Final answer:
a) The net force acting on the chamber is 142,947 N. b) The tension in the cable is the same as the net force, which is 142,947 N.
Step-by-step explanation:
a) To calculate the net force acting on the chamber, we first need to calculate the weight of the chamber. We can use the formula:
weight = mass * acceleration due to gravity
where the mass is given as 78,300 kg and the acceleration due to gravity is approximately 9.8 m/s2. Therefore, the weight of the chamber is:
weight = 78,300 kg * 9.8 m/s2 = 767,940 N
The buoyant force acting on the chamber is equal to the weight of the displaced seawater. The volume of the chamber can be calculated using the formula for the volume of a sphere:
volume = (4/3) * π * (radius^3)
where the radius is half of the diameter, so radius = 5.30 m / 2 = 2.65 m. Plugging in this value, we get:
volume = (4/3) * π * (2.65 m)^3 = 62.28 m3
The mass of the seawater displaced can be calculated using the density of seawater:
mass = density * volume = 1025 kg/m3 * 62.28 m3 = 63,735 kg
The weight of the displaced seawater is then:
weight = mass * acceleration due to gravity = 63,735 kg * 9.8 m/s2 = 624,993 N
Therefore, the net force acting on the chamber is the difference between the weight of the chamber and the weight of the displaced seawater:
net force = weight of the chamber - weight of the displaced seawater = 767,940 N - 624,993 N = 142,947 N
b) To determine the tension in the cable, we need to consider the forces acting on the chamber. The tension in the cable is equal to the net force acting on the chamber:
tension in cable = net force = 142,947 N