Question

A large weather balloon whose mass is 222 kg is filled with helium gas until its volume is 322 m3. Assume the density of air is 1.20 kg/m3 and the density of helium is 0.179 kg/m3.

(a) Calculate the buoyant force acting on the balloon.

          3786.72 N

(b) Find the net force on the balloon.

                      N upward

(c) What additional mass can the balloon support in equilibrium?

                     kg

Please help!

Answer 1

here m_b = 222 kg V = 322 m³   p_a = 1.20 Kg / m³ p_h = 0.179 Kg / m³

as we know that the buoyant force

F_b = p_agV = 3786.72 N

(b) net force on the balloon

F_net = (p_a - p_h)gV - mg

= (1.20 - 0.179) x 9.81 x 322 - 222 x 9.81

= 1047.335 N Ans

(c) for the equilibrium condition

F_buoyant = F_{gravitational}

3786.72 = m_b g

m_b = 3786.72 / 9.81

= 386.006 Kg Ans