height of the water column. In this case, the radius is given as 3 cm (or 0.03 m) and the height is 3 m. So, V = π(0.03²)(3) = 0.085 m³.
2. Convert the volume of the water column to mass. The density of water is given as 1000 kg/m³, which means that each m³ of water has a mass of 1000 kg. Therefore, the mass of the water column is: Mass = Volume × Density = 0.085 m³ × 1000 kg/m³ = 85 kg.
3. Now, calculate the weight of the water column using the formula W = m × g, where m is the mass and g is the acceleration due to gravity. The value of g is approximately 9.8 m/s². So, W = 85 kg × 9.8 m/s² = 833 N.
Therefore, the vertical force with which the water presses on the object is 833 N.