Archimedes Principle - Structure Question 3

A balloon filled with helium gas has negligible mass. The volume of the balloon is 120cm³. [Density of air = 1.23 kg/m³.Density of helium gas = 0.18 kg/m³]

1. 
   
1. Calculate the mass of the helium gas in the balloon?
$$\begin{array}{l}m=\rho V\\ m=(0.18)(120\times {10}^{-6})=2.16\times {10}^{-5}kg\end{array}$$
2. Find the weight of the helium gas?
   $$\begin{array}{l}W=mg\\ W=(2.16\times {10}^{-5})(10)=2.16\times {10}^{-4}N\end{array}$$
2. 
   The balloon is then tied to a load of mass m kg, as shown in figure above. The balloon and the load float in the air stationary.
1. Mark in the diagram, all the forces that acted on the balloon.



2. Write an equation to relate all the forces in )b) (i).
   
   All the 3 forces are in equilibrium

Upthrust = Weight of the Load + Weight of Helium Gas


3. Calculate the mass of the load, m.
$$\begin{array}{l}\text{Upthrust }=\text{ Weight of the Load }+\text{ Weight of Helium Gas}\\ \rho Vg=mg+2.16\times {10}^{-4}\\ (1.23)(120\times {10}^{-6})(10)-2.16\times {10}^{-4}=m(10)\\ m=1.26\times {10}^{-4}kg\end{array}$$
3. If the string that is tied to the balloon is cut, Find upward acceleration experienced by the balloon?
   
   Net force acted on the balloon = mg = (1.26 x 10^-4)(10) = 1.26 x 10^-3N
   Mass of the helium gas, m = 2.16 x 10^-5kg
$$\begin{array}{l}F=ma\\ (1.26\times {10}^{-3})=(2.16\times {10}^{-5})a\\ a=\frac{1.26\times {10}^{-3}}{2.16\times {10}^{-5}}=58.3m{s}^{-2}\end{array}$$