Hot Air Balloon

Ballooning is a sport and hobby for many people around the world. Three people were staring ballooning in a cool spring day. Alex, a 11 year old son of one of the ballooning person, was one of the audience. He is full of curiosity about the huge color ball. After his dad came home, he asked some questions about the ballooning.

What is known:

• The balloon is approximately a sphere with a diameter of D = 20 m
• Local pressure P_a = 90 kPa
• Local air temperature T_a = 15 ^oC
• The mass of the empty balloon and the cage m_b = 80 kg
• The mass of each person m_p = 65 kg

• Determine the mass of the hot air in the balloon when the balloon is still in the air
• Determine the average temperature in the balloon in order to keep the balloon still in the air
• What will happen if the local temperature increases to 30 ^oC?

Force Balance on The Balloon

• The force that lifts the balloon upward is:
        F_B = ρ_{cool air} g V_ballon
  
• The forces that will be balanced by the force (F_B) are :
  (1) The weight of the cage, the ropes, and the balloon materials
  (2) The mass of the hot air in the balloon
  (3) The weight of the people and other load in the cage