Ask Question
25 September, 11:40

An empty rubber balloon has a mass of 12.5 g. The balloon is filled with helium at a density of 0.181 kg/m3. At this density the balloon has a radius of 0.294 m. If the filled balloon is fastened to a vertical line, what is the tension in the line? The density of air is 1.29 kg/m3.

+3
Answers (1)
  1. 25 September, 12:07
    0
    Answer: 1.14 N

    Explanation:

    As any body submerged in a fluid, it receives an upward force equal to the weight of the fluid removed by the body, which can be expressed as follows:

    Fb = δair. Vb. g = 1.29 kg/m3. 4/3 π (0.294) 3 m3. 9.8 m/s2

    Fb = 1.34 N

    In the downward direction, we have 2 external forces acting upon the balloon: gravity and the tension in the line, which sum must be equal to the buoyant force, as the balloon is at rest.

    We can get the gravity force as follows:

    Fg = (mb + mhe) g

    The mass of helium can be calculated as the product of the density of the helium times the volume of the balloon (assumed to be a perfect sphere), as follows:

    MHe = δHe. 4/3 π (0.294) 3 m3 = 0.019 kg

    Fg = (0.012 kg + 0.019 kg). 9.8 m/s2 = 0.2 N

    Equating both sides of Newton's 2nd Law in the vertical direction:

    T + Fg = Fb

    T = Fb - Fg = 1.34 N - 0.2 N = 1.14 N
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “An empty rubber balloon has a mass of 12.5 g. The balloon is filled with helium at a density of 0.181 kg/m3. At this density the balloon ...” in 📗 Physics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers