Answer to Question #203773 in Mechanical Engineering for Sindiswa

Question

A hot air balloon consists of a gonodola(the basket within in which people sit or stand) and the envelope (the actual balloon filled with hot air). When fully inflated with hot air,the envelope has a volume of 2800(metre cubed). Assume that the nylon skin of the envelope,gondola, burner and propane tanks to heat the air have a combined mass 300kg

If the hot air balloon is secured to the ground with a rope and ground peg and the air inside the fully inflated envelope is heated to 70°, p=1.028kg/m^3, determine the tension in the anchor rope if the ambient air temperature is 10°C, p=1.246kg/m^3

Answer 1

mass = 300kg

∆p = 1.246 kg/m³ - 1.028kg/m³ = 0.218 kg/m³)

m_o =1.246kg/m³ × 2800m³ = 3488.8 kg

m_f = 1.028 × 2800m³ = 2878.4 kg

T_o = {3488.8 - (2878.4 + 300)}kg × 10m/s² = $3104\ N$.