A spherical balloon has a radius of 6.76 m and is filled with helium. How large a cargo can it lift, assuming that the skin and structure of the balloon have a mass of 950 kg? Neglect the buoyant force on the cargo volume itself.
masslifted+massballon=densityair*volume
To determine the maximum cargo weight that a balloon can lift, we need to consider the buoyant force exerted by the helium-filled balloon.
The buoyant force is given by the formula:
Buoyant force = Weight of displaced fluid
Since the balloon is filled with helium, which is less dense than the surrounding air, the buoyant force will be directed upwards.
The weight of the displaced air is equal to the weight of the balloon (including the skin and structure). The displaced air can be considered as a fluid here.
The weight of the balloon can be calculated as follows:
Weight = mass x gravity
Here, the mass of the balloon (including skin and structure) is given as 950 kg. The acceleration due to gravity is approximately 9.8 m/s^2.
Weight of the balloon = 950 kg x 9.8 m/s^2 = 9310 N
Now, let's calculate the volume of the balloon using the formula for the volume of a sphere:
Volume = (4/3) x π x r^3
Given that the radius (r) of the balloon is 6.76 m:
Volume = (4/3) x 3.14 x (6.76 m)^3 = 968.04 m^3
Since the buoyant force is equal to the weight of the displaced air, the buoyant force can be calculated as:
Buoyant force = Weight of the balloon = 9310 N
Now, we need to calculate the weight of the cargo that the balloon can lift.
Weight of the cargo = Buoyant force - Weight of the balloon
Weight of the cargo = 9310 N - 9310 N = 0 N
Therefore, the balloon can lift a cargo with zero weight.
Note: In this calculation, we've neglected the buoyant force on the cargo itself, as mentioned in the question.