A high-altitude balloon is motionless in air at rest. As illustrated in Fig. 2.1, a solid sphere hangs from the balloon by a string.
The volume of the balloon is $7.5\,\text{m}^3$. The combined weight of the balloon, string and sphere is $65\,\text{N}$. The upthrust on the string and sphere is negligible.
(a)[2]
Calculate the density of the air around the balloon.
(b(i))[1]
The string snaps, freeing the sphere. State the magnitude of the sphere’s acceleration immediately after the string snaps.
(b(ii))[3]
State and explain the variation, if any, in the magnitude of the acceleration of the sphere when it is moving downwards before it reaches terminal (constant) velocity.
(c)[2]
The sphere has a mass of $4.0\,\text{kg}$. Calculate the total resistive force acting on the sphere at the instant when its acceleration is $1.9\,\text{m s}^{-2}$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “$65=\rho gV$ or $65=mg$ with $m=\rho V$” …