Using Archimedes’ principle, determine the radius $r$ of the balloon.
The combined weight of the balloon, string and block is $0.053\,\text{N}$. When the external force holding the block on the ground is removed, the released block is lifted vertically upwards by the balloon. Calculate the acceleration of the block immediately after it is released.
The balloon keeps raising the block. The string snaps while the block is travelling vertically upwards at a speed of $1.4\,\text{m s}^{-1}$. After the snap, the detached block carries on upwards for a short time before descending vertically down to the ground. The block strikes the ground at a speed of $3.6\,\text{m s}^{-1}$. Assume that air resistance on the block is negligible.
By examining the block’s motion after the string breaks, calculate how far above the ground the block is when the string breaks.
The string breaks at time $t = 0$ and the block reaches the ground at time $t = T$. On Fig. 2.2, sketch a graph to show how the velocity $v$ of the block varies with time $t$ from $t = 0$ to $t = T$. Numerical values of $t$ are not required. Assume that $v$ is positive upwards.