What is the mass of air in the balloon?

Question

Normal air has a density of 1.22 kg/m³. Air that has been heated in a hot air balloon has a density of 0.95 kg/m³. The hot air balloon has a total volume of 3000 m³.

a. What is the mass of air in the balloon? (1 point)

b. What is the buoyant force acting on the balloon? (1 point)

c. If the basket and riders in the balloon have a mass of 400 kg, what is the acceleration of the balloon? (1 point)

d. What is the minimum volume the balloon can have before it goes downward instead of upward? (1 point)

e. As the balloon rises, the lower air pressure causes the air around the balloon to become less dense. How does this affect the buoyancy of the balloon? (1 point)

f. As the balloon rises, the atmospheric pressure decreases, causing the volume of the balloon to increase. How does this affect the buoyancy of the balloon? (1 point)

Answer 1

a) Mass = volume*density so (3000 m³ )*(0.95 kg/m³) ... notice units left are just kg (mass)

b) Buoyant force = density_surroundings*g*volume = (1.22)*(9.8)*(3000) Newtons upward

c) F_net = m*a so F_net = F_bouyant - F_gravity = (answer from part b) - (400*9.8) = 400*a so solve for a

d) This is where force of gravity = bouyant force so 400*9.8 = (0.95)*(9.8)*volume so solve for volume

e) The buoyant force decreases as it equals density*g*volume and density decreases

f) This would increase the buoyant force of the balloon since it's density*g*volume and volume increases

(something to think about: the density in part e decreases the buoyant force as it rises but there's also the fact that in f the volume increases which would increase buoyant force, so will the overall buoyant force decrease or increase? I think that may be beyond the scope of the class)