An undersea research chamber is spherical with an external diameter of 5.20 m. The mass of the chamber, when occupied, is 74,400 kg. It is anchored to the sea bottom by a cable. What is

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. The buoyancy force equals the weight of the seawater displaced and that's gonna be the density of seawater multiplied by its volume which is the volume of the sphere times g and that's gonna be density of seawater times four-third's πr cubed— that's the volume of a sphere. So we have 1.025 times 10 to the 3 kilograms per cubic meter— density of seawater— times four-third's π times 5.2 meters divided by 2 to get the radius and cubed times 9.8 that gives 7.40 times 10 to the 5 newtons is the upwards buoyancy force. Now to find the tension force in this cable that's anchoring this thing to the seafloor we see that the tension down plus gravity down, it has to equal the buoyancy force upwards and so tension is buoyancy force minus gravity which is buoyancy force minus mg. And here's the buoyancy force we found already 7.3953 times 10 to the 5 newtons minus 74400 kilograms times 9.8 newtons per kilogram which gives 1.0 times 10 to the 4 newtons is the tension force.