Answer to Question #168066 in Molecular Physics | Thermodynamics for Baxiwe556

Question

An empty rubber balloon has a mass of 0.0120 kg. The balloon is filled with helium that has a density of 0.179 kg/m³. The filled balloon has a radius of 0.500 m. (density of air is 1.29 kg/m³ and assume no air resistance). The balloon is now released, find the following:

 

a)   The acceleration of the balloon.

b)   The final velocity of the balloon after 10 s.

c)   The height of the balloon after 10 s.

 

Answer 1

a)

$$(M+m_{He})a=-(M+m_{He})g+\rho gV\\M(g+a)=\frac{4\pi r^3}{3}(\rho g-\rho_{He}(g+a))\\0.012(9.8+a)\\=\frac{4\pi (0.5)^3}{3}((1.29)(9.8)-0.179(9.8+a))\\a=52.8\frac{m}{s^2}$$

b)

$$v=52.8(10)=528\frac{m}{s}$$

c)

$$h=52.8(10)^2(0.5)=2640\ m$$