Newton's+Apple+Theory,+Applied+Once+Again

So it was reported on the news that the fat lady was kicked out of her three millionth bar last Friday. Well, let's just say that we will not see very much more of her very longer. NASA launched a program that led to the transportation of the fat lady to a recently found planet that was discovered to have water on its surface to celebrate this embarrassing accomplishment. NASA kept this recent discovery as a secret specifically for the purpose of reserving the planet just for the fat lady.

NASA has calculated that the gravitational force of this recently discovered planet is 4.5 m/s^2. Assuming that the fat lady's volume is .09m^3 and her density is 920kg/m^3, find the buoyant force that will be applied on the fat lady when she swims on the planet. How much is this buoyant force on the planet different from the buoyant force that would be applied to her on Earth? Will she float as much as she did on Earth due to the change in gravitational force?

To begin, find the buoyant force of the fat lady on the new planet:

B=p(fluid)Vg B=(1000kg/m^3)(.09m^3)(4.5m/s^2) B= 405N

On Earth, her buoyancy would have been:

B=(1000kg/m^3)(.09m^3)(9.8m/s^2) B=882N

The differences in the buoyancies between Earth and the newly found planet would be 882N-405N, or 477N.

Although the buoyant force is lesser on the newly found planet that on Earth, the lady will not float more or less than she did on Earth because her weight must be considered in order to make this assumption. Here is a proof as to why she would not float more or less on the newly found planet than she did on Earth:

B=w p(fluid)Vg=p(object)Vg The g's would cancel out when you divide both sides by g. Therefore, floating is solely based on density and volume. However, buoyancy can be influenced by the gravitational force when the weight of a person is neglected.