A spherical helium filled balloon is attached to a string that is fixed to the ground. the balloon has a volume of .30/4m^3 and helium has a density of .20 kg/m^3. What is the weight of the balloon and helium if the tension on the string is .8N?
What is the Gravitational force on the helium alone?
V=0.3/4 m³
Helium ρ₁=0.2 kg/m³
Air ρ₂=1.33 kg/m³
the buoyant force F = ρ₂Vg
mg+T =F
W=mg = F-T = ρ₂Vg-T=
=9.8•1.33•0.3/4 – 0.8=0.978-0.8=0.178 N
If W₁ is the weight of helium and W₀ is the weight of balloon,
W=W₁+W₀
W₁ =m₁g= ρ₁Vg=9.8•0.2• 0.3/4 =0.147 N
Then
W₀=W-W₁ = 0.178-0.147=0.031 N
To find the weight of the balloon and helium, we need to calculate the total mass of the helium gas inside the balloon. The formula for the weight is given by:
Weight = Mass * Gravitational acceleration
First, we need to find the mass of the helium. We can get the mass by multiplying the volume of the helium with the density of helium:
Mass = Volume * Density
Given:
Volume of helium (V) = 0.30 m^3
Density of helium (ρ) = 0.20 kg/m^3
Substituting these values, we get:
Mass = 0.30 m^3 * 0.20 kg/m^3
Mass = 0.06 kg
Now, we can calculate the gravitational force on the helium alone by multiplying the mass with the gravitational acceleration:
Gravitational force = Mass * Gravitational acceleration
Gravitational acceleration (g) on Earth is approximately 9.8 m/s^2.
Substituting the values, we get:
Gravitational force = 0.06 kg * 9.8 m/s^2
Gravitational force = 0.588 N
Therefore, the gravitational force on the helium alone is approximately 0.588 N.