Question

The Helium balloon shown in the picture can be modeled as a sphere and as a result has a volume of 523.6 [m3]. The total mass of all the people in the balloon is 240 [kg]. If the density of Helium is 1/7 of the density of air and the density of air is about 1.2 [kg/m3], the acceleration of the balloon with the people in the basket is most nearly: Tip: Use Newton's second law. Ignore the weight of the basket, the buoyancy force on the basket, and the buoyancy force on the people. Helium D = 10 m PHe = Pair A. 12.2 [m/s2] B. 32.63 [m/s2] C. 5.921 [m/s2] D. 8.882 [m/s2]

Answer 1

Here, buoyant force is acting on balloon in upward directions. Also, weights of He and persons in baskets are considered here. Using second law of Motion, acceleration is calculated to be 8.88 m/S2.

Detailed solution is given below.

Ghren. V = 523.6 m (Volume of spherica balloon). far. She Total mass of people, M = 2 40 40 kg Ромбу с Иe fut - 2) kg/m2. Free Body Diagra ram Aviso ga FBi ta (VB ne g+mg) Buoyant force is acting (EB) on the balloon. which is FR = Vlairg Using Newton's second Law of motion Sargs -Mg-(M€ Via Vineg

a - fatting value) V (fair - Sued M Mtv she 4 - 523.6_. ( J. २ - +x. 2) x 9.81 - 249 २१.६) 2 40 + 52 3.6 x_113 ----8.882-mts 2