A helium-filled balloon is attached by a string of negligible mass to a small $0.015\,\text{kg}$ object that is just heavy enough to keep the balloon from rising. The total mass of the balloon, including the helium, is $0.0050\,\text{kg}$. The density of air is $\rho_{\text{air}} = 1.29\,\text{kg/m}^3$, and the density of helium is $\rho_{\text{He}} = 0.179\,\text{kg/m}^3$. The buoyant force on the $0.015\,\text{kg}$ object is small enough to be negligible.

Question

A helium-filled balloon is attached by a string of negligible mass to a small $0.015\,\text{kg}$ object that is just heavy enough to keep the balloon from rising. The total mass of the balloon, including the helium, is $0.0050\,\text{kg}$. The density of air is $\rho_{\text{air}} = 1.29\,\text{kg/m}^3$, and the density of helium is $\rho_{\text{He}} = 0.179\,\text{kg/m}^3$. The buoyant force on the $0.015\,\text{kg}$ object is small enough to be negligible.(a) Draw and label the forces (not components) that act on the balloon.
, (b) Calculate the buoyant force on the balloon.
, (c) Calculate the volume of the balloon.
, (d) A child holds the string midway between the balloon and the $0.015\,\text{kg}$ object. The child gets into a car, brings the balloon and the $0.015\,\text{kg}$ object into the car, and holds the string so that neither the balloon nor the $0.015\,\text{kg}$ object touches any surface. The car then begins to move forward, accelerating in a straight line. What behavior does the $0.015\,\text{kg}$ object exhibit when the car accelerates (i.e: it remains vertical, moves towards the front, moves to the right, etc)? Explain your reasoning.
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Jason · Accepted Answer

Bouant force acts upwards, weight and tension act downwards
$\boxed{0.196\,\text{N}}$
$\boxed{0.0155\,\text{m}^3}$
The $0.015\,\text{kg}$ object swings toward the back of the car when it accelerates forward.

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