An undersea research chamber is spherical with an external diameter of 5.80 m. The mass of the chamber, when occupied, is 68400 kg. It is anchored to the sea bottom by a cable. Calculate the following.
(a) the buoyant force on the chamber
N
(b) the tension in the cable
N
bouyant force= volume*densitywater*g
tension= bouyant force-mg
To calculate the buoyant force on the chamber, we need to determine the volume of the chamber and then multiply it by the density of the surrounding fluid. In this case, the surrounding fluid is water.
(a) Buoyant force on the chamber:
Step 1: Determine the volume of the chamber.
The volume of a sphere can be calculated using the formula: V = (4/3)πr³, where r is the radius of the sphere.
Given that the external diameter of the chamber is 5.80 m, we can calculate the radius.
Radius = (diameter / 2) = 5.80 m / 2 = 2.90 m
Substituting the value of the radius into the equation, we get:
V = (4/3)π(2.90 m)³
Step 2: Determine the buoyant force.
The buoyant force can be calculated using the formula: F_buoyant = density × g × V, where density is the density of water and g is the acceleration due to gravity.
The density of water is approximately 1000 kg/m³, and the acceleration due to gravity is 9.8 m/s².
Substituting these values into the equation, we get:
F_buoyant = (1000 kg/m³) × (9.8 m/s²) × V
Now we need to substitute the value of V from Step 1 into this equation to calculate the buoyant force.
(b) Tension in the cable:
The tension in the cable can be calculated by considering the equilibrium of forces acting on the chamber.
In this case, there are two forces acting on the chamber: the downward force due to gravity (weight) and the upward buoyant force.
Since the chamber is anchored to the sea bottom, the tension in the cable has to counteract the weight of the chamber.
Using Newton's second law, we can calculate the weight of the chamber:
Weight = mass × g
The tension in the cable is equal to the weight of the chamber, as it balances out the chamber's weight.
Now that we know the equations to use, let's substitute the values given in the problem statement and calculate the answers.