You want to carry an 800kg object into the air using a helium balloon. What size of a helium balloon (I'm looking for volume) would be required to accomplish such a task? Assume the density of air is 1.25 kg/m3 and the density of helium is 0.18 kg/m3.
the mass of air displaced-mass of helium= 800kg
mass of air displaced=Vol*1.25kg/m^2
mass of helium =Vol*.18kg/m^3
solve for volume.
V=m/d
I understand how to solve for volume but there doesn't seem to be a definitive mass for air and helium in this answer, can I get some more help please? Or should I just do two equations (1.25=800/v and .18=800/v) but then what do I do? Im a little confused
the difference in densities gives you the "lift mass" per m^3
v = 800 kg /
(1.25 kg/m^3 - 0.18 kg/m^3)
To determine the size of the helium balloon required to lift an 800kg object, we need to consider the buoyant force acting on the object. The buoyant force is the force exerted by a fluid on an object immersed in it, and it is equal to the weight of the fluid displaced by the object.
Here's how you can calculate the size of the helium balloon:
1. Calculate the weight of the object:
The weight of the object is given as 800kg.
2. Calculate the weight of the displaced air:
The weight of the displaced air is equal to the volume of air displaced multiplied by the density of air, which is 1.25 kg/m^3.
Let's assume the volume of air displaced is V m^3. Therefore, the weight of the displaced air is 1.25V kg.
3. Calculate the weight of the displaced helium:
Since helium is less dense than air, the volume of helium required to provide the same buoyant force is less than the volume of air displaced.
The weight of the displaced helium is equal to the volume of helium displaced multiplied by the density of helium, which is 0.18 kg/m^3.
Therefore, the weight of the displaced helium is 0.18V kg.
4. Set up an equation for the buoyant force:
The buoyant force is equal to the weight of the displaced air (1.25V kg) minus the weight of the displaced helium (0.18V kg).
The buoyant force is given by the equation:
Bouyant force = Weight of the object = 800 kg
Setting up the equation: 1.25V - 0.18V = 800
Simplifying, we get V = 800 / 1.07 ā 748.83 m^3
Therefore, the size of the helium balloon required to lift the 800kg object would be approximately 748.83 m^3 in volume.