a black of mass 92 kg and volume 0.031 lies at the bottom of the sea how much force is needed to lift it ? take 1.03*10^3 kg/m as the density of sea water
To calculate the force needed to lift the black at the bottom of the sea, we first need to determine the buoyant force acting on it. The buoyant force is equal to the weight of the displaced fluid.
Step 1: Calculate the weight of the black
The weight (W) of the black can be determined using the formula W = m * g, where m is the mass and g is the acceleration due to gravity.
Given:
Mass (m) = 92 kg
Acceleration due to gravity (g) = 9.8 m/s^2
Using the formula:
W = 92 kg * 9.8 m/s^2
W = 901.6 N
Step 2: Calculate the weight of the displaced fluid
The weight of the displaced fluid is equal to the weight of an equal volume of sea water.
Density of sea water (ρ) = 1.03 * 10^3 kg/m^3
Volume of the black (V) = 0.031 m^3
Weight of the displaced fluid (Wf) = ρ * V * g
Using the formula:
Wf = 1.03 * 10^3 kg/m^3 * 0.031 m^3 * 9.8 m/s^2
Wf = 312.94 N
Step 3: Calculate the force needed to lift the black
The force needed to lift the black is equal to the buoyant force acting on it, which is equal to the weight of the displaced fluid.
Force needed to lift the black (F) = Wf
Therefore:
F = 312.94 N
So, the force needed to lift the black at the bottom of the sea is 312.94 Newtons.
To determine the force needed to lift the black, we need to calculate the buoyant force acting on it.
The buoyant force is equal to the weight of the fluid displaced by the object. In this case, the fluid is the sea water and the object is the black.
1. First, we need to calculate the weight of the displaced sea water. The weight is the mass times the acceleration due to gravity:
Weight of displaced sea water = Volume of black * Density of sea water * g
where:
- Volume of black is given as 0.031 m^3
- Density of sea water is given as 1.03 * 10^3 kg/m^3
- g is the acceleration due to gravity, which is approximately 9.8 m/s^2
Weight of displaced sea water = 0.031 m^3 * 1.03 * 10^3 kg/m^3 * 9.8 m/s^2
2. Next, we can calculate the buoyant force, which is equal to the weight of the displaced sea water:
Buoyant force = Weight of displaced sea water
Buoyant force = 0.031 m^3 * 1.03 * 10^3 kg/m^3 * 9.8 m/s^2
3. Finally, to determine the force needed to lift the black, we just need to equate it to the weight of the black:
Force needed to lift = Weight of black = Mass of black * g
where:
- Mass of black is given as 92 kg
- g is the acceleration due to gravity, which is approximately 9.8 m/s^2
Force needed to lift = 92 kg * 9.8 m/s^2
By calculating these values, you can find the force needed to lift the black at the bottom of the sea.
588N
"Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object." - Archimedes of Syracuse
Given:
g = 9.8[m/s^2]
ρ = 1.03e+3 [kg/m^3]
m = 92[kg]
V = 0.031[m^3 ?] ...check volume units.
Use:
F = (m - ρV)g