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CAPE Physics Unit 1 · 2006 · Paper 2 · Question 4(b)(ii)c)

A large helium weather balloon is spherical with a radius of 2.5 m and a total mass of 15 kg (balloon plus helium plus equipment). The balloon is released from sea level and travels vertically upward, quickly reaching its terminal velocity. The drag force acting on the balloon is given by F_D = (1/2)πr²ρv², where r is the radius of the balloon, ρ is the density of air, and v is the ascension speed of the balloon.

Find the time, in minutes, it will take for the balloon to ascend to a height of 10 km. (Density of air, ρ = 1.29 kg m⁻³.) (Volume of a sphere = (4/3)πr³.)

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Other parts of this question

  1. 4(a)(i)State Newton's laws of motion.[8 marks]
  2. 4(a)(ii)Explain why a small sphere, released from rest at the surface to fall through liquid in a deep tank, eventually moves with a constant speed. Sketch a graph…[8 marks]
  3. 4(b)The drag force acting on the balloon is given by F_D = (1/2)πr²ρv², where r is the radius of the balloon, ρ is the density of air, and v is the ascension speed…[1 mark]
  4. 4(b)(i)Draw a free body diagram to show the forces acting on the balloon.[12 marks]
  5. 4(b)(ii)a)Use Archimedes' principle to find the buoyant force acting on the balloon.[12 marks]
  6. 4(b)(ii)b)Calculate the terminal velocity of the balloon.[12 marks]

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