pressure, depth, force, archimedes principle

[Ice-cream]

Can anyone help me with these 2 questions?

 

1. "You step into an elevator holding a glass of water filled to a depth of 6.5cm. After a moment, the elevator moves upward with constant acceleration, increasing its speed from zero to 2.2m/s in 3.1s."

 

a) During the acceleratrion, is the pressure exerted on the bottom of the glass greater than, less than, or the same as before the elevator began to move? Explain.

 

(I know it should be greater...but I didn't come to that conclusion by thinking in terms of forces, pressure, depth etc...in a physics way. can someone explain it in the "physics" way?)

 

b) Find the pressure exerted on the bottom of the glass as the elevator accelerates.

 

(I think that the initial pressure would be the atmospheric pressure + density x gravity x height...but i'm not sure what would happen during the acceleration. I can find the value of the acceleration...but...how does it fit in?)

 

2. A 0.12kg balloon is filled with helium (density = 0.179kg/m^3). If the balloon is a sphere with a radius of 5.2m, what is the maximum weight it can lift?

 

(i thought that all i'd have to do is use density = m/v where density is given and volume is 4/3 pi r^3 but i get 105.43kg which means the weight is 1054N but the answer is 5.7kN. can any1 see what i'm doing wrong??)

[gnpatterson]

two ways to think about this

 

either classical in which you concider the extra force on the bottom of the glass needed to accelerate the water (the fact that it is a liquid is irrelevant, you could concider a cylinder of ice, the area cancels out it is just the height and density that are important)

 

or the GR way were you say acceleration and gravity are indistinguisable and you just you have a new local gravity g'=g+a

 

in fact we informaly recognise the lack of any distinction by talking about pulling a number of Gs when we accelerate and we instinctively think of it in these terms

 

so just use your new g' to calculate the pressure.

 

you can do the same sort of problem with glasses of water in merry-go-rounds or centrifuges

 

for you second question you will have to take a bath, it is the time honoured method of getting the answer to this question