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. A6.00 times 10^4 cm^3gas-filled balloon will provide lift for a 40.0 g package to be accelerated upward at a rate of 3.10 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 rho_air = 1.16 kg/m^3. Neglect the mass of the balloon material and the volume of the package.

Explanation / Answer

Here

Bouyant force = weight of air displaced

F_b = pgV
F_b=ma_y+mg
pgV=ma_y+mg
1.16*9.81*(6.00 *10^4 *10^-6) = m(3.10) + m(9.81)

12.91m = 0.6828
m=0.05289 (this is the mass of both the air in the balloon and the package, you need just the air)

Now,

mass of air in balloon = 0.05289-0.040 = 0.01289kg

Hence

density=mass/volume
=0.01289kg/0.06m^3

=0.21483kg/m^3

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.