Answer to Question #111428 in Physics for John Guz

Question

A balloon is filled with helium and let go. It rises into the air accelerating at a rate of 0.151 m s−2.

If the density of air is 1.22 kg m−3 then what is the average density of the balloon? (to 3 s.f and in kg m−3)

(Note: use g = 9.81 m s−2 and ignore any "drag" forces on the balloon such as air resistance.)

Answer 1

$$ma=ρ _ a ​ gV−mg$$

$$ρ _ b ​ Va=ρ _a ​ gV−ρ _b ​ gV$$

$$ρ _b ​ (a+g)=ρ _ a ​ g$$

$$ρ _ b ​ (0.151+9.81)=1.22(9.81)$$

$$ρ _ b ​ =1.20\frac{kg}{m^3}$$