A WEATHER BALLOON IS TO OPERATE WHERE THE DENSITY OF AIR IS 0.9Kg/m3. THE BALLOON HAS A VOLUME OF 20cm3 AND IS FILLED WITH NITROGEN WITH DENSITY 0.09Kg/m3. IF THE BALLOON BAG WEIGHS 118N, WHAT LOAD CAN IT SUPPORT AT THIS ALTITUDE?
just figure total load weight so that it equals the weight of the air displaced.
To determine the load the weather balloon can support at this altitude, we need to consider the buoyant force acting on the balloon.
The buoyant force is equal to the weight of the air displaced by the balloon. It can be calculated using the following formula:
Buoyant Force = Weight of the displaced air
The weight of the displaced air can be determined by subtracting the weight of the nitrogen gas inside the balloon from the weight of the balloon bag itself.
Given:
Density of air (ρ_air) = 0.9 kg/m^3
Volume of the balloon (V_balloon) = 20 cm^3 = 20/1000000 m^3 (converted to cubic meters)
Density of nitrogen (ρ_nitrogen) = 0.09 kg/m^3
Weight of the balloon bag (W_balloon) = 118 N
First, we need to find the weight of the nitrogen gas inside the balloon:
Weight of nitrogen gas = (Density of nitrogen) * (Volume of the balloon)
= ρ_nitrogen * V_balloon
Next, we can calculate the weight of the displaced air:
Weight of displaced air = (Density of air) * (Volume of the balloon)
Finally, we can determine the load the balloon can support:
Load = Weight of displaced air - Weight of nitrogen gas - Weight of the balloon bag
Now, let's plug in the values and calculate:
Weight of nitrogen gas = 0.09 kg/m^3 * (20/1000000 m^3)
≈ 0.0000018 kg
Weight of displaced air = 0.9 kg/m^3 * (20/1000000 m^3)
= 0.000018 kg
Load = 0.000018 kg - 0.0000018 kg - 118 N
≈ -118 N
Since the load with a negative value does not make sense in this context, we can conclude that the weather balloon cannot support any load at this altitude.