Calculating Payload for Helium and Hydrogen Balloons | Buoyant Forces Explained

[ramin86]

(a) A light balloon is filled with 371 m3 of helium. At 0°C, the balloon can lift a payload of what mass?

(b) In Table 14.1, observe that the density of hydrogen is nearly half the density of helium. What load can the balloon lift if filled with hydrogen?

I really have no clue where to start for these problems. You're given the volume and that the denisty of helium is 1.79E-1, but I don't get how to find the payload.

 

[Doc Al]

Both problems require understanding of Archimede's principle: The buoyant force on an object imersed in a fluid equals the weight of the displaced fluid. In these problems, the balloons displace air. So start by figuring out the buoyant force acting (upward) on each balloon.

 

[wais]

To calculate the payload for a helium or hydrogen balloon, we need to understand the concept of buoyant force. Buoyant force is the upward force exerted by a fluid on an object immersed in it. In the case of balloons, the fluid is the surrounding air and the object is the balloon itself.

(a) To calculate the payload for a helium balloon, we can use the following equation:

Payload = (Volume of balloon) x (Density of air – Density of helium)

In this case, the volume of the balloon is given as 371 m3 and the density of air at 0°C is 1.29 kg/m3. The density of helium is 0.179 kg/m3. Plugging these values into the equation, we get:

Payload = (371 m3) x (1.29 kg/m3 – 0.179 kg/m3) = 371 m3 x 1.111 kg/m3 = 412.28 kg

Therefore, the balloon can lift a payload of 412.28 kg.

(b) To calculate the payload for a hydrogen balloon, we can use the same equation, but with the density of hydrogen instead of helium. The density of hydrogen is approximately 0.09 kg/m3. Plugging this value into the equation, we get:

Payload = (371 m3) x (1.29 kg/m3 – 0.09 kg/m3) = 371 m3 x 1.2 kg/m3 = 445.2 kg

Therefore, the balloon can lift a payload of 445.2 kg if filled with hydrogen. This is almost twice the payload that the balloon can lift with helium, due to the lower density of hydrogen. However, it is important to note that hydrogen is highly flammable and not commonly used in balloon flights for safety reasons.