Answer:
The lifting force of a balloon is equal to the weight of the air it displaces, minus the weight of the balloon itself and any cargo it is carrying. We can calculate the lifting force using the following formula:
Lifting force = (4/3) x π x r^3 x ρair x g - m_balloon - m_cargo
where:
- r is the radius of the balloon (in meters)
- ρair is the density of air (in kg/m^3), which we'll assume is 1.2 kg/m^3 at sea level and standard temperature
- g is the acceleration due to gravity (in m/s^2), which we'll assume is 9.81 m/s^2
- m_balloon is the mass of the balloon (in kg)
- m_cargo is the mass of the cargo (in kg)
- π is pi (approximately 3.14)
Substituting in the values given in the problem, we get:
Lifting force = (4/3) x π x (7.15 m)^3 x (1.2 kg/m^3) x 9.81 m/s^2 - 930 kg - m_cargo
Simplifying and solving for m_cargo, we get:
m_cargo = (4/3) x π x (7.15 m)^3 x (1.2 kg/m^3) x 9.81 m/s^2 - 930 kg - Lifting force
Plugging in the lifting force we want the balloon to have, which we'll call L, we get:
m_cargo = (4/3) x π x (7.15 m)^3 x (1.2 kg/m^3) x 9.81 m/s^2 - 930 kg - L
Assuming we want the balloon to lift 5000 kg of cargo, we can solve for L:
L = (4/3) x π x (7.15 m)^3 x (1.2 kg/m^3) x 9.81 m/s^2 - 930 kg - 5000 kg
L = 281,581 N
Therefore, to lift 5000 kg of cargo, the balloon needs to have a lifting force of approximately 281,581 N.