Solving Fluids Questions: Helium-Filled Balloon & Sealed Spherical Shell

[novelized]

Homework Statement

A helium-filled balloon is tied to a 2.00-m-long, 0.0500-kg uniform string. The balloon is spherical with a radius of 0.400m. When released, it lifts a length h of string and then remains in equilibrium, as in the figure. Assuming envelope of the balloon has mass 0.250 kg and that the balloon raises a height less than the length of the string, determine the value of h.

and

A sealed spherical shell of diameter d is rigidly attached to a cart that is moving horizontally with an acceleration a to the right as shown in the picture. The sphere is nearly filled with a fluid having density ρ and also contains one small bubble of air at atmospheric pressure.

a) When a = 0, determine the pressure at the center of the sphere.

b) Now assume a ≠ 0, determine the pressure again at the center of the sphere. (Hint. Think of what water does in a glass when you accelerate it to the right or which way you feel the force when you accelerate your car. Don't forget you now have two forces.)


I have no idea where to even begin with these two problems. Could someone please point me in the right direction?

 

[mgb_phys]

1, Work out the mass of helium in the balloon, and the mass of air this displaces. That gives you the load the balloon can lift. Remember the load is the string + envelope.

 

[novelized]

I calculated the mass of helium to be .047718 kg. Is the mass of air displaced equal to this too?

And this would be equal to mass of string * height + mass of envelope?