A balloon 20m in diameter is filled with helium at a gauge pressure of 2.0atm. A man is standing in a basket suspended from the bottom of the balloon. A restraining cable attached to the basket keeps the balloon from rising. The balloon (not including the gas it contains), the basket, and the man have a combined mass of 150 kg. The temperature is 24°C that day, and the barometer reads 760 mm Hg.

(a) Calculate the mass (kg) and weight (N) of the helium in the balloon.

(b) How much force is exerted on the balloon by the restraining cable? (Recall: The buoyant force on a submerged object equals the weight of the fluid—in this case, the air—displaced by the object. Neglect the volume of the basket and its contents.)

(c) Calculate the initial acceleration of the balloon when the restraining cable is released.

(d) Why does the balloon eventually stop rising? What would you need to know to calculate the altitude at which it stops?

(e) Suppose at its point of suspension in midair the balloon is heated, raising the temperature of the helium. What happens and why?