Q1. What is the minimal mass of helium (density 0.18) needed to lift a balloon carrying two people in a basket, if the total mass of people, basket, and balloon (but not gas) is 320?
Q2. In Santa's workshop, a mass m is attached to the rectangular frame by 4 springs and is constrained to move in the horizontal plane. The springs are not stretched in their equilibrium position. As everyone knows, Santa's workshop is located at North Pole and Earth is rotating around its axis.
a) Write down the system of disparity equations for small oscillation of the mass in the x-y plane.
b) Introduce a variable s=x+iy and combine the two equations. Write down the general solution of resulting differential equation.
c) Can you guess what would be the motion of the mass?