A consumer upset with the latest trend of postal rate increases has decided to t

Question

A consumer upset with the latest trend of postal rate increases has decided to try to send letters by balloon even though they may not reach their intended destination. A 6.00 times 10^4 cm^3 gas-filled balloon will provide enough lift for a 40.0 g package to be accelerated upward at a rate of 2.65 m/s^2. For these circumstances, calculate the density of the gas the consumer fills the balloon with. The acceleration due to gravity is g = 9.81 m/s^2 and the density of air is p_air = 1.16 kg/m^3. Neglect the mass of the balloon material and the volume of the package. rho =

Explanation / Answer

here,

v1 = 6 *10^4 cm^3

m = 40 gm = 0.040 Kg

a = 2.65 m/s^2

let the density of gas inside the ballon is p

pa = 1.16 Kg/m^3

Balancing the forces

m * g = V * g * (pa - p)

0.040 * 9.8 = 6 *10^4 * 1 *10^-6 * 9.8 * (1.16 - p)

solving for p

p = 0.4933 Kg/m^3

the density of gas inside the balloon is 0.4933 Kg/m^3

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