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?
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
But do I have to include He density in this equation at all?
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 buoyant force acting on the balloon.
The buoyant force can be calculated using Archimedes' principle, which states that the buoyant force exerted on an object immersed in a fluid (in this case, the helium-filled balloon in air) is equal to the weight of the fluid displaced by the object.
First, let's find the mass of the helium inside the balloon. We can calculate this by multiplying the volume of the balloon by the density of helium:
Mass of helium = Volume of balloon × Density of helium
= 0.30 m^3 × 0.20 kg/m^3
= 0.06 kg
Next, we need to find the weight of the helium-filled balloon. The weight is equal to the force of gravity acting on the mass:
Weight = Mass × Acceleration due to gravity
= 0.06 kg × 9.8 m/s^2
≈ 0.588 N
So, the weight of the balloon and helium is approximately 0.588 N.
Now, let's address the tension in the string. The tension in the string is equal to the sum of the weight of the balloon and the weight of the helium:
Tension = Weight of balloon + Weight of helium
Since the tension is given as 0.8 N, we can set up the equation:
0.8 N = Weight of balloon + Weight of helium
Substituting the calculated weight values, we have:
0.8 N = 0.588 N + Weight of helium
Now, let's solve for the weight of the helium:
Weight of helium = 0.8 N - 0.588 N
= 0.212 N
So, the weight of the balloon and helium is approximately 0.588 N, and the weight of the helium alone is approximately 0.212 N.