On Fig. 2.1, add labelled arrows to show the directions of the three forces acting on the balloon.
Calculate the volume of the balloon, giving your answer to three significant figures.
The balloon is let go from the rope. Calculate the initial acceleration of the balloon.
The balloon is motionless at a height of $500\,\text{m}$ above the ground. A tennis ball is dropped from rest and falls vertically from the balloon. A passenger in the balloon uses the equation $v^{2} = u^{2} + 2as$ to calculate that the ball will be moving at about $100\,\text{m s}^{-1}$ when it strikes the ground. Explain why the actual speed of the ball will be much less than $100\,\text{m s}^{-1}$ when it reaches the ground.
Before the balloon is released, the rope supporting the balloon has a strain of $2.4 \times 10^{-5}$. The rope has an unstretched length of $2.5\,\text{m}$. The rope obeys Hooke’s law. Show that the extension of the rope is $6.0 \times 10^{-5}\,\text{m}$.
Calculate the elastic potential energy $E_p$ stored in the rope.
The rope holding the balloon is substituted with another rope of the same original length and cross-sectional area. The tension stays the same and the new rope also obeys Hooke’s law. The new rope is made from a material with a lower Young modulus. State and explain the effect of the lower Young modulus on the elastic potential energy of the rope.