A balloon of negligible mass is filled with 300 m³ of helium.How big a payload can the balloon lift? (The density of air is 1.29 kg/m³;the density of helium is 0.18 kg/m³. )

Question

Quizplus · Accepted Answer

The buoyant force acting on the balloon is given by:

Buoyant force = weight of fluid displaced
             = density of fluid * volume of fluid displaced * g

Since the balloon displaces its own volume of air, the buoyant force is equal to the weight of the helium in the balloon:

Buoyant force = weight of helium
             = density of helium * volume of helium * g

Solving for the volume of helium:

volume of helium = weight of helium / density of helium / g
                 = 300 / 0.18 / 9.81
                 = 1713.95 m^3

Now we can calculate the maximum weight the balloon can lift:

maximum weight = buoyant force - weight of balloon
              = density of air * volume of air displaced * g - mass of balloon
              = 1.29 * 1713.95 * 9.81 - 0
              = 21323.78 N

Converting to kg:

maximum weight = 21323.78 / 9.81
              = 2173.69 kg

Therefore, the balloon can lift a payload of up to 333 kg (since we need to subtract the weight of the helium). Choice C is the correct answer.

A Balloon of Negligible Mass Is Filled with 300 M3

A Balloon of Negligible Mass Is Filled with 300 M³