Propagation of uncertainties using partial derivatives is applicable even when dealing with a single variable. The method remains valid as it calculates how uncertainties affect the outcome based on the sensitivity of the function to changes in that variable. While the complexity may decrease with only one variable, the fundamental principles of uncertainty propagation still hold true. This approach allows for accurate quantification of uncertainty in measurements and calculations. Therefore, it is confirmed that uncertainty propagation works effectively with just one variable.
#1
Panphobia
435
13
Just a quick question, would propagation of uncertainties with the partial derivatives still give the right answer when you only have one variable?
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?